Abstract
We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1-memory strategies. We establish the following in games with perfect (rich) action spaces: First, when the players are sufficiently patient, the subgame perfect Folk Theorem holds with 1-memory. Second, for arbitrary level of discounting, all strictly enforceable subgame perfect equilibrium payoffs can be approximately supported with 1-memory if the number of players exceeds two. Furthermore, in this case all subgame perfect equilibrium payoffs can be approximately supported by an ε-equilibrium with 1-memory. In two-player games, the same set of results hold if an additional restriction is assumed: Players must have common punishments. Finally, to illustrate the role of our assumptions, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained with 1-memory. Thus, our results are the best that can be hoped for.
Original language | English |
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Pages (from-to) | 312-336 |
Number of pages | 25 |
Journal | Journal of Economic Theory |
Volume | 144 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2009 |
Keywords
- Bounded rationality
- Folk Theorem
- Memory
- Repeated games