On the existence of pure-strategy perfect equilibrium in discontinuous games |
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| Authors: | Oriol Carbonell-Nicolau |
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| Affiliation: | 1. CONICET, INGEIS, Ciudad Universitaria, C1428EHA Buenos Aires, Argentina;2. CONICET, FCEN - Dpto. Ciencias Geológicas, Universidad de Buenos Aires, C1428EHA - Buenos Aires, Argentina;3. Department of Earth and Space Sciences, Box 351310, University of Washington, Seattle, WA 98195, USA;1. Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Depto. De Ciencias Geológicas, Buenos Aires, Argentina;2. CONICET-Universidad de Buenos Aires, Instituto de Geociencias Básicas, Aplicadas y Ambientales de Buenos Aires (IGeBA), Buenos Aires, Argentina;3. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Trieste, Italy;4. Dipartimento di Scienze Pure ed Applicate, Università di Urbino, Italy;1. Institut für Erdwissenschaften, Universität Graz, Universitätsplatz 2, A-8010 Graz, Austria;2. Geology Department, Faculty of Science, Tanta University, Tanta, Egypt;3. Geology Department, Faculty of Science, United Arab Emirates University, United Arab Emirates;4. Sciences Department, College of Basic Education, PAAET, Kuwait;5. Egyptian Institute of Geodynamic, Cairo, Egypt;6. Geology Department, Faculty of Science, Suez Canal University, Ismailia, Egypt |
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| Abstract: | We provide sufficient conditions for a (possibly) discontinuous normal-form game to possess a pure-strategy trembling-hand perfect equilibrium. We first show that compactness, continuity, and quasiconcavity of a game are too weak to warrant the existence of a pure-strategy perfect equilibrium. We then identify two classes of games for which the existence of a pure-strategy perfect equilibrium can be established: (1) the class of compact, metric, concave games satisfying upper semicontinuity of the sum of payoffs and a strengthening of payoff security; and (2) the class of compact, metric games satisfying upper semicontinuity of the sum of payoffs, strengthenings of payoff security and quasiconcavity, and a notion of local concavity and boundedness of payoff differences on certain subdomains of a player's payoff function. Various economic games illustrate our results. |
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