Abstract
A strategic situation with payoff-based externalities is one in which a player’s payoff depends on her own action and (continuously) on the payoffs of other players. Every action profile therefore induces an interdependent utility system. If each utility system is bounded, with a unique payoff solution for every action profile, we call the strategic situation coherent, and if the same condition also applies to every subset of players, we call the situation sub coherent. A coherent and sub-coherent situation generates a standard normal form, referred to as a game of love and hate. Our central theorem states that every equilibrium of a game of love and hate is Pareto optimal, in sharp contrast to the general prevalence of inefficient equilibria in the presence of externalities. While externalities 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, subcoherence and continuity requirements are tight.
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Host: Kalle Moene