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Strategic complexity in repeated extensive games
Affiliation:1. College of Pharmacy, CMRI, Research Institute of Pharmaceutical Sciences, Kyungpook National University, Daegu 702-701, Republic of Korea;2. Department of Biochemistry and Cell Biology, BK21 Plus KNU Biomedical Convergence Program, School of Medicine, Kyungpook National University, Daegu 702-701, Republic of Korea;3. Department of Ophthalmology, School of Medicine, Kyungpook National University, Daegu 700-721, Republic of Korea;1. Shanghai University of Finance and Economics, School of Economics, Guoding Road 777, Shanghai 200433, China;2. Korea University, Department of Economics, Sungbuk-gu Anam-ro 145, Seoul 136-701, Republic of Korea;3. Institute of Economic Theory I, Humboldt University at Berlin, Spandauer Str. 1, 10178 Berlin, Germany
Abstract:This paper studies a machine (finite automaton) playing a two-player repeated game of a simple extensive-form game with perfect information. We introduce a new complexity measure called multiple complexity which incorporates a strategyʼs responsiveness to information in the stage game as well as the number of states of the machine. We completely characterize the Nash equilibrium of the machine game. In the sequential-move prisonerʼs dilemma, cooperation can be sustained as an equilibrium.
Keywords:Strategic complexity  Finite automaton  Repeated game  Extensive game  Prisonerʼs dilemma  Multiple complexity
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