WP 1.13-3.2011.E
Game Theory – a Promising Tool for the Value Chain Analysis
Petr Budinský
Introduction
When we worked on a project for the Grant Agency of the Czech Republic, called Investing
into Social Capital and Effectiveness, specifically, when we investigated the relations in
development of social networks that influence the utilization and appreciation of human
capabilities, it turned out that it was necessary to use the game theory in order to answer many
of the associated questions. At the beginning of 2006 a redistribution system model was
gradually developed and formalized – as a tool to analyze various situations in the concerned
area - i.e. a system with deviations of payoffs from the performance of the players and, as a
result, also the decrease in the performance of the entire system. Since 2008 this issue has
been addressed in a project sponsored by the Grant Agency of the Czech Republic, called The
Theory of Redistribution Systems, which is one of the original directions in research of the
game theory. The results available up to now from the elaboration and application of the
theory of redistribution systems suggest that it may serve as a promising tool for the value
chains analysis.
The use of the concept of a redistribution system has exposed a number of significant
phenomena and relations, which make it possible to examine what is happening in companies,
including conflicts of interest that may arise. At the same time, it turned out that it was
necessary to investigate how the individual games (in the context of the game theory) were
mutually interrelated, i.e. we opened the issue of the so-called contextual games, i.e. games in
which the player realizes its relation to another game, and decides also based the parameters
of the latter. A research program was formulated which, among other things , seeks to reveal
why people behave in a particular manner, why people accept various roles and what are the
impacts on their personal characteristics, what remains hidden in their mutual relations and
even what is kept hidden intentionally.
Czech theoretical literature dealing with social or psychological aspects of management
mostly ignores the issue of formation of coalitions asserting redistribution in their favor and a
decrease of the performance of such a system as a result of such redistribution. Typical
examples of representative monographs published in the Czech Republic and intended for the
general public include e.g. (Bedrnová-Nový 2002), (Bělohlávek 2005), (Dědina - Cejthamr
2005), (Koubek 2001), (Mayerová - Růžička 2000), (Nakonečný 2004), (Nový - Surynek
2002), (Stýblo 2003), (Tureckiová 2004) etc., however, they fail to contain a single mention
of relations inside the managed systems that operate against the performance–based rewarding
and reduce effectiveness of organizations. Some positive exceptions include monographs by
Čakrt (2000, e.g. pages 31, 49-54 etc.), Barták (2006, pages 133-135) or Štědroň (2007, pages
29-30).
M. Čakrt mentions the game theory as a tool to analyze conflicts in managed organizations;
however, when presenting the issue, he prefers its description and generalization. In a way, it
is a pity because an application of the game theory would have made it possible for him to
look "under the hat“ of what was happening in this field. He could have analyzed relations
between the formation of coalitions inside companies, changes in coalition structures, role of
negotiation, forms of redistribution and types of conflicts. Let us look at an example provided
and analyzed by the author himself (and we could quote many more from his monograph):
"Let us imagine a dispute that has arisen in a certain company between the production and
sales departments. The issue was, what else, a shortage of financial means from the budget. A
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new product is to be launched on the market and, as it usually happens, the sources are not
bottomless. Either party is able to find "bullet-proof" reasons why it should get more than the
other party." (Čakrt 2000, page 31.)
We can see that the conflict arises from the effort to assert a certain type of redistribution,
while it is necessary to form coalitions for the purpose. This is the way it usually works
everywhere and every time in value chains. The theory of redistribution systems enables to
classify the arising situation, to provide an overview of all alternatives of the development, to
identify a suitable kind of arguments which may support the formation of a coalition capable
of solving the conflict based on improvement of the effectiveness.
Instead, M. Čakrt points out at the end: "It is a classical situation with a zero sum – any extras
I can get consist of what I can grab from the other party´s cake." (Čakrt 2000, page 31.) He is
slightly mistaken here. This is actually not a game with a zero sum. If the resources, i.e.
financial means, are not distributed between the production department and the sales
department in an optimum manner (an economist would say that limit proceeds from the
funds provided to both the departments must be equal) then the performance of the company
will decrease, which will harm both the people in both the departments - production and sales
alike.
One of the most interesting and most contributive parts of the monograph by M. Čakrt is
called The development of an inter-group conflict. (Čakrt 2000, pages 49-54). The very
subtitles in the chapter are worth the attention: "What is happening inside then groups ? And
what is happening between the groups? What is happening in the winners group? Even the
losers group goes through a certain development." Each of those subsections has 5-8 items
and some of them represent relatively accurate descriptions of standard situations arising in
redistribution systems.
