9/12/05
-DRAFT-
Networks and Collective Action:
An Experimental Study of Reputation and Strategy Selection1
by
T. K. Ahn
Justin Esarey
John T. Scholz
Department of Political Science
Florida State University
© 2005 by authors
1
For presentation at the American Political Science Association Annual Conference,
Washington, D.C., September 1-4, 2005.
1
ABSTRACT
We report the results of a laboratory experiment in which subjects continuously select
whom to play, whether to cooperate with them in repeated 2-person prisoners dilemma
games. By manipulating the nature of information exchanged in endogenously-evolving
networks, we observe the impact of reputational information on overall payoffs, levels of
cooperation, the shape of networks, and the kinds of strategies employed under different
information and reputational conditions. Selective networking among cooperators
appears to drive the primary dynamic in our experiments, with information providing
earlier and greater advantages to nice strategies. Our findings suggest that policy actors
tempted to exploit early attempts at creating joint projects are likely to end up ostracized
in a defectors’ getto and unable to gain the potential long-term advantages of mutual
cooperation—provided that there are enough nice strategies among relevant policy actors
to develop the clusters of mutual cooperation that formed in our experiments.
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Networks and Collective Action:
An Experimental Study of Reputation and Strategy Selection
In practically every subfield of political science, scholars claim that networks
provide critical institutional devices to resolve collective action dilemmas. Some
speculation is based on sociological (Coleman 1988) and political (Putnam 1993; Taylor
and Singleton 1992) observations, some on theoretical analyses based on formal models
or computer simulations (Axelrod 1997, Nowak and May 1992), and some based on
quantitative analyses of networks within and among business (Burt 2005) and public
organizations (Schneider et al 2003, Scholz and Wang 2006). Unfortunately, the
combination of widespread interest and the inherent complexity of network
combinatorics have led to a persistent gap between conceptualization and observation,
hampering the ability to answer even a few basic questions.
Can networks overcome social dilemmas in which individual incentives lead to
socially inferior solutions, as the social capital literature suggests? Are information
exchange and the resultant reputations the critical element behind the alleged
effectiveness of networks, as suggested by game theory approaches? Alternatively, does
the ability to choose and reject network partners itself expand the strategic space of social
dilemmas in a way that favors cooperative strategies even in the absence of information,
providing a cooperator’s network advantage somewhat akin to the cognitive miser’s
advantage (Orbell and Dawes, 1991)?
We believe that laboratory experimentation provides a particularly fruitful method
to answer these questions in the process of developing an empirically-based theory of
networks and collective action. By specifying a well-defined social dilemma and
manipulating specified characteristics of network dynamics, we can observe the role of
networks in shaping behavior. We report here the results of a laboratory experiment in
which subjects continuously select whom to play, whether to cooperate with them in
repeated 2-person prisoners dilemma games. By manipulating the nature of information
exchanged in endogenously-evolving networks, we can observe the impact of
reputational information on overall payoffs, levels of cooperation, the shape of networks,
and the kinds of strategies employed under different information and reputational
conditions. This abstract setting replicates numerous decision situations, but was
designed explicitly to reflect the choice of government agencies in local policy arena to
work together on common projects.
1. Network Dynamics and Cooperation: Information and Selection Effects
The early studies by Coleman (1986; 1987; 1988), Granovetter (1985), Putnam
(1992) and others have contributed to the widespread belief that networks enhance the
ability of its members to resolve common collective action problems. For them,
cooperation in collective action situations is a byproduct of existing social networks and
the trust, identity, and converging beliefs and preferences that arise from tightlyclustered, overlapping, reciprocated, multidimensional exchanges in closed communities.
While multiple network characteristics are undoubtedly important in explaining
collective action in a variety of settings, the overdetermined general model does not
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distinguish the critical characteristics of networks for supporting cooperative responses
among heterogeneous, less-connected communities for specific collective action
situations. Nor do the general models address the issue of how the cooperative clusters
evolve endogenously.
Our study aims to address the role of network clusters in facilitating cooperation
and the endogenous evolution of those clusters. In all the sessions of our experiment 14
subjects were engaged in 20 rounds of a two-person prisoner’s dilemma game. In each
round, subjects first chose whom to play with; in the terminology of social networks,
every ego seeks potential alters. Only when both players agreed to play the prisoner’s
dilemma with each other, was the game actually played. Thus, the network of prisoner’s
dilemma games was allowed to evolve endogenously through subjects’ repeated choice.
Payoffs in the PD stage game range from zero to 100, so every game has a non-negative
expected payoff.
To replicate normal conditions that force subjects to choose alters with some care,
subjects are charged a cost for each game played in a round, and the costs increase
exponentially with each additional alter. We calibrate the costs such that the Nash
equilibrium (ego and all alters defect) will still allow ego to profitably retain some ties,
while the socially optimal outcome (ego and all alters cooperate) will not support links
with all thirteen subjects in a given round.
The key difference between the two treatments of our experiment is whether
subjects were allowed to exchange reputational information about others. In the local
information treatment, subjects were allowed to request to any of the currently liked
alters for recommendations for links. When asked for recommendations, a subject would
provide either a positive or negative recommendation, or no recommendation at all. In the
baseline no information treatment, this reputational information exchange was not
allowed.
In prisoner’s dilemma situations like the ones we are interested in, the most
common network characteristic credited with supporting cooperative solutions is
clustering, or the degree to which an individual’s contacts know each other (Watts 1999a,
1999b; Cohen, Riolo, and Axelrod 2001; Axelrod, Cohen, and Riolo 2002; Masuda and
Aihara 2003). Consider for example an ego who is playing continuing 2-person PD with
two alters W and X and is deciding whether or not to enter into a game with one of two
remaining players, Y and Z. Player Y is already playing PD with ego’s two alters, while
player Z is not. If the games are completely independent with no information shared
about the outcomes, then the choice depends only on the expected outcome of the
independent PD game, and there would be no reason for the ego to favor Y or Z.
On the other hand, if ego can share information with alters about each other’s
play, as is generally assumed possible in networks, then ego enjoys several potential
advantages in selecting player Y. First, ego could ask the other players about Y’s
reputation, and choose to enter the game only if Y is cooperative. Second, once ego
commences play with Y, Y’s temptation to defect is reduced (in comparison to Z’s) by
the potential reputational effect—when ego informs alters W and X of Y’s defection, they
in turn may fear Y’s defection and therefore be less willing to cooperate. Third, ego and
her alters may implicitly or explicitly develop a joint strategy of all punishing Y if Y
defects with any of them. Fourth, by inducting Y into the existing network, ego also
increases the potential punishment facing existing alters, thereby increasing their
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incentive to cooperate. Of course, Y’s addition constrains ego just as much as Y
constrains ego’s other alters, imposing the same disincentive to defect on ego. So the
benefit of adding Y is most valuable if ego’s strategy is mainly cooperative. These latter
two advantages essentially increase the potential cost of defection for Y within the closed
network in which all players know each other and can exchange reputational information
among themselves, with the cost of defection growing proportionally with the number of
common alters. Because ego knows Y’s disposition in advance (through
recommendations) and also knows that Y will incur significant costs by defecting, ego
should feel more comfortable taking the risk of requesting a potentially very costly link
with Y; hence, ego will probably attempt and sustain a larger number of relationships
when information is available.
Based on this analysis, we state four hypotheses, which we collectively refer to as
information effect hypotheses. First, in order for our analysis to make sense, the subjects
must make use of the information available to them:
H1: Individuals in networks where partners can exchange recommendations
should be more (less) likely to link about whom they received positive (negative)
recommendations.
H2: Due to reputational considerations, individuals in networks where partners
can exchange recommendations should be more likely to cooperate with alters
than in networks without information exchange.
Second, this information must have the impact that we expect:
H3: Networks where partners can exchange recommendations will be more
closed (or transitive) than those without information exchange.
