Common Pool Games are Convex Games

Meinhardt, Holger Ingmar

doi:10.1111/1097-3923.00011

Cited by 17 publications

(21 citation statements)

References 4 publications

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“…In addition, concentrating on stylized cooperative bargaining arguments offers some insight into how agreement points can be stabilized. Theoretical results from cooperative game theory that foster the hypothesis -obtained from field studies -that the commons can be successfully managed by selfish individuals have been provided by [7,8,9], and by [22,23].…”

Section: Commons Dilemma Situation and Gamesmentioning

confidence: 87%

“…The rich players coalition can guarantee to itself a payoff of 400 units, that is, its coalition value, in contrast to a payoff of 392 units, which it can obtain if their members would accept the egalitarian division (cf. Table 4.1 which is taken from [22]). …”

Section: Example (Hsw1)mentioning

confidence: 99%

“…But for common dilemma games, the core can be expected to be large. This can be derived from the convexity property of such games, proven by [22].…”

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confidence: 99%

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Non-binding agreements and fairness in commons dilemma games

Ostmann

Meinhardt

2007

cent.eur.j.oper.res.

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Usually, common pool games are analyzed without taking into account the cooperative features of the game, even when communication and non-binding agreements are involved. Whereas equilibria are inefficient, negotiations may induce some cooperation and may enhance efficiency. In the paper, we propose to use tools of cooperative game theory to advance the understanding of results in dilemma situations that allow for communication. By doing so, we present a short review of earlier experimental evidence given by Hackett, Schlager, and Walker 1994 (HSW) for the conditional stability of non-binding agreements established in face-to-face multilateral negotiations. For an experimental test, we reanalyze the HSW data set in a game-theoretical analysis of cooperative versions of social dilemma games. The results of cooperative game theory that are most important for the application are explained and interpreted with respect to their meaning for negotiation behavior. Then, theorems are discussed that cooperative social dilemma games are clear (alpha-and beta-values coincide) and that they are convex (it follows that the core is "large"): The main focus is on how arguments of power and fairness can be based on the structure of the game. A second item is how fairness and stability properties of a negotiated (non-binding) agreement can be judged. The use of cheap talk in evaluating experiments reveals that besides the relation of non-cooperative and cooperative solutions, say of equilibria and core, the relation of alpha-, beta-and gamma-values are of importance for the availability of attractive solutions and the stability of the such agreements. In the special case of the HSW scenario, the game shows properties favorable for stable and efficient solutions. Nevertheless, the realized agreements are less efficient than expected. The realized (and stable) agreements can be located between the equilibrium, the egalitarian solution and some fairness solutions. In order to represent the extent to which the subjects obey efficiency and fairness, we present and discuss patterns of the corresponding excess vectors.

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Section: Commons Dilemma Situation and Gamesmentioning

confidence: 87%

Section: Example (Hsw1)mentioning

confidence: 99%

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Non-binding agreements and fairness in commons dilemma games

Ostmann

Meinhardt

2007

cent.eur.j.oper.res.

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“…The issue of coalition formation in common-pool resources in the absence of conflict for control has been explored by Funaki and Yamato (1999) and Meinhardt (1999). If players can communicate, they can form groups in order to exploit the common.…”

Section: Related Literaturementioning

confidence: 99%

Rivalry, Exclusion, and Coalitions

Sánchez‐Pagés

2007

J Public Economic Theory

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We analyze a situation where individuals and coalitions can obtain effective property rights over a resource by means of an exclusion contest. Coalitions face a trade-off when they decide to incorporate new members: Big groups control the resource more likely but individual property rights are more diluted. Under cooperative explotation of the resource the grand coalition is the efficient partition. It is also stable if players are committed to minimize deviators' payoffs. This is not the case when players play best responses and the conflict technology is sufficently effective with respect to the concavity of the production function: Then there is a strong tendency towards bi-partisan conflicts. Moreover, under non-cooperative exploitation of the resource, conflict may be socially efficient and Pareto dominate free access.JEL classification codes: C71, D62, D74

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“…For that purpose, the partition function form (or coalition structure) approach was treated in [3], which deals with the non-cooperative game solution (i.e., Nash equilibrium for a suitably chosen game in normal form) as well as the cooperative game solution (i.e., (non)existence of core allocations for two types of appropriately chosen cooperative TU-games). In this paper we deal with a fully cooperative game theoretic approach to the common pool situation, following the overall treatment in [6], [7], [8]. Our treatment is fully based on the so-called common pool cooperative TU-game, which arises directly from the underlying normal form game by applying the standard maxmin-technique.…”

Section: Introductionmentioning

confidence: 99%

(Average-) Convexity of Common Pool and Oligopoly Tu-Games

Driessen

Meinhardt

2001

Int. Game Theory Rev.

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The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the relevant cost function is a linear function, then the common pool games are convex games. The convexity, however, fails whenever cost functions are arbitrary. We present sufficient conditions involving the cost functions (like weakly decreasing marginal costs as well as weakly decreasing average costs) and the average joint production function in order to guarantee the convexity of the common pool game. A similar approach is effective to investigate a relaxation of the convexity property known as the average-convexity property for a cooperative game. An example illustrates that oligopoly games are a special case of common pool games whenever the average joint production function represents an inverse demand function.

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Common Pool Games are Convex Games

Cited by 17 publications

References 4 publications

Non-binding agreements and fairness in commons dilemma games

Non-binding agreements and fairness in commons dilemma games

Rivalry, Exclusion, and Coalitions

(Average-) Convexity of Common Pool and Oligopoly Tu-Games

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