M. Štědroň deals, among other things, with the so-called paranoid management, whose
principles he formulates as follows:
"- get rid of the best workers and, if this is not possible, do not provide them with the needed
information,
- assign extrovert activities to introverts and vice versa,
- never define clear priorities of a particular activity,
- do not formulate anything clearly and concisely,
- do not clearly define the content and sphere of competence of managers,
- do not surround yourselves with people who think out of the box and who have critical
thinking, as they may destabilize the workplace,
- when the situation requires that, maneuver at the edge of events." (Štědroň 2007, page 29.)
Moreover, the paranoid management needs to ensure the following:
"- intentionally create tension between work team members,
- atmosphere of worries and fear,
- elimination of all independently and critically thinking workers outside the limits of the
organization,
- regular decimation of the work teams." (Štědroň 2007, page 29-30.)
A “successful“ manager of this (paranoid) type needs to :
"- get rid of his/her responsibility,
- systematically belittle the work of experts." (Štědroň 2007, s. 30.)
Considering the possibility of formation of coalitions, their effects on redistribution inside
systems and the effect of redistribution against the output or performance lead to a model
which may seem very complicated at the first sight. However, once you formulate the
redistribution equation (see below) it turns out that the model can be very well analyzed with
the use of the original mathematical apparatus and that the results of the analysis provide
interesting findings that reflect reality and may be utilized in practice.
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The following text summarizes results obtained so far and formulates tasks that can and
should be performed in the nearest future, at the current degree of completion of the issue.
The tasks have been described with three mutually connected forms:
- Basic information about the issue.
- Commentary which in detail clarifies the meaning of terms and content of tasks, integrates
the tasks into a broader context and shows their relation to practical problems.
- Description of outputs which we are gradually obtaining, which may be expected and which
contribute both to the development of the theory and to its practical utilization in the value
chain analysis.
Thus the text provides details and particularly a comprehensive notion of what the team
operating at the University of Finance and Administration deals with and, at the same time, it
outlines potential areas of cooperation. It is original, not only when it comes to the list of the
tasks but also in respect to indication of the procedure to solve them. One of his goals is to
point to the theoretical context, which is used as a basis by other authors of contributions from
the University of Finance and Administration sent to the Conference Value Chain
Management to be held in May 2011, Upper Austria University of Applied Sciences, School
of Management Steyer.
1. Overview and characterization of tasks in the field of the theory of redistribution
systems
We have set the sequence of tasks so that it proceeds from the general to the specific. One of
the key tasks, on which a team operating at the University of Finance and Administration has
concentrated for a long period of time, is to express the process of negotiation in an
elementary redistribution system as a game in an explicit form and subsequently:
- to achieve a full theoretical interconnection of an intuitive concept of negotiation in the
system with the mentioned method of expression.
- to demonstrate a connection between the course of negotiations with various forms of the
redistribution equation.
We will explain the purpose of the task formulated above and its connection with the issue of
value chain analysis. The game theory may be used in the dispute about how much the
individual sections of the value chain should receive (see Čakrt 2000, as mentioned in the
Introduction section). One of the approaches usually used in this connection is the
determination of the Shapley value (Osbourne 2004), (Selten 1999). However, when using it,
we fail to take into account the conflict side of the process of determination of benefits and
the complicated negotiations that are usually conducted between the parties, and also the fact
that the developing coalitions may lead to discrimination of certain players and, last but not
least, also the fact that everything is connected with the overall performance of the system
(the company etc.). Therefore we have introduced the concept of the redistribution system so
that we can analyze events in organizations, institutions and companies, their organizational
units and in some institutions with the following features:
- People are associated in order to jointly perform a particular function, to jointly implement
activities in a certain area and with a certain objective.
- Each of the players (people) in the system needs to face the dilemma between the quantity of
his payoff (reward) and the gain of the whole system as a result of the performance.
- Negotiations and formation of coalitions occur in those systems (the coalitions that win
decisive influence may discriminate against the other players when it comes to the amount of
the payoff).
- The more payoffs of the players deviate from their performance the poorer is the
performance of the system.
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(It is obvious from the above-mentioned that the term “redistribution system“ is defined to
express essential characteristics of a very broad circle of social phenomena.)
The effect of a deviation of the payoff amount of a particular player from his/her performance
is expressed by the redistribution equation. The equation may have different forms defined by
the shape of the respective function and the coefficient of sensitivity. Special features and
characteristics of the redistribution function, redistribution area (maximum – in the sense of
the Paret rule – admissible distributions) and redistributions of the space defined by it, have
been relatively well analyzed for the case of three players. If we anticipate additional
simplification – i.e. not only that we have just three players but all of them have the same
power of influence, there are no limitations for the formation of coalitions etc., then we can
speak of an elementary redistribution system. In order to make the notion more specific we
will now add more parameters:
- the performance of the players is distributed in the ratio of small, easily comprehensible
numbers, e.g. 6:4:2.
- Each player has the same capability to influence the result (i.e. the power of influence equals
1).
- Each player shall get a minimum reward in the system, which in this case will be 1.
