The Berge equilibrium concept formalizes mutual support among players motivated by the altruistic social value orientation in games. We prove some basic results for Berge equilibria and their relations to Nash equilibria, and we provide a straightforward method for finding Berge equilibria in n-player games. We explore some specific examples, and we explain how the Berge equilibrium provides a compelling model of cooperation in social dilemmas. We show that the Berge equilibrium also explains coordination in some common interest games and is partially successful in explaining the payoff dominance phenomenon, and we comment that the theory of team reasoning provides alternative solutions to these problems.

This paper examines the existence of Berge equilibrium. Colman et al. provide a theorem on the existence of this type of equilibrium in the paper [Colman, A. M., Körner, T. W., Musy, O. and Tazdaït, T. [2011] Mutual support in games: Some properties of Berge equilibria, J. Math. Psychol.55, 166–175]. This theorem has been demonstrated on the basis of a correspondence with Nash equilibrium. We propose to restate this theorem without using Nash equilibrium, and deduce a method for the computation of Berge equilibria.

In this paper, we study the dynamics of legal convergence and the comparison between the different instruments of legal convergence based on cooperative strategies (i.e., harmonization and unification) or not. To study these questions we use a model with two nation-states which is inspired in part by that used in Carbonara and Parisi (2008) where preferences of each nation-state are such that it is costly to change the law, but it is also costly to have a different legal system from the other nation-state. We show that legal unification could be achieved in the long-run through small step by step changes despite the existence of huge harmonization costs in the short run. We also show that legal cooperation is not always necessary to achieve legal convergence.

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In this paper, we consider a hierarchical oligopoly model, in which firms compete on quantities of an homogeneous product. We provide a proof and an interpretation that under the three necessary and sufficient conditions of linear aggregate demand, constant and identical marginal costs, the strategy of leaders at any stage depends neither on the number of leaders who play after nor on the number of remaining stages. So, all firms behave as Cournotian oligopolists on the residual demand. We show that these three assumptions are not only sufficient but also necessary. Any departure from any of these assumptions rules out this property