One - Memory in Repeated Games

Abstract:     
We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1 - memory strategies. First, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained by any 1 - memory subgame perfect equilibrium. Then, a complete characterization of 1 - memory simple strategies is provided, and it is employed to establish the following in games with more than two players each having connected action spaces:

1. all subgame perfect equilibrium payoffs can be approximately supported by an ε - sub-game perfect equilibrium strategy of 1 - memory,
2. all strictly enforceable subgame perfect equilibrium payoffs can be approximately supported by a 1 - memory subgame equilibrium, and
3. the subgame perfect Folk Theorem holds for 1 - memory strategies.

While no further restrictions are needed for the third result to hold in 2 - player games, an additional restriction is needed for the first two: players must have common punishments.

Number of Pages in PDF File: 49

working papers series