Common Knowledge and State-Dependent Equilibria
Many puzzling social behaviors, such as avoiding eye contact, using innuendos, and insignificant events that trigger revolutions, seem to relate to common knowledge and coordination, but the exact relationship has yet to be formalized. Herein, we present such a formalization. We state necessary and sufficient conditions for what we call state-dependent equilibria – equilibria where players play different strategies in different states of the world. In particular, if everybody behaves a certain way (e.g. does not revolt) in the usual state of the world, then in order for players to be able to behave a different way (e.g. revolt) in another state of the world, it is both necessary and sufficient for it to be common p-believed that it is not the usual state of the world, where common p-belief is a relaxation of common knowledge introduced by Monderer and Samet . Our framework applies to many player r-coordination games – a generalization of coordination games that we introduce – and common (r,p)-beliefs – a generalization of common p-beliefs that we introduce. We then apply these theorems to two particular signaling structures to obtain novel results.
KeywordsNash Librium Rium Metaphor Cough
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- 2.Andersen, H.C.: The Emperor’s New Clothes. Fairy Tales Told for Children - First Collection (1837)Google Scholar
- 4.Binmore, K.: Game theory - a very short introduction. Clarendon Press (2007)Google Scholar
- 6.Chwe, M.S.-Y.: Rational Ritual: Culture, Coordination, and Common Knowledge. Princeton University Press (2003)Google Scholar
- 14.Harsanyi, J.C., Selten, R.: A General Theory of Equilibrium Selection in Games. MIT Press Books, vol. 1. The MIT Press (1988)Google Scholar
- 15.Lewis, D.: Convention: A Philosophical Study. Harvard University Press, Cambridge (1969)Google Scholar
- 17.Morris, S.: Coordination, communication and common knowledge: A retrospective on electronic mail game. Oxford Review of Economic Policy 18(4) (February 2002)Google Scholar
- 18.Morris, S., Shin, H.S., Yale University. Cowles Foundation for Research in Economics: Global games: theory and applications. Cowles Foundation discussion paper. Cowles Foundation for Research in Economics (2000)Google Scholar
- 19.Morris, S., Shin, H.S.: Unique equilibrium in a model of self-fulfilling currency attacks. American Economic Review 88(3), 587–597 (1998)Google Scholar
- 20.Morris, S., Shin, H.S.: Rethinking multiple equilibria in macroeconomic modeling. In: NBER Macroeconomics Annual 2000, vol. 15, NBER Chapters, pp. 139–182. National Bureau of Economic Research, Inc. (June 2001)Google Scholar
- 21.Perry, S., Manson, J.: Manipulative Monkeys: The Capuchins of Lomas Barbudal. Harvard University Press (2008)Google Scholar
- 23.Rubinstein, A.: The electronic mail game: Strategic behavior under “almost common knowledge”. American Economic Review 79(3), 385–391 (1989)Google Scholar