A model for coopetitive games

Handbook of Utility Theory, 2004

Cooperative game theory begins with descriptions of coalitional behavior. For every permissible coalition, a subset of the players of the game, there is a given set of feasible outcomes for its members. Each outcome is presupposed to arise from cooperative behavior by the members of the coalition; specific individual actions are secondary. Cooperative games take several forms—games with side payments, games without side payments, partition function form games, and others, including, for example, bargaining games. In this paper we focus on games with and without side payments. Cooperative game theory has two parts. One part is the description of game situations, the form or model of the game, and the other part is the description of expected outcomes. The second part is called solution theory. Utility theory is foundational to both parts. Utility theory for a solution theory, however, may involve additional assumptions, sometimes hidden. Therefore the utility theory behind the description of a game situation may not be the same as that behind a solution concept applied to the game. In this chapter, in addition to exploring various models of games, we will consider the assumptions behind various solution concepts. The predominant forms of cooperative games are games with side payments and games without side payments. A game with side payments summarizes the possible outcomes to a coalition by one real number, the total payoff achievable by the coalition. In contrast, a game without side payments describes the possibilities open to a coalition by a set of outcomes, where each outcome states the payoff to each player in the coalition. The concepts of games with and without side payments are not disjoint; a game with side payments can be described as a game without side payments. Because of the simplicity of a game with side payments, cooperative game theory has been more extensively developed for games with side payments than for games without side payments. Because of this simplicity, however, games with side payments require special consideration of the underlying utility theory.

2009

We propose a bargaining process supergame over the strategies to play in a non-cooperative game. The agreement reached by players at the end of the bargaining process is the strategy profile that they will play in the original non-cooperative game. We analyze the subgame perfect equilibria of this supergame, and its implications on the original game. We discuss existence, uniqueness, and efficiency of the agreement reachable through this bargaining process. We illustrate the consequences of applying such a process to several common two-player non-cooperative games: the Prisoner's Dilemma, the Hawk-Dove Game, the Trust Game, and the Ultimatum Game. In each of them, the proposed bargaining process gives rise to Pareto-efficient agreements that are typically different from the Nash equilibrium of the original games.

In the paper a game-theoretical model is set up to describe the conflict situation in which the members of a marketing cooperative may take advantage of an external market price, higher than that offered by the cooperative. Under appropriate conditions on the penalty strategy of the cooperative, the faithfulness of all members will provide a Nash equilibrium for the considered game, which at the same time also is an attractive solution, with the cooperative as a distinguished player.

1992

In this note we challenge the non-cooperative foundations of cooperative bargaining solutions on the grounds that the limit operation for approaching a frictionless world is not robusto We show that when discounting almost ceases to play a role, any individually rational payoff can be supported by some subgame perfect equilibrium. To seLect the "correct" point imposes excessive informationaL requirements on the anaLyst.

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions-or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure.

2012

An oligopoly is a market where a couple of large producers supply some goods. If the oligopoly is collusive, the producers form coalitions. Then, within each of the coalitions, the producers wish to divide their total profit among themselves. They could use a cooperative transferable utility game solution concept, such as the core, if the game were in the coalitional form. This, however, is not the case. In this paper, we propose an approach to overcome that difficulty: converting the collusive oligopoly into the partition function form, we show how the known cooperative game solution concepts (core, bargaining set) can be applied to that game. Actually, the proposed approach is suitable not only for a collusive oligopoly, but, under some assumptions, for any cooperative strategic form game.

2012

In the present work we propose an original analytical model of coopetitive game. We shall apply this analytical model of coopetition (based on normal form game theory) to the Greek crisis, while conceiving this game theory model at a macro level. We construct two realizations of such model, trying to represent possible realistic macroeconomic scenarios of the Germany-Greek strategic interaction. We shall suggest -after a deep and complete study of the two samples -feasible transferable utility solutions in a properly coopetitive perspective for the divergent interests which drive the economic policies in the euro area. * Section 2 of this paper has been written by D. Schilirò while sections from 3 to 7 are due to D. Carfì, however, in strict joint cooperation. Abstract, introduction and conclusions were written by both authors, together.

Discussion Papers in Economic Behaviour, 2011

A value for games with a coalition structure is introduced, where the rules guiding the cooperation among the members of the same coalition are di¤erent from the interaction rules among coalitions. In particular, players inside a coalition exhibit a greater degree of solidarity than they are willing to use with players outside their coalition. The Shapley value [Shapley, 1953] is therefore used to compute the aggregate payo¤s of the coalitions, and the Solidarity value [Nowak and Radzik, 1994] to obtain the payo¤s of the players inside each coalition.

2008

This is the first draft of the entry “Game Theory” to appear in the Sage Handbook of the Philosophy of Social Science (edited by Ian Jarvie & Jesús Zamora Bonilla), Part III, Chapter 16.