H4: Networks where partners can exchange recommendations will have more
mutually cooperative interactions than those without information exchange.
H5: Networks where partners can exchange recommendations will have more
links than those without information exchange.
Although the importance of information and reputation is central to our paper,
clustered networks may evolve even without exchange of reputational information and
support cooperative resolutions of collective action dilemmas. From this perspective,
what is most critical is that players choose with whom to play; while information
exchange has the potential of accelerating the outcome resulting from endogenous partner
selection, it is not the most critical factor in the evolution of cooperative clusters. This
view assumes that players come into the experiment with two relatively fixed heuristics
of playing the game: roughly speaking, cooperators and defectors.
In evolutionary game theory, clustering provides a protective niche in which
cooperative strategies may expand to the point of a self-sustaining equilibrium (Axelrod
1984 1988, Bendor and Swistak 1999, Nowak et al. 2004, Wang and Scholz 2004).
Typically, evolutionary models assume a learning process in which players mimic the
5
most successful strategies among their neighbors. In our experiment, subjects were not
provided information about the total payoffs of their neighbors; clustering of cooperators,
thus, cannot result from evolutionary learning in the usual sense. However, our subjects
were allowed to build new links and cut existing links, which could function as a
protection against invasion of defection strategy into a cooperative cluster.
The evolution of cooperative cluster, in this view, would depend on the extent to
which players with cooperative heuristics (cooperate, keep links if other cooperates, cut
links if other defects) are able to connect to each other. Exchange of reputational
information among players would certainly accelerate this clustering process, but not by
itself the fundamental driving force of cooperative clusters.
When players in repeated PD can choose their games, the ability to exit an
ongoing game when confronting an exploitative strategy provides an extra boost to nice
(never defect first), retaliatory (defect quickly of opponent does) strategies (Bendor and
Swistak 1999). In Axelrod’s tournaments, Tit-for-Tat emerged as the winning strategy
even when forced to continue play with all other strategies. Imagine the added advantage
it would have had if it could have ended any games with exploitative strategies and
replaced them with games with nice strategies.
From the perspective of a potentially exploitative strategy, nice, retaliatory
strategies now have an added punishment in the form of ending the game rather than
simply continuing defection. In large populations where alternatives are always
available, this may not be a problem. In smaller populations, however, the number of
options may quickly be exhausted. Then clustering may occur as a natural result of
selection by nice strategies unwilling to continue games with exploiters.
Consider, for example, the situation that informs the design of our experiment. A
limited number of federal and state agencies work independently in the same geographic
area, but occasionally find it useful to undertake a joint project with another agency.
Joint projects, like continuing PD games, provide potential advantages to both agencies if
they cooperate, but also expose each agency to the risk of shirking (defection) by the
other side. The intense focus on issues of primary concern to each agency ensures that
they spend little time learning about other agencies except through their own experience
with those agencies over time. That is, there are no existing policy networks providing
information about other agencies and the associated benefits as described above.
Assume that there are two types of agencies, cooperators and exploiters, and that
cooperators will continue joint projects only with other cooperators. Even in the absence
of information to help identify cooperators, the trial-and-error process of entering into
joint projects and terminating those with exploitative agencies will evolve a set of joint
project networks that matches cooperators into a clustered group with long-term
cooperative relationships, leaving exploiting agencies in an alternate clustered group that
fitfully enters into joint projects that seldom work out. Since cooperative gains outscore
sequences of temptation and sucker payoffs, cooperators should be able to gain the higher
payoffs in the cooperators’ cluster, while exploiters will be relegated to the lower Nash
equilibrium, as will be defined more explicitly in discussing the experimental design.
We therefore propose four selection hypotheses about behavior that apply across
both information treatments:
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H6: Cooperators will tend to be linked to each other in transitive cluster
formations.
H7: Individual cooperators will seek to maintain links with those who have
cooperated with them in the past, and seek to eliminate links with those who have
not.
H8: On average, cooperators will achieve higher earnings than defectors.
The information and selection hypotheses, when considered together, imply
another phenomenon we can expect to observe. If hypotheses H4 and H8 are true, it
should also be true that:
H9: On average, earnings will be higher in networks where partners can
exchange recommendations than those without information exchange.
That is, if cooperators earn more (H8) and there are more cooperators in networks
with information exchange (H4) then average earnings should be higher in networks with
information exchange.
2. Experimental Design
To test the information and selection hypotheses, our baseline condition replicates
the situation in which subjects must mutually agree to play repeated PD games, and can
terminate the game unilaterally after any round of play. The two treatments of the
experiment differ from each other in terms of whether subjects are able to exchange
information about others’ reputation and if it is possible what mechanisms were used for
the exchange. In the Baseline Treatment, no such informational exchange was allowed.
Thus, the only way that a player can form a belief on another player’s trustworthiness is
by actually playing the PD game with her. As the works on repeated games show, when
individuals are engaged in repeated interactions, there is an incentive for them to
cooperate with others. Especially when individuals can choose to exit from a relationship,
those who are not cooperative might lose partners. But under this first-hand, experience
based reputation mechanism, the search for worthy partners is limited by ones own
immediate experience.
In the Local Information Treatment, the game links also serve as potential
conduits of information flow. Specifically, a player (X) knows the immediate contacts
(Cb’s) of one’s immediate contacts (Y’s) and can ask Y to provide information on any
Cb’s trustwothiness. Both requesting and responding to request are costly. Responders
may or may not provide the information. Also, responders when they choose to provide
information, may or may not provide truthful information (i.e., information consistent
with a person’s habit of cooperation.). Requesting recommendation costs 1 ECU
(Experimental Currency Unit) per request and providing either positive or negative
recommendation also costs 1 ECU per recommendation. When ego provides
recommendation on an alter the information is sent to all the alters who requested
recommendation.
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Each subject saw his or her current links in the first screen for each period.
Subjects were allowed to break any number of current links or attempt to build links to
any number of the other subjects with whom they had no current links. While building a
new link required both subjects agreeing to build the link, breaking an existing link
required only one of the two choosing to break it.
On the computer screen, subjects saw her past interactions with each of the other
thirteen subjects up to four periods back. This history information was provided in each
period in both of the two treatments. When subjects were making linking decisions for
each of the other subjects and game decisions for each of the linked subjects, they were
able to see the past history. There were seven events that could happen between two
subjects in each period. In three of the seven outcomes, the link between a pair of two
player is not established:
1. Neither ego nor alter tried to link,
2. Ego tried to link but alter did not,
3. Alter tried to link but ego did not.
In the remaining four outcomes both alter and ego tried to link and, thus, a link is
established and the prisoner’s dilemma game played. The four outcomes differ in terms
of the outcome of the game:
4. Both ego and alter defect,
5. Ego cooperates and alter defects,
6. Ego defects and alter cooperates, and
7. Both ego and alter cooperate.
These seven outcomes in the past four periods were shown in a history table on
the screens in which subjects made linking decisions and game decisions. More details of
the experimental procedure can be found in APPENDIX 1, the verbal script used in the
local information treatment. APPENDIX 2 shows snapshots of some of the computer
screens.
The prisoner’s dilemma game used in the experiment has four payoffs: 0, 25, 75,
and 100. (See Table 1 in APPENDIX 1, the verbal script used in the experiment.) The
cost of links were given by a function c= 0 if m=0, and c=4.4 (m-1)2 for m>0, where
m ∈ [0,13] is the number of links the player has in a period. Payoffs during the
experiment were denominated in Experimental Currency Units (ECUs).2 The Nash
equilibrium outcome of the stage game involves each subject having four links and
2
At the conclusion of each session, each subject’s earning in ECUs was translated into dollars at
a rate of 400 ECUs= $1. Subjects were also paid a ten dollar show-up fee in addition to their cash
earning during the experiment. Average earnings were in the range of $20-25. A total of six
sessions were, three under the baseline no information condition and the other three under the
local information condition. Exactly 14 subjects participated in each of the six sessions. No
subject participated in more than one session. Sessions lasted on average an hour to an hour and a
half. Subjects were recruited from various social science courses at the Florida State University.