- The sensitivity of the system to a deviation from the actual payoff based on the performance
of the players (i.e. parameter η) shall be 0.5.
- The function of distance is defined and Euclidean metric, i.e. positive value of a square root
of the sum of squares of differences between the payoffs based on the performance of the
players and the actual payoffs.
The following shall apply for all permissible distributions:
x1 + x2 + x3 < E – η.R(x1 – e1; x2 – e2; x3 – e3)
(2)
or
x1 + x2 + x3 < 12 – 0,5.√[(x1 – 6)2+ (x2 – 4) 2+ (x3 – 2) 2])
(2a)
This means that permissible distributions are inside the redistribution area or below (so far we
only consider positive values of the payoffs), while inside the redistribution area there are all
points of the Paret optimum and every point inside the redistribution area is Paret-optimized
(i.e. any distribution of payoffs among players positively corresponds to a certain point on the
redistribution area.)
Figure No. 1: Redistribution area
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(Source: Budinský, Valenčík a kol. 2011)
Any two of the players may always improve their situation in comparison with any
distribution of payoffs, i.e. no coalition is stable. See Figure No. 2 (dark colored sectors show
the areas of points in which a certain pair of players receives higher payoffs):
Figure No. 2: Redistribution area with a marked area of improved payoffs
(Source: Budinský, Valenčík a kol. 2011)
Apart from the Euclidean metrics, other methods can be used to express deviations of the
actual payoffs from the performance of the players. The methods are as follows:
- Square of the Euclidean metric. The square can be obtained simply by leaving out the square
root. This metric is also easy to interpret and the initial relations are simpler:
R[(x-6); (y-4); (z-2)] = (x-6)2+(y-4)2+(z-2)2
(In this case, however, all the points inside the redistribution area are not Paret-optimized.)
- The Manhattan metric as a sum of absolute values of differences between performances and
payoffs of the individual players:
R[(x-6); (y-4); (z-2)] = |x-6|+|y-4|+|z-2|
- The Chebyshev metric, which selects from among differences between performances and
payoffs of the individual players the difference that belongs to the player with the biggest
difference:
R[(x-6); (y-4); (z-2)] = max [(x-6); (y-4); (z-2)]
The conclusions we get, even if the deviations are expressed with the various above-shown
methods, are very similar (a certain exception is the case of the square in the Euclidean
metric). In other words, it is not dependent on the specific form of the respective function.
The following conclusions follow from the performed analysis of the negotiation process: If
the players create fully discriminating coalitions and if the negotiations among the players are
governed by rules that are acceptable from the intuitive point of view, then the sequence of
payoffs of the players, based on coalitions agreed between any of the two players, converges
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to three points inside the redistribution area, while the set of such points is identical with a
single final internally and externally stable set (in the sense of the original definition by
Neumann – Morgenstern 1944).
We have called those three mentioned points discrimination balances. The fully
discriminating coalition of two players in a system of three players is the one in which the
player outside the coalition gets the smallest possible payoff. If we speak about intuitively
acceptable rules, we mean the following:
- each player proposes such a distribution of payoffs, which will improve his own position
and the position of one of the other players.
- the proposal is submitted to that player with whom the benefit for the proposing player is
higher.
- the proposal of his own payoff ranges from the highest payoff which may be obtained under
the given circumstances and the highest payoff the player could get if dealing with the third
player (i.e. with the player where the highest possible payoff is lower). See Figure No. 3.
Figure No. 3. Redistribution area with bargaining
(Source: Budinský, Valenčík a kol. 2011)
We expect that this analysis of the negotiation process in this system will provide us with
theoretical starting points to answer the question why people behave in a particular way or
what influences the behavior of people in real situations and how. Subsequently, it is
necessary to identify additional aspects we need to take into account in clarification of various
types of human behavior and the causes which influence various kinds of behavior.
By using the term “redistribution“ we express the fact that each condition of the system is a
result of a certain change (redistribution of payoffs) in comparison with the previous
condition. Those changes occur in the process of negotiation.
The analysis of the negotiation process is very demanding. If we want to create a model of
what is happening in the reality we need to consider the broadest possible circle of
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possibilities that are available to each of the players. Only subsequently it is possible to define
and to analyze various formalized negotiation models. The transition from an intuitive
concept of negotiations (which needs to be sufficiently broad so that it does not exclude or
overlook various possibilities in advance) to a formalized model, whose essential
characteristics need to correspond to reality, ranks among the type of tasks that can be only
resolved gradually. This means that there is no definite model but a sequence of models which
ever more completely represent the reality.
The desired outputs from the described method of examination are:
- Various negotiation models expressed as a formalized game in an explicit form, which may
be analyzed through mathematical means and which has a certain intuitively acceptable
interpretation.
