Killingback Timothy, Doebeli Michael
Ecology and Evolution, Eidgenössische Technische Hochschule (ETH) Zurich, 8092 Zurich, Switzerland.
Am Nat. 2002 Oct;160(4):421-38. doi: 10.1086/342070.
Understanding the evolutionary origin and persistence of cooperative behavior is a fundamental biological problem. The standard "prisoner's dilemma," which is the most widely adopted framework for studying the evolution of cooperation through reciprocal altruism between unrelated individuals, does not allow for varying degrees of cooperation. Here we study the continuous iterated prisoner's dilemma, in which cooperative investments can vary continuously in each round. This game has been previously considered for a class of reactive strategies in which current investments are based on the partner's previous investment. In the standard iterated prisoner's dilemma, such strategies are inferior to strategies that take into account both players' previous moves, as is exemplified by the evolutionary dominance of "Pavlov" over "tit for tat." Consequently, we extend the analysis of the continuous prisoner's dilemma to a class of strategies in which current investments depend on previous payoffs and, hence, on both players' previous investments. We show, both analytically and by simulation, that payoff-based strategies, which embody the intuitively appealing idea that individuals invest more in cooperative interactions when they profit from these interactions, provide a natural explanation for the gradual evolution of cooperation from an initially noncooperative state and for the maintenance of cooperation thereafter.
理解合作行为的进化起源和持续性是一个基本的生物学问题。标准的“囚徒困境”是研究通过无关个体间的互惠利他行为实现合作进化的最广泛采用的框架，但它不允许有不同程度的合作。在此，我们研究连续重复囚徒困境，其中合作投入在每一轮中可以连续变化。此前已针对一类反应策略对这个博弈进行过研究，在这类策略中，当前投入基于伙伴之前的投入。在标准的重复囚徒困境中，此类策略不如考虑双方之前行动的策略，如“巴甫洛夫”策略相对于“以牙还牙”策略的进化优势所例证的那样。因此，我们将连续囚徒困境的分析扩展到一类策略，其中当前投入取决于之前的收益，进而取决于双方之前的投入。我们通过分析和模拟表明，基于收益的策略体现了直观上有吸引力的观点，即个体在从合作互动中获利时会在合作互动中投入更多，它为合作从初始的非合作状态逐渐进化以及此后合作的维持提供了一种自然的解释。
