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Awareness in Repeated Games

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  • Mengel Friederike
  • Tsakas Elias
  • Vostroknutov Alexander

    (METEOR)

Abstract

In this paper we provide a framework to reason about limited awareness of the action space in finitely repeated games. Our framework is rich enough to capture the full strategic aspect of limited awareness in a dynamic setting, taking into account the possibility that agents might want to reveal or conceal actions to their opponent or that they might become "aware of unawareness" upon observing non rationalizable behavior. We show that one can think of these situations as a game with incomplete information, which is fundamentally different, though, from the standard treatment of repeated games with incomplete information. We establish conditions on the "level of mutual awareness" of the action space needed to recover Nash and subgame perfect Nash equilibria from the standard theory with common knowledge. We also show that the set of sustainable payoffs in games with folk theorems does not relate in a monotone way to the "level of mutual awareness".

Suggested Citation

  • Mengel Friederike & Tsakas Elias & Vostroknutov Alexander, 2009. "Awareness in Repeated Games," Research Memorandum 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2009010
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    File URL: https://cris.maastrichtuniversity.nl/portal/files/1374168/content
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    References listed on IDEAS

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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, January.
    3. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136 World Scientific Publishing Co. Pte. Ltd..
    4. Jihong Lee, 2008. "Unforeseen Contingency and Renegotiation with Asymmetric Information," Economic Journal, Royal Economic Society, vol. 118(528), pages 678-694, April.
    5. Brandenburger, Adam & Dekel, Eddie, 1987. "Common knowledge with probability 1," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 237-245, June.
    6. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    7. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    8. Jing Li, 2008. "Information Structures with Unawareness," PIER Working Paper Archive 08-024, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    9. Feinberg, Yossi, 2004. "Subjective Reasoning--Games with Unawareness," Research Papers 1875, Stanford University, Graduate School of Business.
    10. Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-922, July.
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    Keywords

    mathematical economics;

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