All sessions were conducted in a computer lab using software created with z-Tree (Fischbacher,
1999). Subjects were recruited from various social science courses at the Florida State University.
8
defecting in all the four games. This is so because while not playing the game at all gives
a zero payoff, playing generates at least 25 ECU’s per game if one defects. But beyond
four games, each additional game costs more than 25 ECU’s while the per-game payoff
from mutual defection is only 25 ECU’s. The payoff at the Nash equilibrium is 60.4
ECU’s per subject.
The socially optimum outcome involves each subject having 10 links each and
cooperating in all the ten games. The payoff at the social optimum is 393.6 ECU’s per
subject. But the marginal increase in payoff for an added link is small on the range of 7 to
10 links (assuming that everyone cooperates.) Given the marginal per link cost of 8.8(m1) for m > 0, adding an additional link is quite costly and requires a high level of trust in
others once a subject has 4 or 5 links.3
3. Aggregate Results: Information Induces Higher Payoffs and More Cooperation.
The data generated by our experiment are at multiple levels, including the
aggregate, the individual, and the dyad levels. In this section, we will first present the
aggregate level results to identify the overall patterns and to see if there are any
noticeable differences between the two treatments. In the following sections, we will
analyze the data at the individual and dyad level and also see the characteristics of the
evolving networks in the two treatments.
The aggregate results provide clear support for hypothesis H9. The average
earnings per period reported in Figure 1 show that the information condition induces
higher average payoffs than the baseline condition in every round, with the baseline
producing an overall average per round per person of 146, or 78% of the information
condition’s 186. The difference is significant both overall, and in 13 of the 20 periods at
p=0.1 level, and in 5 periods in p=0.05 level, in two-sample Wilcox rank-sum (MannWhitney) tests. (See Appendix Table 1 in APPENDIX 3.) In general the average earning
rises in earlier periods as subjects establish the game links, remain relatively steady from
periods 6 to 17, and rapidly decline from period 18 as the end game effect kicks in.
Figure 2 shows that the information condition also induces more links and more
mutual cooperation than the baseline condition. The figure displays the average number
of links (or games played) per period divided into three categories of outcomes: mutual
cooperation (C,C), mutual defection (D,D), and the other category including both (C,D)
and (D,C). Note that C and D stand for the choice to cooperate and defect, respectively,
where the first letter in brackets represents ego’s choice and the second letter represents
alter’s choice. The graphs are stacked, so the uppermost line in both figures indicates the
total number of links.
3
Earnings were accumulated for each subject over the periods. Due to the cost of links it was
possible for subjects to have a negative total earning. To deal with this possibility subjects were
given a starting up fund of 500 ECUs. Also, the following bankruptcy rule was announced to the
subjects at the beginning of the experiment. When the total earning up to a period goes below
zero the first time the subject was declared bankrupt. Upon a first bankruptcy, the bankrupt
subject’s earning was reset to 500 ECUs. If bankruptcy happens for a second time, however, the
subject was asked to leave only with the ten dollar show-up fee. No bankruptcy actually happened
during the experiment and, thus, the bankruptcy rule was never actually implemented.
9
The Information condition develops 4.7 links per person per round compared to
4.2, or 89% for the baseline condition, with higher numbers evident in most rounds,
although significantly higher in only 7 rounds. The greater difference is in the number of
mutually cooperative (C,C) outcomes, indicated by the bottom line in each panel of
Figure 2. In all 20 periods, the information condition has a larger number of per person
(C,C) links. The average links per person per round of 1.6 in the baseline condition is
just 62% of the 2.6 average in the information condition, which has a higher number of
(CC) links in 17 of the 20 rounds, 15 of which are significant. (See Appendix Table 2 in
APPENDIX 3.)
Figure 1. Average earnings are higher in the information than in the baseline
condition
E a rnings o v e r t im e : B a s e line T re a t m e nt
350
Earnings in ECU's
300
250
Low 7
200
High 7
150
Average
100
50
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Period
Earnings over time: Local Information Treatment
350
Earnings in ECU's
300
250
Low 7
200
High 7
150
Average
100
50
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Period
Note: All series are averages of three sessions. Average: average of 42 subjects (14 in each of the
three sessions). Low 7: Average of 21 subjects (seven in each session) whose period 17 earnings
are in the bottom half in each session. High 7: Average of 21 subjects (seven in each session)
whose period 17 earnings are in the top half in each session.
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Figure 2. Information Induces More Mutual Cooperation: Average Number of
Links Per Subject, Stacked by Outcome Category
Baseline Treatment
6
Number of Links
5
4
Other Link
DD Link
3
CC Link
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Period
Local Information Treatment
6
Number of Links
5
4
Other Links
DD Links
3
CC Links
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Period
The power of information to enhance cooperative behavior is even clearer in
Figure 3, which compares the proportion of cooperative choices in each round for the two
conditions. The rates of cooperation generally ranged between 60%-70% in the Local
Information Treatment, and between 40% - 55% in the Baseline Treatment, up to period
19. Then, in period 20, the rated dropped dramatically down to 26% and 16%, exhibiting
the expected end-game effect. Perhaps the most remarkable feature of this figure is the
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ability of both network conditions to preserve very high levels of cooperation.
Cooperation generally falls considerably sooner and farther. Cooperation does fall in the
first several rounds, but appears to pick up again as network features begin playing a
larger role, and is sustained until very close to the end of the game.
Figure 3. Information Induces More Cooperation
80.0
70.0
% Cooperation
60.0
50.0
Baseline
40.0
Local Information
30.0
20.0
10.0
0.0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Period
In sum, the preponderance of the aggregate-level evidence supports our
hypotheses: the information condition produced higher earnings (H8), more links (H5),
more mutual cooperation (H4), and a greater propensity to cooperate (H2) than did the
baseline condition. The higher earnings appear to be most related to the higher
propensity to cooperate rather than a greater propensity to create links: the correlation
between earnings and number of links is the same in both conditions (.74), while the
correlation between earnings and the number of CC links rises from .34 in baseline to .54
in the information condition. This difference reflects the stronger relationship between
the number of CC links and total links in the information condition (.64) than in the
baseline condition (.41). The greater number of CC links in the information condition
produces greater earnings, which subsequently supports more links.
Despite clear support for these hypotheses, several questions remain that require
further investigation. For one thing, the baseline condition does better and the
information condition does worse than the extreme equilibria predicted by the
information hypothesis: average payoffs of 146 in the baseline condition are far above the
predicted Nash payoff of 60 (Figure 1), and payoffs of 186 in the information condition
are less that half of the socially optimal payoff of 400. In addition, Figure 2 appears more
supportive of the selection hypothesis if we compare the average payoffs separately for
the seven highest and lowest earners in each condition as represented by the upper and
lower lines in each panel. The categories represent a division of subjects in each session
12
based on earnings in period 17, just before clear endgame effects set in. Very little
difference is apparent between the lowest earners in the two conditions, which is puzzling
from the perspective of hypothesis H2. The major difference occurs in payoffs to the
highest earners. Even the top earners in the baseline condition seldom earn above 200, or
50% of the socially optimal outcome, while those in the information condition approach
300 in the last half of the game, or almost 75% of the socially optimal outcome. Perhaps
the high earners pursue nice strategies that in both conditions take advantage of selection
to develop clusters of cooperators, and the information condition simply expands the
ability of cooperators to find and cooperate with one another.
4. Network Structure: Information Increases Clustering, but Selection by Strategy is
also Significant
To probe the network structures related to enhanced levels of cooperation and
payoffs in the local information condition, we next turn to SIENA (Simulation
Investigation for Empirical Network Analysis, Snijders et al. 2005) to analyze the choices
made in constructing networks. SIENA is a software package that implements a
maximum likelihood estimator to analyze the impact of selected network characteristics
on observed changes in network structure. In particular, we want to know whether the
availability of information in the local information treatment alters the basic utility
calculations of subjects in constructing their networks, and whether selection by strategy
plays a critical role in constructing networks.