- Identification of various types of strategies associated with a certain type of rationality of the
players. (“Interesting “ mathematically defined strategies are, as a rule, based on an intuitively
more acceptable concept of “rationality“ of the players.)
- The solution of the task to select the optimum strategies in a situation where we know the
type of rationality of the individual players.
Subsequently, after completing the tasks in the first direction of research, it is important (as
the second direction) to analyze conditions under which the system converges to a jointly
acceptable balance and to determine how the balance relates to the other forms of balance
(Nash, Kalai-Smorodinsky, Shaply value etc., that had been identified and defined in the
game theory):
- Particularly important is the relation between the Nash balance and the jointly acceptable
balance.
- It is necessary to make clear whether the Nash program may be implemented in the
elementary redistribution system or in its analogy (i.e. whether the Nash balance in the
respective non-cooperative game may be identical with the result of the Nash solution of the
corresponding non-cooperative game).
Let us try to clarify in detail the meaning of what was said above. When analyzing the process
of negotiation in the elementary redistribution system we identified and calculated values of
the so-called discrimination balance (the term introduced by us). The discrimination balance
can be calculated from the redistribution equation. Its values correspond to the situation in
which each of the players gains the same payoff as the other player with whom he forms a
discriminating coalition, in the case a coalition is formed that fully discriminates against one
of the players. The set of three points of discriminating balances is internally and externally
stable and it is the only discrete and final set inside the redistribution area that is internally
and externally stable. (The above-mentioned statement is based on mathematical evidence and
it is one of the most important results of the research in the given area up to now.)
Based the values of the discriminating balances it is possible to derive a jointly acceptable
balance. Two methods may be used to define it mathematically . From the intuitive viewpoint
it corresponds to the condition in which each of the players has a higher average payoff than
in the case when a discriminating balance is formed in the system and none of the players
knows whether he will be a member of the winning coalition or whether he will be
discriminated.
The outputs from this type of examination, which we are gradually obtaining, are in the form
of:
- Mathematical theorems and evidence (or mathematically formulated hypotheses) about the
relations of the individual types of balances and about calculation of the jointly acceptable
balance.
- Interpretation of the meaning of potential differences between individual types of balances
in the elementary redistribution system.
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The third direction of research is the generalization of the applied methods for the analysis of
systems with more players, or expanding of the analysis with additional aspects (incomplete
information provided to the players etc.).
As we have said, the elementary model has been developed for three players. In real systems
there are naturally more players involved. When analyzing such systems new elements
appear. E.g. , in a system of only four players it is much more complicated to imagine the
redistribution area which is in a four-dimensional space. Equally, there is not only rivalry
among the coalition players but also among those who seek to enter a coalition which will
take control of the system. Therefore the participation of more players brings new non-trivial
moments.
Systems with a high number of players need to be considered separately and tools need to be
identified to analyze them.
However, it is not only the number of players that matters. In an elementary system we
assume that all players are fully informed and have the same power of influence, that there are
no transaction costs for the formation of the coalition or in the process of negotiation, that all
is happening without time delays, that the system is closed and that it is impossible to leave it
or to enter it, that systems are not hierarchical and that there are no relations between them
etc. The expansion of the model in those directions may turn out as useful or even necessary
in many cases.
The desirable results of the respective direction of examining, that we are gradually obtaining,
are the following:
- definition of individual directions of expanding of the elementary redistribution system.
(Some directions of expansion are already known, some have not been identified yet – it is
necessary to characterize and to interpret what the respective expansion of the model may
bring.)
- development of a conceptual and, subsequently, mathematically expressed model of the
respective expansion.
- identification of new phenomena brought about by various directions of the model
expansion.
The last circle of problems associated with the analysis of the redistribution systems is the
issue of endogenous generation of the rules, i.e. how agreements are formed which are
beneficial to keep for all the players, while:
- using a model of endogenous generation of the rules to analyze institutions.
- showing how games associated with endogenous generation of the rules induce games based
on violation of the rules.
It is one of the most important tasks. If we want to create a model corresponding to reality
then we cannot assume that the rules are introduced from outside, i.e. that they have an
exogenous character. This is not only because the rules developed long time ago along with
the development of the system but particularly because that they may be and are violated by
certain players. Actually, the most important questions we ask are: when and how some
players may violate (any) rules and how the other players may prevent it (how to “keep“ the
rules stable). Consequently, however, the development of the model becomes much more
demanding than if we simply defined certain rules as inviolable and analyzed the behavior of
the players in the system under such conditions. It is one of the main reasons why the
development of the initial model (i.e. model of the elementary redistribution system) is so
complicated. It reflects the issue that can be, in an analogy with a similar scientific situation in
physics, described as the “absence of the place to stand on“, i.e. absence of something, we can
lean against.
From the methodic or methodological point of view it means e.g. that the model of players´
behavior (including their negotiation) cannot include any limitations whose violation would
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not be possible, as long as it brings any (at least immediate) advantage to some of the players.
