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Perfect correlated equilibria in stopping games

Heller, Yuval (2009): Perfect correlated equilibria in stopping games.

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Abstract

We define a new solution concept for an undiscounted dynamic game - a perfect uniform normal-form constant-expectation correlated approximate equilibrium with a canonical and universal correlation device. This equilibrium has the following appealing properties: (1) “Trembling-hand” perfectness - players do not use non-credible threats; (2) Uniformness - it is an approximate equilibrium in any long enough finite-horizon game and in any discounted game with a high enough discount factor; (3) Normal-form correlation - The strategy of a player depends on a private signal he receives before the game starts (which can be induced by “cheap-talk” among the players); (4) Constant expectation - The expected payoff of each player almost does not change when he receives his signal; (5) Universal correlation device - the device does not depend on the specific parameters of the game. (6) Canonical - each signal is equivalent to a strategy. We demonstrate the use of this equilibrium by proving its existence in every undiscounted multi-player stopping game.

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