We interpret each game as a link that is mutually proposed, but can be unilaterally
broken (undirected network model 2 in SIENA). Thus the set of games in a given period
defines an undirected network matrix, denoted x, among the 14 subjects, in which (i, j)th
entry equals one when players i and j are linked and, thus, a game is played, and zero
otherwise. To test the information hypothesis, we first consider actor’s preferences for
three types of closed network structures in which reputation and joint punishment
strategies may provide additional support for cooperative solutions. The most common
representation is in terms of transitivity or closed triads, in which actors i, j, and h are
linked to each other. Ego’s preference for transitivity is represented by the utility term
siT(x)=Σ xijxihxjh ,where xij equals 1 if i and j are linked in a game and zero otherwise.
That is, to maximize utility, ego seeks to maximize the number of triads.
The second structure represents a quest for overlapping friendships or, in
SIENA’s terminology, balance. Balance is represented by the utility term
siB(x)=ΣjxijΣh≠i,j(1-| xih - xjh|). That is, ego i seeks alter j with the highest count of
mutual alters; when h is an alter to both i and j, the expression (1- |xih - xjh|) = 1.4 Whereas
transitivity simply counts triads, balance accounts for the specific number of mutual
alters that enhance the potential reputation and joint punishment effects noted in the
discussion of the information hypothesis.
Finally, we include alter popularity, represented by a count of alter’s contacts:
siP(x)=ΣjxijΣh≠i,jxjh. This represents the idea that the greater the number of links of alter j,
the greater the constraint and hence the greater the likelihood of cooperation.
4
SIENA replaces 1 with a parameter b0 calculated to reduce the correlation between this term and triads,
since each mutual alter added by subject j would also represent a completed triad.
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Ego maximizes the objective function uiK(x)=βKsiK, where K={T, B, P} and βK is a
vector of parameters representing the strength of each elements in K. The estimation
model with SIENA assumes that changes in observed networks are manifestations of an
underlying continuous Markov process in which network actors make decisions about
adding or breaking network connections at randomly-determined intervals. When a
choice opportunity occurs, ego selects the change that optimizes utility based on the
existing network structure at the time of choice (which is not the same as the structure at
the moment of observation). The strong assumption is that this change is not forwardlooking or coordinated with others, but simply reflects the immediate utility-optimizing
choice of the individual. Given a set of selected variables representing hypotheses about
the utility function, SIENA estimates both a rate function (for choice opportunities) and
utility function that maximizes the likelihood of observing the transitions between
observed networks.5
Table 1 compares the utility functions estimated for the three sessions in the two
treatments, with the average for each condition included in brackets. Each row provides
the coefficients for the variable in each column for one session, estimated for all 20
transitions of observed matrices beginning with the null or empty matrix prior to the first
period in the game. All models were significant. Consistent with our hypotheses,
transitivity and balance have higher average coefficients and more significant coefficients
in the information condition (H3) but are generally significant in both conditions (H6).
Alter popularity is never significant in either condition, but also is the least relevant of the
three network structures to the hypotheses.
Table 1. Local Information Increases the Utility of Network Closure
Baseline
All sessions
Session 1
Session 2
Session 3
Transitivity
Balance
Alter Popularity
.07
.10**
.00
.12**
.34
.37
.12
.52*
-.19
-.36
-.08
-.13
Local Information
All Sessions
.14
1.00
.24
Session 1
.23**
.95**
.60
Session 2
.09**
.60*
.01
Session 3
.11**
1.44**
.10
Note: Coefficients estimated using SIENA for 20 periods and 14 subjects in each
condition. ** indicates p<.01, *p<.05, two-tailed test.
The evidence for transitivity and closure are consistent with the selection
hypotheses (specifically H7), but a better test would directly estimate the importance of
alter’s cooperative behavior in shaping ego’s network. To do so, we add a term to the
5
For more information on this complex analytic framework, see Snijders (2001) and Steglich, Snijders and
West (2005).
14
utility function that reflects a preference for cooperative similarity. The term assumes that
egos with a high proportion of cooperation seek alters with similarly high proportions of
cooperation, as represented by: siC ( x ) = ∑ j xij ( simij − Meansim ) , where simij is the
difference between i and j at the start of the transition period normalized as a percentage
of maximum difference (so it varies between 0 for no similarity and 1 for complete
similarity), and Meansim is the mean for the full period. The normalizations help ensure
better convergence of the estimation algorithm. In addition, we add a term to the rate
function that determines the speed of choice to test whether more cooperative egos tend
to be more stable in their choice of alters, preserving cooperative links and not
continuously changing links as suggested in the selection hypothesis.
Table 2 reports the results of this new estimation. The coefficients for
cooperative similarity are significant in two of the three cases in each session, confirming
that subjects prefer links with others of similar levels of cooperation. In both cases,
cooperators seek out other cooperators, leaving less cooperative subjects to link with each
other. Furthermore, the negative and generally significant coefficients for the impact of
cooperation on choice rate shows that cooperators change links less frequently than less
cooperative egos.
Table 2. Cooperators Change Links Less Frequently and Select Each Other
Transitivity
Balance
Cooperative
Similarity
Cooperative
Rate Effect
Baseline
Average
Session 1
Session 2
Session 3
[.04]
-0.4**
.03**
.06**
[.57]
.99**
.53**
.20
[.46]
.45**
.21
.71**
[-4.10]
-9.37**
-1.01
-1.93
Local Information
Average
Session 1
Session 2
Session 3
[.06]
.05
.05**
.09**
[1.03]
1.63**
.42
1.04**
[.67]
.25
.92**
.84**
[-2.76]
-2,78**
-2.79**
-2.70**
Note: Coefficients estimated using SIENA for periods 8 to 17 for 14 subjects in each condition. **
indicates p<.01, *p<.05, two-tailed test.
Both results are consistent with the selection hypothesis (H7) that cooperators
seek other cooperators and remain linked with them once they are found. The selection
hypothesis argues that it is this quest for cooperators that produces transitivity and
balance observed in the networks under both experimental conditions—selection effects
determine network structure. From this perspective, the average coefficients in each
condition suggest that the effects are somewhat stronger in the information condition,
although the variance in coefficients and significance levels across sessions does not
provide conclusive evidence that these processes are significantly greater in the
information condition.
15
Figure 5. Cooperators Form and Maintain Core Groups (dots indicate subjects, and links
represent games with CC outcomes in indicated period)
Baseline Session 1
Period 5
Period 11
Period 17
Information Session 2
Period 5
Period 11
Period 17
16
The development of clusters of cooperators as predicted by hypothesis H6 is
illustrated in Figure 5, which utilized UCINET’s (Borgatti et al., 2002) network
illustration to display the CC outcomes in periods 5, 11, and 17 from an illustrative
session for each condition. Dots or nodes represent the 14 subjects, and lines or links
indicate all sets of two players who both cooperated in a game in that period. As can be
seen, most players with CC links in round 5 not only keep those links, but continue to add
additional CC links over time as they become the core of a highly interrelated group of
mutual cooperators. The same process occurs under both conditions, but occurs earlier
and more extensively in the information condition.
Figure 6 uses histograms of the distribution of CC links per subject to illustrate
the increasing separation of subjects into either the cooperative clusters illustrated in
Figure 5 or the remaining noncoopertive clustering among those excluded from the CC
links. Even by period 2 the information condition has several subjects with more CC
links than the 4 links that tops the distribution in the baseline condition. By period 16,
the bimodal separation into cooperators with more than 4 CC links and noncooperators
with less is very clear in the information condition, and is also visible, though less
pronounced, even in the baseline condition. Separate clustering of cooperators and
defectors is one of the most strong and consistent results observed in all sessions of both
treatments, though the tendency is even stronger in the local information treatment.
