Convexity of oligopoly games without transferable technologies

Driessen, Theo; Meinhardt, Holger Ingmar

doi:10.1016/j.mathsocsci.2005.01.003

Cited by 18 publications

(11 citation statements)

References 10 publications

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“…For the class of oligopoly TU-games, this assumption seems more appropriate than the standard assumption for which those external agents act to minimize the coalitional profit and used to define the β-characteristic function. Oligopoly TU-games in β-characteristic function form were studied, among others, by Zhao (1999a,b), Norde et al (2002), Driessen and Meinhardt (2005). Unsurprisingly, the γ-core is included in the β-core.…”

Section: Discussionmentioning

confidence: 99%

“…Concerning oligopoly TU-games without transferable technologies, Zhao (1999b) proves that the β-core is non-empty if every individual profit function is continuous and concave. 2 Furthermore, Norde et al (2002) show that these games are convex in case the inverse demand function and cost functions are linear, and Driessen and Meinhardt (2005) provide economically meaningful sufficient conditions to guarantee the convexity property in a more general case.…”

Section: Introductionmentioning

confidence: 99%

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The γ-core in Cournot oligopoly TU-games with capacity constraints

Lardon

2011

Theory Decis

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In cooperative Cournot oligopoly games, it is known that the β-core is equal to the α-core, and both are non-empty if every individual profit function is continuous and concave (Zhao 1999b). Following Chander and Tulkens (1997), we assume that firms react to a deviating coalition by choosing individual best reply strategies. We deal with the problem of the non-emptiness of the induced core, the γ-core, by two different approaches. The first establishes that the associated Cournot oligopoly TU(Transferable Utility)-games are balanced if the inverse demand function is differentiable and every individual profit function is continuous and concave on the set of strategy profiles, which is a step forward beyond Zhao's core existence result for this class of games. The second approach, restricted to the class of Cournot oligopoly TU-games with linear cost functions, provides a single-valued allocation rule in the γ-core called NP(Nash Pro rata)-value. This result generalizes Funaki and Yamato's core existence result (1999) from no capacity constraint to asymmetric capacity constraints. Moreover, we provide an axiomatic characterization of this solution by means of four properties: efficiency, null firm, monotonicity and non-cooperative fairness.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The γ-core in Cournot oligopoly TU-games with capacity constraints

Lardon

2011

Theory Decis

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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: 91%

“…In this case, we observe a strong incentive to merge economic activities into a cartel or monopoly ([cf. 8,9]). …”

Section: Theorem 41 ([22]) Common Pool Games Are Convex Gamesmentioning

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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Toward an Analysis of Cooperation and Fairness That Includes Concepts of Cooperative Game Theory

Ostmann

Meinhardt

2008

New Issues and Paradigms in Research on Social Dilemmas

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Convexity of oligopoly games without transferable technologies

Cited by 18 publications

References 10 publications

The γ-core in Cournot oligopoly TU-games with capacity constraints

The γ-core in Cournot oligopoly TU-games with capacity constraints

Non-binding agreements and fairness in commons dilemma games

Toward an Analysis of Cooperation and Fairness That Includes Concepts of Cooperative Game Theory

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