Infinitely repeated games is the pre-dominant paradigm within which economists study long-term strategic interaction. The standard framework allows players to condition their strategies on all past actions; that is, assumes that they have unbounded memory. That is clearly a convenient simplification that is at odds with reality. In this paper we restrict attention to one-period memory and characterize all totally mixed equilibria. In particular, we focus on strongly mixed equilibria. We provide conditions that are necessary and sufficient for a game to have such an equilibrium. We further demonstrate the exact set of payoffs that can be generated by such equilibria.
Siconolfi, Paolo, and Prajit Dutta. "Mixed Strategy Equilibria in Repeated Games with One-Period Memory." International Journal of Economic Theory 6, no. 1 (March 2010): 167-187.
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