Hidden stochastic games and limit equilibrium payoffs.

Summary We introduce the model ofhidden stochastic games, which are stochastic games where players observe pastactions and public signals on the current state. The natural state variable for these games is the commonbelief over the current state of the stochastic game. In this setup, we present an example in which the limitset of equilibrium payoffs, as the discount factor goes to 1, does not exist. Although the equilibrium payoffsets have full dimension, there is no converging selection of equilibrium payoffs. The example is symmetricand robust in many aspects, and in particular to extensive-form correlation or communication devices. Noreasonable limit equilibrium payoff exists, and it is difficult to give any good answer to the question: “In thegame played by extremely patient players, what are the possible outcomes?” The construction generalizes ona recent zero-sum example [23], while improving significantly its properties.