(Appendix Figure 1 in APPENDIX 3 shows how cooperators and defectors form separate
clusters in Period 17 in all of the sessions.)
Figure 6. Mutually-Cooperative Links Become Bimodally Distributed
(Histograms of the number of mutually cooperative (CC) links per subject)
Period 2
Baseline
Period 16
Baseline
Information
Information
0
2
.5
2
0
.25
Density
.25
0
Density
.5
0
0
2
4
6
8
10
0
2
4
6
8
10
0
2
numcclink
Graphs by treatment
4
6
8
10
0
2
4
6
8
10
numcclink
Graphs by treatment
17
The SIENA analysis has confirmed that cooperators tend to link with each other
and that, controlling for this selection, clustering (transitivity and balance) also increases
over time. But does clustering also tend to increase cooperation, as the information
hypothesis suggests as an alternative explanation for the longevity of mutual
cooperation? SIENA has the capability of simultaneously estimating both the selection
effects of behavior on network structure (associated with the selection hypothesis, as
tested here) and the “assimilation” effects of network structure on behavior (associated
with the information hypothesis), but we have not yet been able to get convergence of the
estimating algorithm.
5. Strategic Behavior in Dyads: Mutual Cooperation increases the probability of
requesting links and cooperating
To determine how the subjects used recommendations received from their
partners and past experience with others to change their link structure, we conducted a
logit analysis of the probability that an agent will request a link with a given partner in a
period. The 14 subjects in a session face 13 such linking decisions in each of 20 periods,
giving us 3,640 observations on directed dyads per session for a total of 10,920
observations in the local information treatment condition. The dependent variable is the
binary observation of whether the subject requested a link with a partner in a period. The
primary explanatory variable of interest, per hypothesis H1, is the total number of
positive and negative recommendations that a subject received about a given partner in
that period. Dummies for the 7 possible prior outcomes of the link (namely: no history,
ego requests link, alter requests link, DD, CD, DC, and CC) in the 4 periods prior to the
observation are introduced as explanatory variables (due to hypothesis H7) and to control
for potential serial correlation of the errors; the selection of 4 lags was motivated by the
fact that 4 periods of interaction history were displayed to the subject in the experimental
software. The number of links the agent had in the prior period (and the square of the
same) is used to account for the cost structure of forming new links. Finally, dummy
variables for each subject are included to control for inherent personality differences (or
other sources of unobserved unit heterogeneity) that affect propensity to link. Table 3
shows the estimated beta coefficients of the model.
5.1. The Use of Information
The analysis of Table 3 confirms hypothesis H1: information is used to select
among links to choose the most favorable candidates. The coefficient for the total number
of positive recommendations received is positive and highly significant, indicating that
positive recommendations increase the probability that a subject will try to link (or to
maintain an existing link) with one of his/her partners. Conversely, the coefficient on
number of negative recommendations is negative and highly significant, indicating that
negative recommendations decrease the probability of linking with a potential partner.
The impact of positive recommendations is larger than that of negative
recommendations, as a Clarify analysis (Tomz, Wittenberg, and King 2003) of the
marginal effect on the linking probability of changes in independent variables reveals in
Table 4. In conducting the Clarify analysis, all the fixed effects FE dummies set to their
mean. This means that the model’s marginal changes in probability are estimated at the
18
Table 3. Linking Decisions: Logit Model with Fixed Effect Dummies
Variable Name
# of Positive
Recommendations
# of Negative
Recommendations
Alter Tries Link t-1
Ego Tries Link t-1
DD Outcome t-1
CD Outcome t-1
DC Outcome t-1
CC Outcome t-1
Alter Tries Link t-2
Ego Tries Link t-2
DD Outcome t-2
CD Outcome t-2
DC Outcome t-2
CC Outcome t-2
Alter Tries Link t-3
Ego Tries Link t-3
DD Outcome t-3
CD Outcome t-3
DC Outcome t-3
CC Outcome t-3
Alter Tries Link t-4
Ego Tries Link t-4
DD Outcome t-4
CD Outcome t-4
DC Outcome t-4
CC Outcome t-4
# of Links t-1
(# of Links t-1)2
Period
Final Period
Constant
No Information
Coefficient
Std. Error
.599***
1.17***
1.65***
1.39***
2.00***
4.27***
.114
.419***
.470***
.0825
.820***
1.13***
-.0406
.245***
.184**
-.108
.259*
.0766
.107
.139*
.156*
-.347***
.512***
.691***
-.246***
.0140***
-.0268***
.596***
.828
.0680
.0676
.0910
.124
.142
.260
.0718
.0707
.0924
.128
.140
.224
.0741
.0731
.0955
.135
.138
.210
.0736
.0733
.0932
.138
.140
.206
.0388
.00458
.00516
.120
.178
Local Information
Coefficient
Std. Error
.868***
.0796
-.544***
.148
.762***
1.35***
2.25***
1.77***
2.24***
6.05***
-.0325
.433***
.0187
-.0313
.152
.509***
-.126
.231***
.00259
-.0241
.241
-.0902
-.0613
.190**
.223*
.0539
.0217
.430***
-.241***
.00439
-.0140**
.717***
-2.40
.0766
.0730
.119
.138
.154
.286
.0827
.0776
.123
.150
.149
.203
.0861
.0809
.129
.153
.155
.195
.0858
.0815
.124
.154
.148
.175
.0375
.00420
.00582
.131
.223
Note: Coefficients for dummies omitted.
19
population average individual propensity to form a link. A single positive
recommendation has a relatively small impact on the probability of attempting a link
(increasing it by .16), but two or three positive recommendations drastically increase the
probability of attempting a link (by .37 and .56, respectively.) But even three negative
recommendations causes a mere .14 reduction in the probability of link attempt from the
baseline. Negative recommendations are not particularly important because the baseline
probability of requesting a link is so low (.20) that, in the absence of a pre-existing link,
negative recommendations merely make the chances of linking go from slim to none. In
addition, and counter to our initial beliefs, negative recommendations do not seem to
prompt punishment by an agent: when mutual cooperation in the prior period is the
baseline condition (probability of requesting a link = .98), three negative
recommendations cause a -.04 change in predicted probability of requesting a link, even
lower than at the baseline.
Table 4. Mutual Cooperation and Positive Recommendations Increases the
Likelihood of Linking
Baseline Pr(request link):
Ego Tries Link t-1
Alter Tries Link t-1
DD Outcome t-1
CD Outcome t-1
DC Outcome t-1
CC Outcome t-1
Positive Recommendations: 0 to 1
Positive Recommendations: 0 to 2
Positive Recommendations: 0 to 3
Negative Recommendations: 0 to 1
Negative Recommendations: 0 to 2
Negative Recommendations: 0 to 3
No Information
.207
Local Information
.191
Change in Pr(request link)
.115
.145
.249
.287
.368
.500
.306
.390
.454
.499
.741
.799
-
.158
.367
.561
-.0693
-.115
-.143
NOTE: Figures are calculated probabilities associated with the Treatment 2 model in Table 3 for
period 10, the average of 4.66 links, and the average of .15 positive recommendations and .06
negative recommendations received. The value of fixed effect dummies is set at the mean,
meaning that the probability represented in the model is the average of the sample’s individuallevel propensities. The other rows are calculated when the indicated variable is changed from 0
to 1 (or as stated).
5.2 The impact of past actions
Table 3 also shows that subjects were most likely to maintain links with mutually
cooperative partners, as is consistent with our selection hypothesis. The coefficients on
any type of link in the past period are positive and significant, indicating that subjects
have a tendency to request links to those with whom they have previously had any sort of
20
contact. However, the coefficients are highest on prior CC interactions, indicating that
subjects are most likely to request links to those with whom they have enjoyed mutual
cooperation in the past.
