Fixation Probabilities of Strategies for Bimatrix Games in Finite Populations

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• 作者：Takuya Sekiguchi ; Hisashi Ohtsuki
• 关键词：Bimatrix games ; Equilibrium selection ; Finite population ; Fixation probability ; Stability ; Stochastic evolution
• 刊名：Dynamic Games and Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：7
• 期：1
• 页码：93-111
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Game Theory, Economics, Social and Behav. Sciences; Economic Theory/Quantitative Economics/Mathematical Methods; Operations Research, Management Science; Economics, general; Communications Engineering
• 出版者：Springer US
• ISSN：2153-0793
• 卷排序：7

文摘

Recent developments in stochastic evolutionary game theory in finite populations yield insights that complement the conventional deterministic evolutionary game theory in infinite populations. However, most studies of stochastic evolutionary game theory have investigated dynamics of symmetric games, although not all social and biological phenomena are described by symmetric games, e.g., social interactions between individuals having conflicting preferences or different roles. In this paper, we describe the stochastic evolutionary dynamics of two-player \(2 \times 2\) bimatrix games in finite populations. The stochastic process is modeled by a frequency-dependent Moran process without mutation. We obtained the fixation probability that the evolutionary dynamics starting from a given initial state converges to a specific absorbing state. Applying the formula to the ultimatum game, we show that evolutionary dynamics favors fairness. Furthermore, we present two novel concepts of stability for bimatrix games, based on our formula for the fixation probability, and demonstrate that one of the two serves as a criterion for equilibrium selection.