Tracy N D, Seaman J W
Department of Mathematics, Computer Science, and Statistics, McNeese State University, Lake Charles, LA 70609, USA.
J Theor Biol. 1995 Nov 21;177(2):193-8. doi: 10.1006/jtbi.1995.0238.
Suppose a strategy for learning the optimal behavior in repeatedly played games is genetically determined. Then the animal is engaged in a learning game as well as the repeatedly played game. Harley (1981, J. theor. Biol. 89, 611-633) considers evolutionarily stable strategies in such learning games, called evolutionarily stable (ES) learning rules. Harley's work, though significant, is limited in that he does not establish the stochastic convergence of ES learning rules. Furthermore, his study of the relative payoff sum (RPS) approximation is limited to simulation experiments. Here, the stochastic convergence of ES learning rules and the RPS approximation is established. The ES learning rules and the RPS approximation were found to converge to the same quality, the so-called matching ratio, with probability one.
假设在重复进行的博弈中学习最优行为的策略是由基因决定的。那么动物既参与了一个学习博弈，也参与了重复进行的博弈。哈雷（1981年，《理论生物学杂志》89卷，611 - 633页）考虑了此类学习博弈中的进化稳定策略，称为进化稳定（ES）学习规则。哈雷的工作虽然意义重大，但存在局限性，即他没有确立ES学习规则的随机收敛性。此外，他对相对收益总和（RPS）近似的研究仅限于模拟实验。在此，确立了ES学习规则的随机收敛性以及RPS近似。结果发现，ES学习规则和RPS近似以概率1收敛到相同的质量，即所谓的匹配率。