Table 4 shows the substantive impact of past interactions on the probability of
requesting a link. In the no information treatment, mutual defection in the prior period
increases the probability of requesting a link in the current period by .37, with a .37
bonus for mutual cooperation and a .06 penalty for being suckered in the prior round.
Results are basically similar in the local information treatment, although a higher mutual
defection effect (increasing the probability of a link request by .50) means that the
advantage to cooperation is somewhat smaller (.30). From these results, it appears clear
that the subjects are focusing most of their link requests on those with whom they have
enjoyed cooperation in the past (H7).
One minor falsification of our theoretical expectation is worthy of note: contrary
to our expectations, agents do not seem to be more willing to take risks on creating a new
link in the information treatment than in the no information treatment. At the baseline and
given only past requests for a link, the two treatments have virtually identical predicted
probabilities. The information treatment therefore seems to give the subjects little
generalized confidence in the power of reputation on the behavior of others, although
receiving direct recommendations from partners does increase their willingness to trust.
5.3 The Advantage of Niceness
Consistent with hypotheses H8 and H9, niceness in particular plays a critical role
in determining the relative success of strategies. This result is apparent when we look
closely at the strategic choices of (eventual) high and low earners (Figure 2) in the early
and late periods. Table 5 presents the proportion of choice situations (continuing links)
following each of the possible outcomes in the upper panel and the proportion of
cooperative choices made in each situation in the lower panel, using period 2 to represent
early strategic choices and period 17 to represent later choices. Recall that in the
following discussions as well as in Figure 2, high and low earners are defined by their
single period earnings in period 17, not by the cumulative earnings in all periods. This
division is done to identify the linking and game strategies that prove to be successful in
the long run, if not immediately.
Even by the second period, high earners already had almost 50% more links, and
had a slightly greater proportion of CC links and slightly lower proportion of new links.
By period 17, the differences in CC links were magnified dramatically: mutually
cooperative links made up over 85% of high earner’s links, compared to just 24% for low
earners. Low earners on the other hand were more reliant on new links (40% versus 8%),
and were trapped into more low-payoff mutual-defect links (26% versus 5%).
How did these differences emerge? In the early rounds, high earner strategies
were considerably nicer than low earner strategies. High earners cooperated with new
alters 73% of the time, compared with 54% for low earners. Perhaps more importantly,
high earners continued cooperation with mutually cooperative links 90% of the time,
compared with 56% for low earners. Although low earners’ willingness to exploit in
both situations gained them higher payoffs when they met high earners in these early
encounters, it apparently sealed their fate by disrupting the possibility of continuing CC
relationships. Low earners tended to be more retaliatory against alter’s defection
21
following CD encounters, but there were too few encounters in these categories to give
reliable impressions of retaliation.
Table 5. Eventual High Earners Are Much More Nicer Than Eventual Low Earners in
Earlier Periods. All Strategies Become Nicer to Cooperators and Nastier to Newcomers.
PERCENT OF LINKS BY PRIOR OUTCOMES (LOCAL INFORMATION TREATMENT ONLY)
Period 2
Prior Outcome
(ego’s choice first)
no prior link
CC
DC
CD
DD
Total links
Period 17
Low Earner
(N=21)
High Earner
(N=21)
Low Earner
(N=21)
High Earner
(N=21)
0.62
0.29
0.03
0.03
0.03
63
0.55
0.33
0.03
0.03
0.04
91
0.40
0.24
0.03
0.07
0.26
100
0.08
0.85
0.03
0.00
0.05
132
Note: Each column divides total links by previous period outcome. High/Low earners are by
period 17 single period earnings.
PERCENT COOPERATIVE CHOICES BY EGO FOLLOWING PRIOR OUTCOMES (LOCAL
INFORMATION TREATMENT ONLY)
Period 2
Period 17
Prior Outcome
(ego’s choice first)
Low Earner
(N=21)
High Earner
(N=21)
Low Earner
(N=21)
High Earner
(N=21)
no prior link
CC
DC
CD
DD
Total links
0.54 (21/39)
0.56 (10/18)
0.00 (0/2)
0.50 (1/2)
0.00 (0/2)
63
0.73 (37/51)
0.90 (27/30)
0.33 (1/3)
0.67 (2/3)
0.00 (0/4)
91
0.25 (10/40)
0.96 (23/24)
0.33 (1/3)
0.71 (5/7)
0.08 (2/26)
100
0.20 (2/10)
0.95 (106/112)
0.00
(0/4)
N/A
0.00
(0/6)
132
Note: Each cell entry shows the probability of cooperation conditional on the previous period
outcome. N/A: No Observation. High/Low earners are by period 17 single period earnings. Raw
counts in parantheses.
By the later periods, low earners have also learned to be nice in response to
mutual cooperation, with both strategies cooperating 95% of the time. However, this
change appeared to come too late to build up the repertoire of mutual cooperation, which
remained at only 24% of low-earner connections. Their continuing reliance on new
relationships—still 40% of their links in period 17—became an increasing burden as both
low and high earners became increasingly nasty to new links, cooperating only 25% and
20% of the time, respectively. The ability to convert mutual-defection links to mutual
22
cooperation was even more limited; high earners never cooperated after mutual defection,
and low earners cooperated only 8% of the time. Low earners had a greater likelihood of
converting mixed links within their group to mutual cooperation (.33*.71=.24), but high
earners had become totally vengeful in their few remaining mixed relationships, not
cooperating in any of them. That is, the high earners not only gained the advantage of
their large proportion of mutual cooperation links, but also were able to exploit low
earners who were desperately seeking more mutual cooperation.
In sum, the detailed view of strategic choices in Table 5 suggests a vivid picture
of how this sorting process works to provide a cooperative advantage to nice strategies.
In the dynamic network setting in which defectors can be punished not only by mutual
defection but also by ostracism, attempts at exploitation can condemn early exploiters to
a defectors’ ghetto (Also see Appendix 3, Appendix Figure 1). Once trapped in this
ghetto, early exploiters themselves become increasingly exploited by those safely
ensconced in their clusters of mutual cooperation.
6. Conclusion
We designed our experiment to analyze the role of information and selection in
determining the ability of networks to resolve collective action dilemmas. Our aggregate
findings demonstrate clearly that the ability to trade information about the performance of
alters plays a critical role in increasing earnings and the level of cooperation in
endogenously-selected repeated prisoners dilemmas. Subjects in the information
condition produced higher earnings, more links, more mutual cooperation, and a greater
propensity to cooperate than did the baseline condition.
On the other hand, a closer look at the dynamic processes of network selection
calls into question the adequacy of the information hypotheses in which reputation and
mutual punishment strategies within clusters of subjects account for the effectiveness of
information in supporting mutual cooperation. As the SIENA analysis shows, clustering
does occur in the information condition, but also occurs in the baseline condition in
which ego does not even know who his alters’ alters are, let alone how they behave! This
analysis also shows the tendency for cooperators to prefer links with other cooperators,
and also for the links of cooperators to be more stable than the links of less cooperative
subjects. Clustering, selection by type, and stability of cooperators’ links occurs in both
conditions, although the informational condition appears to accelerate these dynamics.
By analyzing choice within the ego-alter dyad, we see that reputation indeed plays
a significant role in determining ego’s selection of alters. This information enables
cooperators to find other cooperators considerably more rapidly than in the baseline
condition, where only ego’s individual experience with alter provides the matching
mechanism. But the bigger story is not the role of information, but the enormous impact
of prior mutual cooperation (CC) on the probability both of sustaining a link and of
cooperating. Indeed, it appears that the success of the high earners comes primarily from
their greater niceness—their willingness to cooperate with new links and to sustain
mutual cooperation. Early niceness translates into a growing proportion of mutually
cooperative links for high earners, and an increasing marginalization of early exploiters.