(This is, among other things, also the reason why the development of a general model of
negotiation is so demanding.) And this is simply due to the fact that the purpose and the goal
of such a model is to identify the very moments of players behavior that will make it possible
to achieve an immediate advantage for them by violating some of the limitations.
This is associated with the related approach to the analysis of institutions. If we want to see
(through a prism of theory) what is particularly important in real systems then we cannot use
the “crutch “ of looking at institutions only as at something what enables to follow the rules of
the game. We need to understand them, to analyze them and to express them as a result of the
games, as something that is generated in the games and, consequently, as something which –
as soon as it was formed – not only enters the game but becomes a target of various games.
Simply speaking – it is necessary to show (and to analyze) how “games without rules “
transform into games with rules, which however may be violated, but with the risk of
potential sanctions.
The expected and desirable outputs from the respective directions are:
- development of a model with indicates how “games without rules“ transform into “games
with rules“ (i.e. it is advantageous for the players to follow the rules under certain conditions).
- development of a model of related (contextual ) games (see the following item), which
describes the issue of violation of the rules.
- show the benefits of the above-described approach to the traditional issue of formation and
development of institutions.
- application of the acquired findings to the development of codes of conduct for company
employees, partner networks, customer relations etc.
2. Overview and characterization of tasks in the field of theory of contextual games
We have encountered the issue of contextual games (the term introduced by us) on two
occasions:
- When we analyzed situations which were considered an example of discrepancy between
how people should behave in theory and how they behave in reality: A superficial
interpretation of those seeming discrepancies is used to clearly demonstrate that people
behave irrationally, in conflict with the theory and that the theory can hardly say anything
about the real human behavior. The examples to demonstrate this include games, in which
two players are asked to divide a particular amount between them (one proposes the division
and the other has to agree or else he gets nothing) or game situations based on the prisoner´s
dilemma (including cases in which one of the players may have additional information about
how the other player behaved ). The analysis and interpretation performed by us, with the
application of the model of contextual games, have shown that the seeming discrepancies
between the theory and reality may be relatively easily and conclusively explained, without
violating the assumption that players act in a rational manner.
- When we analyzed situations in which players concluded an agreement which was
advantageous for all the involved parties (e.g. in the case that they negotiates a jointly
acceptable balance): After conclusion of any agreement subsequent games appear which are
associated with the possibility of violation of the rules in order to get an advantage at the
expense of those who observe the agreement. The mutual connection between the original and
subsequent games is a typical example of a contextual game.
Moreover, it has turned out that both the cases that initiated the introduction of the concept of
a contextual game and the development of the apparatus that is based on it, are mutually very
closely connected. For the sake of completeness we should add that a contextual game means
that two or more games are mutually (in different ways) connected to each other, while the
behavior of players in one game is influenced by the concurrent playing of another game.
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Every real game (or when in a real situation a certain game comes “to the surface” in form of
a recognizable and citable model ) can be understood as a big quantity of most diverse and
mutually interacting games. Naturally, the questions will arise about how such individual
games are related (what type of relations may be identified) and what apparatus can be
developed and used for their analysis.
Let us present an example of one type of contextual games. During experiments examining
human behavior in situation games of the prisoner´s dilemma type a significant conflict has
been found between the theory and real behavior of people. In the prisoner´s dilemma both
the players have two options – to cooperate or to betray. The egoistic option of betrayal
results in a higher gain than cooperation, as long as the other player was willing to cooperate,
but it results in a lower gain, as long as he also betrayed. The rational behavior of the two
prisoners is to turn in the accomplice, although the optimum solution for both is to keep quiet.
The result, when the betrayal is the right decision, has lead to many discussions and attempts
for explanation. Also several broadly published experiments have been performed. Let us see
the names of persons who conducted the experiments and their respective years (see also the
list of sources):
Shafir, Tversky (1992)
97
84
63
Li, Taplan
(2002)
83
66
60
Busemeyer
(2006)
91
84
66
The numbers in the individual columns represent percentage of "betrayals", i.e. cases in which
the respective player, who had a guaranteed information that the other player did betray (the
first column) or did not betray (the second column) or was not informed about the decision of
the other player (the third column, which is the true case of the prisoner´s dilemma), chose the
non-cooperative strategy. Additional experiments have shown that the willingness to betray or
to cooperate is, to a big extent, influenced by the size of the award (punishment).
Now we will see in detail the difference between how the players (i.e. specific people ) should
"theoretically" behave and how they behave “in real life ":
1. If we do not know the decision of the other person then we should always betray (and not
only in 60-66 % cases of non-cooperative behavior).
2. If we know that the other person has betrayed us we should again betray as well (and not
only in 83-97 % cases of non-cooperative behavior).
