Fudenberg Drew, Nowak Martin A, Taylor Christine, Imhof Lorens A
Department of Economics, Harvard University, Cambridge, MA 02138, USA.
Theor Popul Biol. 2006 Nov;70(3):352-63. doi: 10.1016/j.tpb.2006.07.006. Epub 2006 Aug 12.
We study stochastic game dynamics in finite populations. To this end we extend the classical Moran process to incorporate frequency-dependent selection and mutation. For 2 x 2 games, we give a complete analysis of the long-run behavior when mutation rates are small. For 3 x 3 coordination games, we provide a simple rule to determine which strategy will be selected in large populations. The expected motion in our model resembles the standard replicator dynamics when the population is large, but is qualitatively different when the population is small. Our analysis shows that even in large finite populations the behavior of a replicator-like system can be different from that of the standard replicator dynamics. As an application, we consider selective language dynamics. We determine which language will be spoken in finite large populations. The results have an intuitive interpretation but would not be expected from an analysis of the replicator dynamics.
我们研究有限种群中的随机博弈动态。为此，我们扩展了经典的莫兰过程，以纳入频率依赖选择和突变。对于2×2博弈，当突变率很小时，我们对长期行为进行了全面分析。对于3×3协调博弈，我们提供了一个简单规则来确定在大种群中会选择哪种策略。当种群规模较大时，我们模型中的预期动态类似于标准复制者动态，但当种群规模较小时，在性质上有所不同。我们的分析表明，即使在大型有限种群中，类似复制者系统的行为也可能与标准复制者动态不同。作为一个应用，我们考虑选择性语言动态。我们确定在有限大种群中将使用哪种语言。结果有直观的解释，但从复制者动态分析中无法预期到。