23
Early exploiters gain a growing proportion of mutually defecting links, and continuously
seek new links even as all strategies become increasingly exploitative of these new links.
In short, selection appears to drive the primary dynamic in our experiments, with
information providing earlier and greater advantages to nice strategies. If the information
hypothesis alone were relevant to our experiment, those stuck in the exploiters’ ghettos
should also have been able to overcome their disadvantage through mutual clustering.
And indeed, we do not rule out the possibility that in a longer time frame the low
earners may also have been able to evolve more cooperative relationships. By the later
periods they clearly recognized the advantage of maintaining mutually cooperative
relationships that they were more willing to exploit earlier on in the game. But the
conversion of mutual defection and mixed links was too slow to occur within the limited
time of our experiment (and patience of our subjects.) Furthermore, the dominance of
selection effects that we find in our experiment may be less damaging to exploitative
strategies in larger populations, particularly if “a sucker is born every minute”…
Nonetheless, to understand the short-term dynamics of policy networks in the
relatively small, disconnected political arenas that we had in mind in defined the
experimental setting, our findings suggest that the dominant role of information is in
accelerating the ability of potential cooperators to find each other. These findings
strongly suggest that policy actors tempted to exploit early attempts at creating joint
projects are likely to end up ostracized in a defectors’ ghetto and unable to gain the
potential long-term advantages of mutual cooperation—providing that there are enough
nice strategies among relevant policy actors to develop the clusters of mutual cooperation
that formed in our experiments.
24
APPENDIX 1. Verbal script used in Local Information treatment
Thank you for participating in today’s experiment. This instruction explains the nature of
today’s experiment as well as how to navigate the computer interface you will be
working with. We ask that you please refrain from talking or looking at the monitors of
other participants during the experiment. If you have a question or problem please raise
your hand and one of us will come to you.
In the instructions that follow, all monetary amounts, earnings, and costs are denominated
in Experimental Currency Units or ECUs. At the end of the experiment, your earnings in
ECUs will be translated into US$ at the rate of 400 ECUs equals $1. So if you end up
with a balance of 10,000 ECUs you will be paid $25, 6,000 ECUs equals $15 and 4,000
ECUs equals $10. In addition to your earnings from your decisions over the course of the
experiment, you will also receive your $10 show-up fee regardless of what happens. We
will make our payment to you by check at the end of the experiment.
Description of the decisionmaking situation
Today’s experiment consists of 20 periods. In each period, you will be linked to between
0 and 13 other participants. For each of the participants with whom you are linked, you
will make a choice between options A and B. The other participant will also make a
choice between A and B.
Table 1 below shows the nature of the decisionmaking situation that you face with each
of the other participants you are linked to in a period. (The way you get to be linked to
other participants will be explained shortly.) For example, if You choose A and the other
participant also chooses A, each earns 75 ECUs. If You choose A and the other chooses
B, you get 0 and the other gets 100. If you choose B and the other chooses A, you get 100
and the other gets 0. If you choose B and the other also chooses B, both get 25.
TABLE 1. YOUR EARNINGS TABLE
If Other Chooses
If You
Choose
A
B
A
You get 75 ECUs
Other gets 75 ECUs
You get 0 ECUs
Other gets 100 ECUs
B
You get 100 ECUs
Other gets 0 ECUs
You get 25 ECUs
Other gets 25 ECUs
You will be facing this decision situation for each of the participants you are linked with
in a period. Your GROSS EARNGING in a period is the sum of the payoffs you get in all
the decision situations in that period. For example, if you are linked with three other
25
participants in a period and earn 25, 75, and 100 ECUs respectively in those three
decisionmaking situations, your GROSS EARNING in that period will be 200 ECU’s.
Cost of Link and Cost of Information
Your NET EARNING in a period is your GROSS EARNING minus your COST in that
period. There are two kinds of costs in each period: cost of links and cost of information.
The link cost in a period depends on the number of links you have in that period. If you
have x number of links your cost will be 4.4( x − 1) 2 ECUs. TABLE 2 calculates this cost
for you. (READ A FEW EXAMPLES FROM THE TABLE). The second cost is the cost
of information. You will be allowed to provide and receive information about other
participants in each period. The exact mechanism of information will be explained in
detail later. For each piece of information you provide to others or you request from
others you will be charged 1 ECU. For example, if your GROSS earning is 200 and you
have three links, and your information cost is 8 your NET EARNING will be 200 – 17.6
– 8 = 176.4 ECU’s.
TABLE 2. COST OF LINKS
# links
0
1
2
3
4
cost
0
0
4.4
17.6
39.6
# links
5
6
7
8
9
cost
70.4
110.0
158.4
215.6
281.6
# links
10
11
12
13
Cost
356.4
440.0
532.4
633.6
It is possible for you to obtain a negative payoff. To allow for the possibility of a negative
payoff, everyone will start with an initial balance of 500 ECUs. As you make your
decisions over the course of the experiment, this balance will rise or fall. If you lose so
much that your overall balance goes below 0, you will be declared bankrupt. The first
time this happens to you, we will re-initialize you, starting you over with a new positive
initial balance of 500 ECUs. If your earnings balance goes negative a second time,
however, you will be asked to leave the experiment with only your $10.00 show up fee.
Now please turn to your computer screens. We have prepared several demonstration
screens to help you get familiar with the actual screens you will be seeing during the
experiment.
Establishing and Terminating Links
(SHOW SCREEN 1) What you see is the first screen that you will see in each period.
Please to not press OK until you are asked to do so. The upper left corner of the screen
will show your own Participant Number, which, once assigned, will remain the same
26
throughout the experiment. The first column identifies thirteen other participants in this
room by their own Participant Number. The numbers will be randomly arranged and
ordered differently for each of you. There is also a bar at the top of the page indicating
the period (this is Trial Period 1) and the Time Remaining in the period. We suggest that
you make your decisions for a screen within the time limit, but you will not be forced to
make decisions in that time.
This screen allows you to establish and terminate links. At the start of period one, you are
not linked to any of the other participants. Thus, your first task is to decide whether or not
to try to establish links. It is entirely up to you whether or not and with whom to try to
establish links and how many links to try to establish. To be linked with another
participant, the other participant also needs to choose Yes to link with you. Otherwise,
the link will not be established.
For each of the other participants with whom you are linked, you will be facing the
decisionmaking situation described in TABLE 1. After period 1, when you have some
links already established, you also have a choice of terminating any number of current
links.
The second column on the screen asks “DO YOU WANT TO LINK TO THIS
PARTICIPANT?” By clicking the Yes button, you are expressing that you do want to
link to the participant. ((Now choose Yes or No for each of the other participants and
click OK button at the bottom. We are not in the actual experiment yet. Thus, your choice
will not affect your earnings.))
(SCREEN 2) This screen shows, first, the result of the linking stage. The screen is predetermined independently of the choices you made in the previous screen. For now, we
are just explaining what the screens will look like in the actual experiment. In the actual
experiment, the results displayed on the screen will depend upon the choices you and
other participants actually make. The screen shows that you are linked to 4 other
participants. At this stage you make a choice between A and B (as shown in TABLE 1)
for each of the linked others. This will determine your GROSS EARNING in a period as
explained before. Consult TABLE 1 and choose A or B for each of the links and click
OK.
(SCREEN 3) This screen, again pre-determined, shows the results of the previous stage
and your GROSS and NET EARNINGs in the period. It shows, for each of your links,
the choice you made, the choice the other made, your earning in the decision situation
with that link, and your GROSS EARNING. On the right side of the screen your link
costs (shown in TABLE 2) are subtracted from your gross earning and your NET
EARNING for that period is shown. (PAUSE A FEW SECOND FOR THE SUBJECTS
TO STUDY THE SCREEN.) If you understand the display Click OK to move on.
