Rewards and Punishments in Bargaining
Svetlana Pevnitskaya and Dmitry Ryvkin
Florida State University
June 5, 2009
Moscow
Introduction
• Economic and social activity is usually preceded by bargaining
between the interested parties
• Bargaining fails when participants do not reach an agreement
despite an opportunity for Pareto improvement
• Bargaining positions are often asymmetric
• The deal still hinges on a decision of voluntary engagement from
the other party
• Can the acceptance decision be facilitated?
In this paper:
• asymmetric bargaining with two parties employing the
setting of ultimatum games
– acceptance decision is required for positive payoffs
– extensively studied (robust and well understood
behavior)
– most responders do not agree to low offers resulting in
monetary efficiency losses
• review of early ultimatum experiments e.g., Guth 1995,
Roth 1995, Camerer and Thaler 1995
Introduction
In this paper:
• augment the mechanism to adjust behavior
• rewards and punishments:
– reward desirable and sanction undesirable actions by changing
payoffs
– feedback and emotional expressions (see e.g. Xiao, et al., 2005,
Brandts and Cooper, 2007, Casari and Luini, 2008)
• Punishment – decrease in payoff that a second-stage player
imposes on a first stage player;
• Reward – increase in payoff to a first stage player imposed by a
second stage player.
(Andreoni et al, 2003)
Introduction
Previous studies of rewards and punishments:
• provision of public goods (e.g. Fehr and G¨achter, 2000,
Sefton et al., 2007, Nikiforakis and Normann, 2008)
• common pool resources (e.g. Ostr¨om et al., 1992)
• dictator games (e.g. Ahlert et al., 1999, Andreoni et al.,
2003b),
• investment games (e.g. Abbink et al., 2000, Houser et al.,
2008)
• general result that they are, to various degrees, effective in
increasing contributions and promoting cooperation.
Implementation of rewards and punishments:
• one-to-one application
• both instruments
• fixed cost (or inverse effectiveness) of reward or
punishment that is equal to one
Key findings:
• availability of instruments promotes the acceptance decision
• proposers are most generous when responders can reward
and punish, and offer least when responders can only
reward
• for a population of proposers where a significant number of
low offers is present, punishment only leads to greater
efficiency
Experimental Design
The first-stage player (proposer) chooses amount x such that he gets
(500-x) cents and the second-stage player (responder) gets x.
x – offer
U: second-stage player can reject or accept the offer resulting in payoffs
(0,0) and (500-x, x) respectively.
UR: second-stage player can reject or accept the offer. In the former case
payoffs are (0,0). In the latter case responder chooses transfer
0 ≤ y ≤ x such that resulting payoffs are (500-x+y, x-y)
UP: second-stage player can reject or accept the offer. In the former case
payoffs are (0,0). In the latter case responder chooses reduction
0 ≤ z ≤ min{x, 500-x} such that resulting payoffs are (500-x-z, x-z)
UPR: second-stage player can reject or accept the offer. In the former
case payoffs are (0,0). In the latter case responder chooses either
transfer, y, or a reduction, z, such that the payoffs are as specified
above for corresponding option.
Theoretical Considerations
Individual payoff maximization framework:
(U, UR, UP and UPR) responders accept any x > 0, and y=z=0.
Experimental evidence
U: low offers are likely to be rejected, and many proposers offer
0.5S.
R&P in other mechanisms: substantial demand even when costly
Theoretical Considerations: choice of parameters
Effectiveness of reward and punishment, k and l:
Reward: reward spending of 1 increases proposer’s payoff by k
Punishment: punishment spending of 1 decreases proposer’s payoff
by l
(possibility for efficiency enhancement)
Models of other-regarding preferences (Rabin 1993, Fehr and
Schmidt 1999, Bolton and Ockenfels 2000, etc.)
relative payoffs
Theoretical Considerations
Using Fehr and Schmidt (1999) model with inequality aversion:
This study: k = l = 1
Separate the effect of reward from efficiency enhancement
Hypotheses
• Proposers increase their offers in the UR, UP and UPR games
compared to the U game.
• Responders’ likelihood of accepting a given offer is larger in the UR,
UP and UPR games compared to the U game.
• Responders reward (in UR and UPR) and punish (in UP and UPR)
mostly by symbolic amounts.
• Proposers adjust their offers to maximize their expected payoff given
the behavior of responders.