3. If we know that the other person is cooperating then we have no reason to betray (and why
even in 66-84 % cases)? (For accuracy reasons we should add that this is not only a
discrepancy between the theory and experiment but – at least at the first sight – a flagrant
conflict between the two cases tested by the experiment.)
So how can we explain the “irrational“ behavior ( if it truly is irrational)? We need to consider
the contextual nature of the game. In reality it only rarely occurs that a game of the prisoner´s
dilemma type appears unrepeatedly and in isolation from other games. Mostly, the course of
the games and the way the individual players decide are seen or potentially seen by other
people (who we can view as players in other games) and based on the obtained information
they create their relations to the players of the concerned game.
Every game that we play in real life can be considered a contextual game , i.e. a game we play
in the context of other games. We introduce the concept of a contextual game as an original
term. Theoretical literature contains only some outlines of some starting points we are
working with, see e.g. Meliers – Birnabou (1981). It is, however, only a partial view without
an apparatus enabling to analyze the phenomenon of contextual games.
Our decision-making in real games is significantly conditional upon how we reflect the
contextual games. The reflection of contextual games as such is substantially conditional on
our experience and our “melting“ of the experience into “on-line“ mechanisms of our (human)
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decision-making, which is strongly influenced by imagination, emotions and other mental
attributes. Let us show how a game of the prisoner´s dilemma changes if we see it as a game
played in a context of other games.
Tab. 1: Payoff matrix of the games of the prisoner´s dilemma type on an example of
observation or non-observation of an agreement
X1
observes
the agreement
observes the agreement
X1
does not observe the agreement
does not observe
the agreement
6; 6
0; 8
8; 0
3; 3
Source: Our own product commonly used to explain games of the prisoner´s dilemma type
X1, X2 are players with two strategies – to observe or not to observe the agreement (to violate
the agreed or recognized rules). The matrix contains their payoffs. Now let us assume that
from the viewpoint of one of the players (e.g. X1) the game has a certain context, or it is
played as a contextual game in the sense that the community in which the player lives may (or
may not) be informed about the result. If the player observes the agreement and the other
players in the given community will find out about it then it will contribute to an increase of
his credibility capital (reputation). If he does not observe the agreement and the other players
in the community find out about it then his credibility capital (reputation) decreases. Further,
let us assume that the credibility capital (reputation) may be (at least approximately) appraised
in units in which payoffs from games of the prisoner´s dilemma type are realized and that the
respective player also appraises them. For example, the loss in cases of non-observation of the
agreement is appraised by the player with -3 points and the gain in the case of observation
with +2 point ( the credibility is lost faster than gained). The following table shows how the
situation changes.
Tab. 2: Payoff matrix of games of the prisoner´s dilemma type with regard to the role of the
credibility capital (reputation)
X2
observes
the agreement
does not observe
the agreement
observes the agreement
6+2; 6+2
0+2; 8-6
does not observe the agreement
8-6; 0+2
3-3; 3-3
X1
Source: Our own product developed by the team, for the first time presented by ŠnajdarValenčík (2010)
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We can see that the situation has changed dramatically. It is worthwhile to cooperate for both
the players. However, only in case that the original payoff and payoffs associated with the
gain or loss of credibility capital (reputation) have specific values. For different values the
situation may be different.
The initial task in the area of analysis of contextual games is to elaborate a list of individual
types of relations and transitions between various games, and for this purpose:
- to develop an apparatus which would enable to analyze some cases
- to concentrate on the connection between redistribution games and other cases of games.
- to verify conclusions from the theoretical analysis by means of experiments with groups of
persons (with a link to available results of similar experiments).
- to express the seeming “irrationality“ of the players as a result of influence of contextual
games and to experimentally verify hypotheses formulated on this basis.
It is important to know which contextual games are being played and how the individual
players identify them, in order to understand psychological aspects of behavior of the players.
The desirable outputs from the respective direction, from which some are already available,
include:
- typology (and potentially a complete well-structured list) of links between games , i.e. how
the individual games are linked to each other.
- formulation and solution of mathematical tasks consisting in expansion of one game of a
certain type with a contextual game of another type.
- performance of original experiments that verify an explanatory role of the contextual games
models.
- analysis of the relation between weights assigned by the players to the parameters of
contextual games and their anticipated experience with contextual games (influences
exercised by the contextual games ). (This is one of the important moments which enable to
get an insight into complex regularities of human mind by means of the game theory).
- development of a model of a game associated with the formation and application of
structures based on mutual cover-up of violation of rules (for more information about this
concept see below) as one of the specific cases of contextual games.
By using the starting points obtained from the theory of redistribution systems and contextual
games it is important to analyze the process of real negotiations in order to:
- identify and systematically classify (by means of a complete well-structured list) the most
important types of arguments used in real negotiations.