(SCREEN 4) Now we have completed period 1 and are at the beginning of period 2. Pay
attention to the right side of the screen titled HISTORY OF LINK INTERACTIONS IN
THE PAST FOUR PERIODS. This history table shows what happened between you and
27
each of the other participants in the past, up to four periods back. Because we are only in
period 2, you see the history of only one period back, the first period. t-1 in the history
table means one period back, t-2 means two periods back, and so on. For example, if you
are in period 7, t-3 column will show you what happened in period 4. There are several
possible entries to the cells of the table. They are summarized in TABLE 3.
TABLE 3. EXPLANATION OF MESSAGES IN THE HISTORY TABLE
Message
Meaning
You Tried to Link
You chose YES in the column “Do you want to link to
this participant?” but the other chose No
The other chose YES in the column “Do you want to link
to this participant?” but you chose No.
You and the other were linked in that period and
You chose A and the other chose A
You and the other were linked in that period and
You chose A and the other chose B
You and the other were linked in that period and
You chose B and the other chose A.
You and the other were linked in that period and
You chose B and the other chose B
Tried to Link to You
You: A, Other: A
You: A, Other: B
You: B, Other: A
You: B, Other: B
Notice that, as a result of link choices you and others made in period 1 you currently have
four links established. Participants 9, 10, 2, and 8 are those with whom you are currently
linked. Before you make link decisions for this period, you may ask those who are
currently linked with you to recommend some other participants for you to link with. The
second column shows the number of links the other participants have. For example, the
column shows that Participant #9 is linked to three others (including you); Participant 10
has five links. Based on the information provided in the History table and the second
column, you may choose to request to any number of your current links to recommend
other participant. Remember that requesting information costs you 1 ECU per request.
Please make some choices now; these choices are for practice only and will not cost you
anything. Click OK to move to next screen.
(SCREEN 5) This is the screen on which you respond to others requests for
recommendations. Only those to whom you are currently linked may request
recommendations from you. The row below your participant number shows which
participants are requesting recommendations. In this case, participants 2, 8, 9, and 10 are
requesting recommendations. In the second column you make recommendation decisions
about each person to whom you are linked. Notice that there are three buttons. The
default is the center button, which corresponds to giving no recommendation about the
subject in that row. You can also give a positive or negative recommendation about the
subject by clicking the corresponding button. You do not pay the recommendation cost of
1 ECU when you do not make a recommendation, but for either positive or negative
recommendations, you must pay 1 ECU per recommendation. When you click OK, your
28
recommendations are sent to every participant who requested recommendation from you.
Please make some recommendations, which are for practice only and will not be sent to
other participants, then press OK.
(SCREEN 6) On this screen you will be again making decisions whether to link to each
of the other participants by clicking YES or NO in the second column. You will notice
that the four other participants with whom you were linked in the previous period have
YES already chosen as default. This means that you have four current links established.
You can, of course, change any of the YES’s to NO if you want. Here you may use the
recommendations (provided by those who responded your request in the previous screen)
as you make the link decisions. The third column shows how your current links have
responded to your requests for recommendation. (Recall that you can request
recommendation only to those who are currently linked with you, and not every person
may choose to respond to your request.) The third column of the first row has 2 and 10 in
the row corresponding to participant 14, and 8 in the rows corresponding to participants 7
and 3. That means that participants 2 and 10 who are currently linked with you (as you
can verify from the HISTORY window on the right side of the screen) recommend
participant 14 positively, while participant 8 positively recommends participants 7 and 3.
The fourth column shows that participant 8 negatively recommends participant 11, while
participant 2 negatively recommends participant 7. You may now make your link
decisions by clicking YES’s and NO’s in the second column. These decisions, for now,
are for practice only and will not affect your earnings.
The remainder of this period will be the same as the previous period. That is, you will
make a choice between A and B for each of the other participants who are currently
linked with you, the outcomes will be revealed to you along with your earnings, and then
you will move on to the next period. This concludes the demonstration screens. Click OK
to move on. We are now ready to start the actual experiment. Are there any questions
before we start?
We suggest that you make your decisions for a screen within 60 seconds, but you will not
be forced to make decisions in that time. Of course, we expect that in earlier periods it
might take you more than 60 seconds to make decisions for a screen. You will get more
accustomed to the tasks as the experiment progresses. As mentioned before, this
experiment consists of 20 periods, and each period contains several stages. Thus, it is
important that you pay attention to the screen and try to make decisions in the suggested
time frame.
We ask that you follow the rules of the experiment. Anyone who violates the rules may
be asked to leave the experiment with only the $10.00 show-up fee.
29
APPENDIX 2. Experimental Software Screen Snapshots
30
31
APPENDIX 3. Additional Tables and Figures
Appendix Table 1. Earnings per person over time.
Baseline
Local Information
Period
Mean Std. Dev.
Min
Max
Mean Std. Dev.
Min
Max Diff (L-B) significance
1
101
99
-40
359
109
98
-4
340
8
2
133
94
-18
380
154
98
-22
430
21
3
129
83
-8
310
168
96
0
382
40
*
4
133
93
-158
367
186
92
-57
357
53
**
5
153
80
-18
315
181
91
-15
366
28
6
140
98
0
367
187
108
5
384
47
**
7
144
93
-57
367
208
104
-45
384
64
**
8
161
85
15
367
209
99
-1
384
49
**
9
154
106
10
367
202
110
-10
375
48
*
10
155
100
21
409
207
122
-45
379
52
*
11
170
95
0
367
207
113
0
409
38
12
157
99
-16
340
208
129
0
395
51
*
13
166
109
-83
367
213
118
0
415
47
*
14
157
96
0
367
205
121
0
571
48
*
15
157
98
0
367
209
119
0
378
53
**
16
166
89
0
340
215
125
0
391
49
*
17
170
108
21
367
206
125
-41
542
36
18
159
98
25
340
201
121
-20
380
42
*
19
143
96
-57
340
163
113
0
467
20
20
75
80
-106
340
88
94
-84
265
12
Note: Significance tests are based on two-sample Wilcoxon rank-sum (Mann-Whitney) test. *: p<0.10, **:
p<0.05.
32
Appendix Table 2. Number of Links Per Person, Number of (C,C) Links Per Person
Local Information
Baseline
(L)
(B)
Period CC Links Links CC Link Link
1
1.14
2.14
0.57
2.48
2
1.57
3.67
1.00
3.52
3
2.05
4.00
0.95
4.29
4
2.38
4.52
1.19
3.67
5
2.43
4.76
1.48
4.05
6
2.71
4.95
1.48
4.14
7
2.95
5.14
1.52
4.67
8
3.00
5.38
1.71
4.52
9
2.95
4.81
1.71
4.19
10
3.10
4.67
1.86
3.95
11
3.14
4.52
1.90
4.33
12
3.24
4.81
1.90
4.62
13
3.14
5.24
2.00
4.38
14
3.00
4.86
1.90
3.95
15
3.29
4.71
1.95
4.57
16
3.24
4.67
2.05
4.33
17
3.00
5.52
2.10
4.38
18
3.05
5.10
2.05
4.57
19
1.67
4.48
1.62
4.10
20
0.29
5.29
0.29
5.33
SignifiDiff (L-B) cance
Link
-0.33
0.14
-0.29
*
0.86
0.71
0.81
0.48
**
0.86
0.62
**
0.71
0.19
0.19
*
0.86
**
0.90
0.14
0.33
**
1.14
*
0.52
0.38
-0.05
Diff(L-B)
Cclink
0.57
0.57
1.10
1.19
0.95
1.24
1.43
1.29
1.24
1.24
1.24
1.33
1.14
1.10
1.33
1.19
0.90
1.00
0.05
0.00
Significance
**
**
*
**
**
**
**
**
**
**
*
**
**
**
*
Note: Significance tests are based on two-sample Wilcoxon rank-sum (Mann-Whitney) test. *: p<0.10, **:
p<0.05.
33
Appendix Figure 1. Clustering of Cooperators and Defectors in Period 17
34
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