Games of love and hate - Debraj Ray; Rajiv Vohra (Brown University, Department of Economics, 2018)
A game of love and hate is one in which a player's payoff is a function of her own action and the payoffs of other players. For each action profile, the associated payoff profile solves an interdependent utility system, and if that solution is bounded and unique for every profile we call the game coherent. Coherent games generate a standard normal form. Our central theorem states that every Nash equilibrium of such a game is Pareto optimal, in sharp contrast to the general prevalence of inefficient equilibria in the presence of externalities. While externalities in our model are restricted to flow only through payoffs there are no other constraints: they could be positive or negative, or of varying sign. We further show that our coherence and continuity requirements are tight.
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