- to discern, in particular, that type of arguments which are associated with the influences that
can be compensated by concessions in the distribution of payoffs and with the influences that
cannot be compensated (and which enter the redistribution system as a certain contextual
game).
- to register the relation between obvious and direct arguments on one side and indirect and
hidden arguments on the other side, as they are used by the individual players in various (for
them convenient ) contexts , while the other players not always realize that they are
negotiating about coalitions and distribution of payoffs.
- from this viewpoint a relation was presented between arguments used in a real process of
negotiation and its results.
It is a significant step from formalized or mathematically expressed reality to practically
usable findings, concepts and recommendations. In every system, in which people associate to
jointly implement a certain performance and which has the attributes of a redistribution
system, the common communication includes negotiations about formation of coalitions and
distribution of payoffs. A general theoretical model makes it possible to see (to identify) what
is not obvious at the first sight and, at the same time, to classify forms of argumentation based
on various viewpoints. Particularly the following is important in this respect:
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- to discern negotiations about formation of coalitions and distribution of payoffs in the
respective coalitions.
- to discern situations in which the composition of coalitions may be changed (a player
outside the coalition underbids the size of his payoffs to the players who form the coalition)
from situations in which the underbidding by a certain player in the distribution of payoffs
does not lead to a change in the coalition (the player remains excluded from the coalition).
- the above-mentioned allows to discern between influences that can be compensated by a
concession of a particular player and those that cannot be compensated (then it is important to
identify which influences cannot be compensated and what is the mechanism of their
operation).
- Arguments that occur in usual communication may explicitly disclose the goal of their use,
however, more frequently the goal remains hidden – a resolution between the two forms of
argumentation is important from a practical point of view.
“Mapping“ the arguments from the viewpoint of their identification and sorting of their
individual types has an important dimension of empiric research. It is possible to effectively
use the well-proven method of a complete, well-structured list.
It is expected that a research conducted in this direction will provide a morphological
description of arguments of the most diverse type, specifically:
- classification of the respective argument.
- its characterization and method of identification.
- method of practical utilization .
(If we look at the type of argumentation through a prism of a formalized description of the
negotiation process then we can see much better what is happening when we use this type of
argumentation, what the expected goals of the use are and the reasons behind the used
argumentation method; this has a particularly important role in management of various critical
situations in companies and also on other occasions, such as the assessment of workers etc.)
The analysis of redistribution and contextual games enables to derive definitions of:
- parallel redistribution games
- structures based on mutual cover-up of violation of rules
- cross-coalitions (i.e. coalitions between various redistribution systems) and social networks
derived from them.
Three phenomena have been identified, when we tried to identify what predetermines
formation of discriminating coalitions , with the following characteristics:
- Parallel games are games played in the redistribution system. They are played only by a part
of the players and only a part of the players is informed about them. The means distributed by
players in this game are obtained either a) from the environment of the given redistribution
system and they reduce performance of the redistribution system, of which the given
redistribution system is a part of , or b) they are drawn from the given redistribution system
and they reduce its performance.
In parallel redistribution games the individual players have their specific roles which
significantly determine their subjective characteristics. With a certain exaggeration we can
say that parallel games “choose “ their players and imprint in them their personal
characteristics. The application of the model of parallel redistribution games makes it possible
to recognize the individual types of players and subsequently to identify them in real-life
situations. (For details see Havlíček-Valenčík 2010.)
- Structures based on mutual cover-up of violation of rules and generally accepted principles
(hereinafter “structures based on mutual cover-up “) are something like a “mirror reflection“
of gaining of credibility capital. A player who finds out that another player is violating the
rules has two options (strategies) – he can either spread the respective information and this is
followed by sanctions against the player in breach or he can use the respective information to
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his advantage and make the player in breach do something which will enable to him (i.e. to
the player who exposed the violation of the rules) to violate the rules as well. This results in a
formation of structures based on mutual cover-up which compete in the respective social
environment or which are governed by rules similar to the natural selection. The surviving
ones become very resistant, their structure is branched and they can penetrate all institutional
structures created to expose and sanction violation of rules.
- Cross-coalitions are coalitions between various redistribution systems. They are able to
predetermine formation of coalitions inside them and to create branched social networks,
penetrating the most diverse redistribution systems, both at the same hierarchic level and at
lower and higher levels of the respective hierarchical redistribution system.
At present, there are various models of individual types of the above-described phenomena.
Those models are at a level of the conceptual nature. It is necessary to improve the respective
models, to accurately discern between individual types of games we encounter within those
types, to interconnect the formalized and mathematical expressions of the respective
phenomena with mathematical models of the negotiation process. The tools to analyze
structures based on mutual cover–up of violation of rules and generally accepted habits are
important particularly because the formation and operation of the above-mentioned structures
in a company represents the biggest danger for its existence.
