TIT FOR TAT (TFT) is the familiar strategy of returning like for like, good for good, bad for bad. Recently Robert Axelrod has shown this rule to be remarkably effective in promoting co-operation among egoists.1Nevertheless, it has been morally denigrated, most notably in the Sermon on the Mount but also by the modern patron of TFT, Anatol Rapoport:Of the contingent strategies, Tit-for-tat elicits consistently the most cooperation in the Prisoner's Dilemma. Obviously, it would be fatuous to interpret this result as (...) a vindication of the “eye-for-an-eye” principle. The success of Tit-for-tat may be no more than that of a simple reinforcement schedule in à two-choice situation, devoid of ethical overtones. (shrink)

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, 198Ob, 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 l/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 GIFT 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. (shrink)

To understand the meaning of evolutionary equilibria, it is necessary to comprehend the ramifications of the evolutionary model. For instance, a full appreciation of Axelrod's The Evolution of Cooperation requires that we identify assumptions under which conditionally cooperative strategies, like Tit For Tat, are and are not evolutionarily stable. And more generally, when does stability fail? To resolve these questions we re-examine the very foundations of the evolutionary model. The results of this paper can be analytically separated into three parts. (...) The first part is conceptual: it identifies the evolutionary model's assumptions and shows how different assumptions imply different types of evolutionary stability. The second part is deductive: it establishes necessary and sufficient conditions for the types of evolutionary stability identified in the first part, and demonstrates in which games these kinds of stability can (and cannot) be attained. The third and final part is applied: it relates the general findings (which are independent of the specific payoffs of any particular evolutionary game) to the issue of the evolutionary stability of cooperation. Results on cooperation appear throughout the paper as they both exemplify and motivate the general results. These results essentially explain when cooperation is and is not stable, and why, thus shedding new light on the meaning and applicability of Axelrod's widely known claims. (shrink)

The simple model of conflict-prone situations called Prisoner’s Dilemma is discussed. Whereas the best strategy for the model is to defect, in the case of its iterated version (Iterated Prisoner’s Dilemma—IPD) it is possible and more profitable to cooperate with the opponent.The simple strategy called Tit for Tat (TFT) which is easy to recognize, never defects first, punishes every defection but is also forgiving is presented. The TFT strategy is very successful being able to establish the cooperation with its opponents. (...) The possible outcome of the competition between the TFT strategy and non-cooperative strategies is considered. It turns out that even small number of TFT strategies can overcome the greater number of more “egoistic” strategies.The described model can give the better understanding of some psychological, sociological and biological processes as well as help to propagate the altruistic attitudes in the society. (shrink)

The computer simulation study explores the impact of the duration of social impact on the generation and stabilization of cooperative strategies. Rather than seeding the simulations with a finite set of strategies, a continuous distribution of strategies is being defined. Members of heterogeneous populations were characterized by a pair of probabilistic reactive strategies: the probability to respond to cooperation by cooperation and the probability to respond to defection by cooperation. This generalized reactive strategy yields the standard TFT mechanism, the All-Cooperate, (...) All-Defect and Bully strategies as special cases. Pairs of strategies interacted through a Prisoner's Dilemma game and exerted social influence on all other members. Manipulating: (i) the initial distribution of populations' strategies, and (ii) the duration of social influence, we monitored the conditions leading to the emergence and stabilization of cooperative strategies. Results show that: (1) The duration of interactions between pairs of strategies constitutes a crucial factor for the emergence and stabilization of cooperative strategies, (2) Unless sufficient learning intervals are provided, initializing the simulations with cooperative populations does not guarantee that cooperation will sustain. (shrink)