Abstract
Cooperation through repetition is an important theme in game theory. In this regard, various celebrated “folk theorems” have been proposed for repeated games in increasingly more complex environments. There has, however, been insufficient attention paid to the robustness of a large set of equilibria that is needed for such folk theorems. Starting with perfect public equilibrium as our starting point, we study uniformly strict equilibria in repeated games with private monitoring and direct communication (cheap talk). We characterize the limit equilibrium payoff set and identify the conditions for the folk theorem to hold with uniformly strict equilibrium.
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References
Abreu, D., Pearce, D., Stacchetti, E.: Toward a theory of discounted repeated games with imperfect monitoring. Econometrica 59, 1041–1063 (1990)
Aoyagi, M.: Communication equilibria in repeated games with imperfect private monitoring. Econ. Theory 25, 455–475 (2005)
Ben-Porath, E., Kahneman, M.: Communication in repeated games with private monitoring. J. Econ. Theory 70, 281–297 (1996)
Bhaskar, V., Obara, I.: Belief-based equilibria in the repeated Prisoners’ dilemma with private monitoring. J. Econ. Theory 102, 40–69 (2002)
Compte, O.: Communication in repeated games with imperfect private monitoring. Econometrica 66, 597–626 (1998)
Ely, J., Välimaki, J.: A robust folk theorem for the Prisoner’s dilemma. J. Econ. Theory 102, 84–105 (2002)
Fudenberg, D., Levine, D.K.: Efficiency and observability with long-run and short-run players. J. Econ. Theory 62, 103–135 (1994)
Fudenberg, D., Levine, D.K.: The Nash-threats folk theorem with communication and approximate common knowledge in two player games. J. Econ. Theory 132, 461–473 (2007)
Fudenberg, D., Levine, D.K., Maskin, E.: The Folk theorem with imperfect public information. Econometrica 62, 997–1039 (1994)
Green, Edward J., Porter, Robert H.: Noncooperative collusion under imperfect price information. Econometrica 52, 87–100 (1984)
Hörner, J., Olszewski, W.: The Folk theorem for games with private, almost-perfect monitoring. Econometrica 74, 1499–1544 (2006)
Kandori, M., Matsushima, H.: Private observation and collusion. Econometrica 66, 627–652 (1998)
Laclau, M.: A Folk theorem for repeated games played on a network. Games Econ. Behav. 76, 711–737 (2012)
Laclau, M.: Communication in repeated network games with imperfect monitoring. Games Econ. Behav. 87, 136–160 (2014)
Mailath, G., Morris, S.: Repeated games with almost-public monitoring. J. Econ. Theory 102, 189–228 (2002)
Mailath, G., Olszewski, W.: Folk theorems with bounded recall under (almost) perfect monitoring. Games Econ. Behav. 71, 174–192 (2011)
Matsushima, H.: Repeated games with private monitoring: two players. Econometrica 72, 823–852 (2004)
Obara, I.: Folk theorem with communication. J. Econ. Theory 144, 120–134 (2009)
Piccione, M.: The repeated Prisoner’s dilemma with imperfect private monitoring. J. Econ. Theory 102, 70–83 (2002)
Renault, J., Tomala, T.: Repeated proximity games. Int. J. Game Theory 27, 539–559 (1998)
Sekiguchi, T.: Efficiency in repeated Prisoner’s dilemma with private monitoring. J. Econ. Theory 76, 345–361 (1997)
Sugaya, T.: Folk theorem in repeated games with private monitoring. Rev. Econ. Stud. 89, 2201–2256 (2022)
Tomala, T.: Perfect communication equilibria in repeated games with imperfect monitoring. Games Econ. Behav. 67, 682–694 (2009)
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McLean, R., Obara, I. & Postlewaite, A. Uniformly strict equilibrium for repeated games with private monitoring and communication. Econ Theory (2024). https://doi.org/10.1007/s00199-024-01561-0
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DOI: https://doi.org/10.1007/s00199-024-01561-0