Iterated weak dominance and subgame dominance |
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| Institution: | 1. Graduate School of Information Sciences, Tohoku University, 6-6-6 Aoba, Sendai, Miyagi 980-8579, Japan;2. School of Management, Tokyo University of Science, 1-11-2, Fujimi, Chiyoda, Tokyo 102-0071, Japan;3. Institute of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan;1. SAIF/(CAFR) and Mathematics Department, Shanghai Jiao Tong University, 211 Huaihai Road, Shanghai, 200030, China;2. Konstanz University, Universitätsstraße 10, 78464 Konstanz, Germany;1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;2. Department of Finance and Insurance, Lingnan University, Hong Kong;1. School of Business Administration, University of Miami, United States;2. Department of Economics, Faculty of Economics and Business, University of Chile, Chile |
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| Abstract: | In this paper, we consider finite normal form games satisfying transference of decisionmaker indifference. We show that any set of strategies surviving k rounds of elimination of some weakly dominated strategies can be reduced to a set of strategies equivalent to the set of strategies surviving k rounds of elimination of all weakly dominated strategies in every round by (at most k) further rounds of elimination of weakly dominated strategies. The result develops work by Gretlein Gretlein, R., 1983. Dominance elimination procedures on finite alternative games. International Journal of Game Theory 12, 107–113]. We then consider applications and demonstrate how we may obtain a unified approach to the work by Gretlein and recent results by Ewerhart Ewerhart, C., 2002. Iterated weak dominance in strictly competitive games of perfect information. Journal of Economic Theory 107, 474-482] and Marx and Swinkels Marx, L.M., Swinkels, J.M., 1997. Order independence for iterated weak dominance. Games and Economic Behavior 18, 219-245]. |
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