Geodesic
On Games with Constant Nash Sum
Contributions to game theory and management, Tome 4 (2011), pp. 294-310

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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. 
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     author = {Pierre von Mouche},
     title = {On {Games} with {Constant} {Nash} {Sum}},
     journal = {Contributions to game theory and management},
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     volume = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2011_4_a21/}
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Pierre von Mouche. On Games with Constant Nash Sum. Contributions to game theory and management, Tome 4 (2011), pp. 294-310. http://geodesic.mathdoc.fr/item/CGTM_2011_4_a21/