Experimental Design
Treatment
U
UR
UP
UPR
Sessions
2
2
2
2
Subjects
36
40
34
34
Procedures:
Subjects: FSU undergraduate students
Z-tree (Fischbacher, 2007)
Session: 60-90 minutes
Zipper matching
Payment based on 2 randomly chosen rounds
$10 show up fee, approx. $20 average total payment
Proposers
Responders
Average offer
Acceptance rate
U
UR
U
UR
**
206.7
(5.0)
205.8
(12.7) *
183.8
(10.3)
219.7
* (7.5)
***
UP
UPR
.83
(.04)
.83 *
(.04)
.75
(.05)
.88
(.04)
UP
UPR
**
Frequency of Reward/Punishment Instruments Use
U
UP
UPR
.10 (.04)
.12 (.04)
.14 (.05)
reject/all (std. error)
.17 (.04) .25 (.05) .17 (.04)
.12 (.04)
accept/all (std.error)
.83 (.04) .75 (.05) .83 (.04)
.88 (.04)
transfer>0/all (std. error)
reduct>0/all (std. error)
UR
.13 (.04)
UP smaller rejection frequency than UR – supports the explanation that use P as a
feedback, correspondingly in R – greater frequency of rejection since this is the only
way to send negative feedback
Proposers: Distributions of Offers by Treatment
Proposers: Cumulative Distributions of Offers
Result 1. The empirical distributions of offers are different. Offers
in all treatments FOS dominate those in UR and offers in the UPR
treatment FOS dominate offers in all other treatments.
Responders
Prob(accept)
offer
U
UR
UP
UPR
Coeff.
.058***
.028***
.008***
.036***
Intercept
-9.4***
-3.5***
-0.54
-4.7***
.023***
.011***
.003***
.014***
Marginal Effect
(Random Effects Probit regressions)
All pairwise comparisons except UR-UPR are significant
Responders: Probability to Accept
Result 2. The presence of rewards and/or punishments facilitates
acceptance of offers. The most dramatic difference is observed in
UP where even very low offers have a good likelihood of being
accepted.
Responders: Probability of Reward
Responders: Probability of Punishment
Responders: Reward and Punishment
Result 3. The probability of using rewards and punishments
depends asymmetrically on the presence of the other instrument.
Rewards are less likely in the presence of punishment than without
it, but punishments are more likely in the presence of reward than
without it.
Result 4. (i) Rewards are statistically significant and larger in
magnitude in the presence of punishment than without it.
(ii) Punishments are statistically significant in the presence of
reward but are essentially zero without reward, indicating they are
used as feedback.
Responders: Estimated Update
(conditional on acceptance)
Update=transfer*prob(transfer>0) – reduction*prob(reduction>0)
Proposer’s Expected Payoff (and average offers)
Result 5. Proposers’ average offers are consistent with the expected
payoff maximization
Total expected payoff
Consider population of proposers with offers distributed uniformly
over [0, 250].
Total expected payoffs (proposer’s payoff, responder’s payoff):
332.8 (235.4, 97.4) in UP
251.4 (159.8, 91.6) in UR
242.0 (151.8, 90.2) in UPR
177.1 (104.8, 72.3) in U
Result 6. In environments with substantial presence of low offers
(i) introducing the costly reward and/or punishment options
increases efficiency; (ii) a punishment-only scheme leads to the
largest gain in efficiency.
Proposers:
Dynamics of Offers
Offer
U
UR
UP
UPR
const
167.7***
75.8***
146.3***
192.1***
accept_lag
-20.1***
-21.4
-4.2
-55.1***
*** p<0.01, ** p<0.05, * p<0.10
const:
accept_lag:
offer_lag:
UPR>UR, p<0.01; U>UR, p<0.01
UP>UPR, p=0.02, U>UPR, p<0.08
UR>UPR, p<0.08; UR>U, p<0.03
offer_lag
.26**
.68***
.31
.36***
Dynamics
Result 7. Responders do not exhibit (statistically significant)
adjustment in our setting.
Result 8. Proposers’ adjustment depends on the availability of the
reward and punishment options to responders.
In U and UPR, proposers react to past acceptance decisions, while
in UR they ignore past acceptances but reciprocate past rewards.
In UP, neither acceptances nor punishments affect proposers’
decisions.
Conclusions
• Conducted conservative test of the effect of rewards and punishments
in bargaining
• The likelihood of agreement is increasing if the responding party has
an option to apply a costly reward and/or punishment after accepting
the offer.
• The least generous terms, which typically lead to lost opportunities
due to rejection, have the highest chance to be accepted in the
presence of punishment only.
• Proposers make more generous offers when the responders can reward
and punish, and offer least (even compared to the baseline) when
responders can only reward.
• The presence of the symbolic amounts of both suggests feedback from
the responding to the proposing party.
Conclusions
• Did not observe adjustment in responders’ behavior.
• Proposers adjust behavior in U, UR and UPR. based on
acceptance (decrease) in U, UPR and reward (increase) in UR
Proposers: Average Offer (over time)
Responders: Probability to Accept (over time)
Responders: Probability of Positive Transfer (over time)
Responders: Probability of Positive Reduction (over time)
Feasible Payoffs
Responder’s payoff
500
0
Proposer’s payoff
500