Takada T, Kigami J
Department of Biophysics, Kyoto University, Japan.
J Math Biol. 1991;29(6):513-29. doi: 10.1007/BF00164049.
In this paper, the attainability of ESS of the evolutionary game among n players under the frequency-independent selection is studied by means of a mathematical model describing the dynamical development and a concept of stability (strongly determined stability). It is assumed that natural selection and small mutations cause the phenotype to change gradually in the direction of fitness increasing. It is shown that (1) the ESS solution is not always evolutionarily attainable in the evolutionary dynamics, (2) in the game where the interaction between two species is completely competitive, the Nash solution is always attainable, and (3) one of two species may attain the state of minimum fitness as a result of evolution. The attainability of ESS is also examined in two game models on the sex ratio of wasps and aphids in light of our criterion of the attainability of ESS.
本文通过描述动态发展的数学模型和稳定性概念（强确定稳定性），研究了频率独立选择下n个参与者之间进化博弈的ESS可达性。假设自然选择和小突变导致表型朝着适应度增加的方向逐渐变化。结果表明：（1）在进化动力学中，ESS解并不总是进化可达的；（2）在两个物种间相互作用完全竞争的博弈中，纳什解总是可达的；（3）两个物种中的一个可能因进化而达到最低适应度状态。还根据我们的ESS可达性标准，在关于黄蜂和蚜虫性别比的两个博弈模型中检验了ESS的可达性。