Based on the above said it is possible to analyze mutual relations and transitions between
parallel redistribution games, structures based on mutual cover-up of violation of rules, crosscoalitions and resulting social networks. For this purpose it is essential:
- to discern types of players, their roles and influence of such roles on the minds of such
players in parallel redistribution games, structures based on mutual cover-up of violation of
rules, cross- coalitions and resulting social networks.
- to develop an illustrative model (with several layers of understanding the “real issue“),
which may help to read what is not usually visible and what remains hidden.
- to focus on identification of the basis of stability of parallel redistribution games, structures
based on mutual cover-up of violation of rules, cross-coalitions and resulting social networks ,
and to use the basis to formulate options or strategies that may be used when the stability is
disturbed, as well as preconditions necessary to utilize such options or strategies.
Everything suggests that all the three phenomena (i.e. parallel redistribution games, crosscoalitions consisting of players operating in various redistribution systems and structures
based on mutual cover-up) are interrelated or even that it may be a single phenomenon ,
which has the three described forms, based on the angle from which we look at it. For
example in the following sense:
- Parallel games are a source of means to create structures based on mutual cover-up and for
formation of cross- coalitions.
- Structures based on mutual cover-up of violation of rules are a necessary precondition for a
given parallel game to exist in a certain system, in order to meet the assumption of different
information provided to players in the respective redistribution system.
- Cross- coalitions ensure stability of parallel redistribution games and structures based on
mutual cover-up by the fact that they predetermine formation of coalitions in individual
redistribution systems, which occur in specific mutual relations and form a specific
hierarchical structure.
There are probably more connections between the above-mentioned phenomena and they will
be the subject matter of a further analysis. An important part of such an analysis is to discern
individual types of players and their roles. The above-mentioned implicates another aspect of
importance of the redistribution systems theory. It analyzes what is “visible “ or what all the
players are informed about. On the contrary, parallel games, structures based on mutual
cover-up and cross-coalitions between redistribution systems are something that may exist
14
only thanks to a limited information available to some players, i.e. based on the fact that those
phenomena are “not visible “. In this respect the redistribution systems theory enables to
analyze things that are “not visible” (i.e. things about which players using the theory are not
informed) based on things that are “visible “ (things about which all players are informed).
This has a critical importance for managers working in areas affected by various relations and
interests, which is typical for value chain management.
The desired and continually achieved outputs of the examination in this direction are:
- description and analysis of mutual connections between parallel redistribution games,
structures based on mutual cover-up and cross-coalitions.
- Identification of structures of the mentioned phenomena from the viewpoint of hierarchic
organization of sophisticated redistribution systems. (It is possible to assume that some
significant phenomena occurring in practice are associated with this very hierarchic structure.)
- Identification of structures of the mentioned phenomena from the viewpoint of formation of
institutional structures of sophisticated redistribution systems. (Also here it is possible to
assume that some significant social phenomena are associated with the very “attack” against
institutional structures by some of the phenomena described above.)
- Description of roles into which the players are selected or situated in the process of parallel
redistribution games, formation of structures based on mutual cover-up and formation of
cross-coalitions and mechanisms which are employed to select them and which imprint the
players with certain psychological and personal characteristics. (They include, among others,
the fact that a player engaged in a certain parallel game, in structures based on mutual coverup or in a cross- coalition, or a player connected to a certain social network derived from the
cross-coalition, gains certain advantages when it comes to distribution of payoffs and to
achieving of a certain position. However, this is at the expense of affecting his/her human,
mental, personal etc. characteristics. Any complex redistribution game associated with the
above-mentioned phenomena always finds “its“ player of its particular type because in every
system there is a competition among players who may be considered suitable for the role.)
- Exposing the role of replicators in finalization of personal characteristics of the players who
enter the parallel redistribution games, participate in formation of structures based on mutual
cover-up and formation of cross- coalitions.
Conclusions
It may appear that the outline of the research program is too ambitious to be fully or
successfully implemented. It is true that its implementation requires an extremely high
number of various activities to complete the task. There are many ways that may or have to be
followed and many possibilities that may and need to be tried. Still, not all of them will lead
to the goal. The experience from the preceding procedure has shown that similar rules apply
here as in development of any theoretical concept. Specifically, that every step results in
many more questions ( and thus results in a certain scientific skepticism about whether the
goal can be achieved) but, at the same time, casts a new light on what has been already done.
Any step usually makes the situation a little bit better understandable and simpler. It reveals
better the purpose of what has been completed and relations between various directions of
research. If this situation continues we can presume that we are going in the right direction.
Contours of what can be achieved in the future are still far away, which may serve as the
evidence of the good prospects of the described program.
You can follow the progress of work performed by the team dealing with this issue in a ongoing theoretical seminar www.vsfs.cz/?id=1111. The website continually publishes, among
other things , input materials (in form of presentations and progress reports) from weekly
meetings since the beginning of works on the given topic.
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