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Pairwise epistemic conditions for Nash equilibrium
Institution:1. Department of Quantitative Economics, Maastricht University, Netherlands;2. Department of Economics, Maastricht University, Netherlands;1. Department of Economics, The Ohio State University, 1945 North High Street, Columbus, OH 43210, USA;2. Department of Economics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;3. Department of Economics, Stanford University, 579 Serra Mall, Stanford, CA 94305, USA;1. John F. Kennedy School of Government, Harvard University, 79 JFK Street, Cambridge, MA 02138, United States;2. Department of Economics, 107 Gardner Hall, CB 3305, University of North Carolina, Chapel Hill, NC 27599, United States;1. Institute for International Economics Studies, Stockholm University, 106 91 Stockholm, Sweden;2. Department of Economics, University of Mannheim, L7, 3-5, 68163 Mannheim, Germany;1. Northwestern University, USA;2. Tel Aviv University, Israel;3. Arizona State University, USA
Abstract:We introduce a framework for modeling pairwise interactive beliefs and provide an epistemic foundation for Nash equilibrium in terms of pairwise epistemic conditions locally imposed on only some pairs of players. Our main result considerably weakens not only the standard sufficient conditions by Aumann and Brandenburger (1995), but also the subsequent generalization by Barelli (2009). Surprisingly, our conditions do not require nor imply mutual belief in rationality.
Keywords:Nash equilibrium  Pairwise common belief  Pairwise mutual belief  Pairwise action-consistency  Rationality  Conjectures  Biconnected graph  Epistemic game theory
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