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Register a new userThe Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects
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We show that, with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents substitution effects, not their income effects. Our Equilibrium Existence Duality allows us to transport results on the existence of competitive equilibrium from settings with transferable utility to settings with income effects. One consequence is that net substitutability---which is a strictly weaker condition than gross substitutability---is sufficient for the existence of competitive equilibrium. We also extend the ``demand types classification of valuations to settings with income effects and give necessary and sufficient conditions for a pattern of substitution effects to guarantee the existence of competitive equilibrium.
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This paper proposes a new equilibrium concept robust perfect equilibrium for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed strategies and in pure strategies) and satisfy the important properties of admissibility, aggregate robustness, and ex post robust perfection. These properties strengthen relevant equilibrium results in an extensive literature on strategic interactions among a large number of agents. Illustrative applications to congestion games and potential games are presented. In the particular case of a congestion game with strictly increasing cost functions, we show that there is a unique symmetric robust perfect equilibrium.
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Evidence games study situations where a sender persuades a receiver by selectively disclosing hard evidence about an unknown state of the world. Evidence games often have multiple equilibria. Hart et al. (2017) propose to focus on truth-leaning equilibria, i.e., perfect Bayesian equilibria where the sender prefers disclosing truthfully when indifferent, and the receiver takes off-path disclosure at face value. They show that a truth-leaning equilibrium is an equilibrium of a perturbed game where the sender has an infinitesimal reward for truth-telling. We show that, when the receivers action space is finite, truth-leaning equilibrium may fail to exist, and it is not equivalent to equilibrium of the perturbed game. To restore existence, we introduce a disturbed game with a small uncertainty about the receivers payoff. A purifiable equilibrium is a truth-leaning equilibrium in an infinitesimally disturbed game. It exists and features a simple characterization. A truth-leaning equilibrium that is also purifiable is an equilibrium of the perturbed game.
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