Eran Shmaya

Signaling and Mediation in Games with Common Interests

Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential stochastic signals that depend on the actual state of nature. These signals provide the players with partial information about the state of nature and may also serve as a means of correlation. Different information structures induce different outcomes. An information structure is better than another, with respect to a certain solution concept, if the highest solution payoff it induces is at least that induced by the other structure. This paper characterizes the situation where one information structure is better than another with respect to various solution concepts: Nash equilibrium, strategic-normal-form correlated equilibrium, agent-normal-form correlated equilibrium and belief-invariant Bayesian solution. These solution concepts differ from one another in the scope of communication allowed between the players. The characterizations use maps that stochastically translate signals of one structure to signals of another.

Two-player nonZero–sum stopping games in discrete time

We prove that every two player non zero-sum stopping game in discrete time admits an -equilibrium in randomized strategies, for every > 0. We use a stochastic variation of Ramsey Theorem, which enables us to reduce the problem to that of studying properties of -equilibria in a simple class of stochastic games with finite state space.

Lipschitz Games

The Lipschitz constant of a finite normal-form game is the maximal change in some players payoff when a single opponent changes his strategy. We prove that games with small Lipschitz constant admit pure e-equilibria, and pinpoint the maximal Lipschitz constant that is sufficient to imply existence of a pure e-equilibrium as a function of the number of players in the game and the number of strategies of each player. Our proofs use the probabilistic method.

Comparison of information structures and completely positive maps

A theorem of Blackwell about comparison between information structures in classical statistics is given as an analogue in the quantum probabilistic set-up. The theorem provides an operational interpretation for trace-preserving completely positive maps, which are the natural quantum analogue of classical stochastic maps. The proof of the theorem relies on the separation theorem for convex sets and on quantum teleportation.

Non-existence of subgame-perfect ε-equilibrium in perfect information games with infinite horizon

Every finite extensive-form game with perfect information has a subgame-perfect equilibrium. In this note we settle to the negative an open problem regarding the existence of a subgame-perfect

General revealed preference theory

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On behavioral complementarity and its implications

ε-equilibrium in perfect information games with infinite horizon and Borel measurable payoffs, by providing a counter-example. We also consider a refinement called strong subgame-perfect