Grim P
Department of Philosophy, SUNY at Stony Brook 11794, USA.
Biosystems. 1996;37(1-2):3-17. doi: 10.1016/0303-2647(95)01541-8.
The iterated Prisoner's Dilemma has become the standard model for the evolution of cooperative behavior within a community of egoistic agents, frequently cited for implications in both sociology and biology. Due primarily to the work of Axelrod (1980a, 1980b, 1984, 1985), a strategy of tit for tat (TFT) has established a reputation as being particularly robust. Nowak and Sigmund (1992) have shown, however, that in a world of stochastic error or imperfect communication, it is not TFT that finally triumphs in an ecological model based on population percentages (Axelrod and Hamilton 1981), but 'generous tit for tat' (GTFT), which repays cooperation with a probability of cooperation approaching 1 but forgives defection with a probability of 1/3. In this paper, we consider a spatialized instantiation of the stochastic Prisoner's Dilemma, using two-dimensional cellular automata (Wolfram, 1984, 1986; Gutowitz, 1990) to model the spatial dynamics of populations of competing strategies. The surprising result is that in the spatial model it is not GTFT but still more generous strategies that are favored. The optimal strategy within this spatial ecology appears to be a form of 'bending over backwards', which returns cooperation for defection with a probability of 2/3--a rate twice as generous as GTFT.
重复囚徒困境已成为利己主体群体中合作行为进化的标准模型，在社会学和生物学领域的影响常被提及。主要由于阿克塞尔罗德（1980a、1980b、1984、1985年）的研究，以牙还牙策略（TFT）树立了特别稳健的声誉。然而，诺瓦克和西格蒙德（1992年）表明，在存在随机误差或沟通不完美的世界中，在基于种群百分比的生态模型（阿克塞尔罗德和汉密尔顿，1981年）里最终胜出的并非以牙还牙策略，而是“慷慨以牙还牙”（GTFT），它以接近1的合作概率回报合作，但以1/3的概率原谅背叛。在本文中，我们考虑随机囚徒困境的空间实例化，使用二维细胞自动机（沃尔弗拉姆，1984、1986年；古托维茨，1990年）来模拟竞争策略种群的空间动态。令人惊讶的结果是，在空间模型中受青睐的并非GTFT，而是更为慷慨的策略。这种空间生态中的最优策略似乎是一种“拼命迎合”的形式，它以2/3的概率用合作回报背叛——这一比例是GTFT慷慨程度的两倍。
