On the existence of subgame-perfect equilibrium in infinite-action games of perfect information |
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| Institution: | 1. Centre for Wireless Communications (CWC), P.O. Box 4500, FI-90014 University of Oulu, Finland;2. Department of Computer and Information Science, Linköping University, SE-581 83 LINKÖPING, Sweden;3. SCA Research Lab, ITMO University, St. Petersburg, 197101, Russia;4. Center for Ubiquitous Computing (UBICOMP), P.O. Box 4500, FI-90014 University of Oulu, Finland;1. Faculty of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland;2. Department of Business Administration, Aichi University, Nagoya Campus, Hiraike 4-60-6, Nakamura, Nagoya, Aichi, 453-8777, Japan;1. LEEPS Lab, University of California, Santa Cruz, United States;2. Department of Economics, University of California, Santa Cruz, United States;1. Key Laboratory of Math.-Mech., AMSS, Chinese Academy of Sciences, 100190 Beijing, China;2. INRIA, 91120 Palaiseau, France |
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| Abstract: | We study infinite-action games of perfect information with finitely or countably many players. It is assumed that payoff functions are continuous, strategy sets are compact, and constraint correspondences are continuous. Under these assumptions we prove the existence of subgame-perfect equilibria in pure strategies which are measurable functions. If for any date t, the subgame that is played from date t on depends on the history up to t only as this history affects some vector of “state” variables, then equilibrium strategies admit a “closed-loop” representation as measurable functions of the “state” trajectories. |
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