This article is cited in 1 paper

On Games with Constant Nash Sum

Pierre von Mouche

Wageningen Universiteit, Hollandseweg 1, 6700 EW, Wageningen, The Netherlands

Abstract: A class of games in strategic form with the following property is identified: for every $\mathbf{n} \in E$, i.e. Nash equilibrium, the (Nash) sum $\sum_l n^l$ is constant. For such a game sufficient conditions for $E$ to be polyhedral and semi-uniqueness (i.e. $\# E \leq 1$) are given. The abstract results are illustrated by applying them to a class of games that covers various types of Cournot oligopoly and transboundary pollution games. The way of obtaining the results is by analysing so-called left and right marginal reductions.

Keywords: Oligopoly, transboundary pollution, Hahn conditions, aggregative game, co-strategy mapping, marginal reduction, non-differentiable payoff function, structure of set of Nash equilibria, game in strategic form, convex analysis.

Language: English