Stochastic Uncoupled Dynamics and Nash Equilibrium

• Authors: Andreu Mas-Colell.
• BSE Working Paper: 110647 | September 15
• Keywords: uncoupled , Nash equilibrium , stochastic dynamics , bounded recall
• JEL codes: C7, D83
• uncoupled
• Nash equilibrium
• stochastic dynamics
• bounded recall

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence to Nash equilibria, and present a number of possibility and impossibility results. Basically, we show that if in addition to random moves some recall is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it suffices to recall the last two periods of play.