Conflict and Cooperation in Symmetric Potential Games

Abstract

In this paper we consider a special class of n-person potential games and investigate partial cooperation between a portion of the players that sign a cooperative agreement. Existence results of partial cooperative equilibria are obtained and some possible applications are discussed, particularly a Cournot oligopoly and an international water resources management model.

Vector Games with Potential Function

“…Furthermore, these have interesting applications in real life: e.g., network models, environment problems and telecommunication models. For application in the scalar case, see: [6,11,22].…”

“…(6) Some applications to network and telecommunication problems and environmental models could be investigated via potential games ( [6,11]). …”

“…In [11], potential games were applied to environmental problems where the cooperation among players is partial. To reduce pollution, not all the countries agree and therefore a partial cooperative game arises.…”

Partial Cooperative Equilibria: Existence and Characterization

“…All these examples share a joint cooperate/compete feature that has a long and checkered history within the framework of non-cooperative games. In this literature, it is assumed that coalitions are given, and each coalition, rather than maximizing its individual payoff, maximizes a group payoff function, which can range from a simple sum of individual payoff functions (Mallozzi and Tijs [1][2][3]) to a vector valued function choosing points on the Pareto frontier of the individual payoffs of the members of the coalition (Ray and Vohra [4], Ray [5]). In order to allow for payoff transfers among the players, we choose the sum of payoffs as the cooperators's objective function rather than a point in the Pareto frontier.…”

“…Two such focal equilibria are the one that is best from the point of view of the coalition, that is maximizes its group payoff function (the coalition is optimistic in its mental outlook) and the other is the worst Nash equilibrium, namely it minimizes the coalition's group payoff function (the coalition is pessimistic or risk averse in this mental outlook). These ideas have been explored in Mallozzi and Tijs [1][2][3] and Chakrabarti et al [6]. Other articles that have similar themes are Barrett [15], D'Aspremont et al [16] and Diamantoudi and Sartzetakis [17].…”