Universality of Nash components |
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| Institution: | 1. Department of Economics, University of Exeter, Rennes Drive, Streatham Court, Exeter, EX4 4PU, UK;2. Department of Quantitative Economics, University Maastricht, P.O. Box 616, 6200 MD Maastricht, The Netherlands;1. Control System Laboratory, Department of Electrical Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC;2. Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC;3. Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204-4005, USA;1. Center of Economic Research at ETH Zürich (CER-ETH), Switzerland;2. Department of Economics, Maastricht University, Netherlands;1. Guanghua School of Management, Peking University, Beijing, China;2. University of Pittsburgh, United States;1. Singapore Management University, Singapore;2. Indian Statistical Institute, New Delhi, India |
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| Abstract: | We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game—a game where all players have two pure strategies and a common utility function with values either zero or one—whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets.We discuss implications of our results for the strategic stability of success sets, and use the results to construct a Nash component with index k for any fixed integer k. |
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| Keywords: | Strategic form games Nash equilibrium Nash component Topology |
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