Department of Industrial Organization, University of Valladolid, 47011 Spain.
J Theor Biol. 2010 Nov 7;267(1):76-84. doi: 10.1016/j.jtbi.2010.07.039. Epub 2010 Aug 3.
Conditional dissociation, i.e. the option to leave an interacting partner in response to his behaviour, is a mechanism that has been shown to promote cooperation in several settings, but the fundamental features that make conditional dissociation work in this way are not yet fully understood. This paper identifies some of the key conditions that make conditional dissociation lead to high levels of cooperation, explains how this mechanism can support the evolutionary coexistence of cooperative and non-cooperative behaviour typically observed in nature, and provides an analytical formula to estimate the expected degree of cooperation thus achieved. Our model involves a population of individuals who are paired to play an iterated prisoner's dilemma. All individuals share the same capacity to react to the action previously chosen by their partner and, without any other a priori constraint or exclusion, they may use any behavioural rule that is compatible with this capacity. The dynamic evolution of the population eventually enters either a non-cooperative or a partially cooperative regime, depending mainly on the expected lifetime of individuals. Whenever the partially cooperative regime materializes, the cornerstone of its long-run stability is the coexistence of defectors and "Out-for-Tat" strategists, the latter being those who start cooperating and respond to defection by merely leaving. We find, therefore, that conditional dissociation is the essential disciplinary device supporting cooperation, whilst other conditional strategies (such as Tit-for-Tat) remain present only in small population shares. These conclusions are obtained both by extensive numerical simulations and through analytical mean-field methods that approximate the stochastic simulation dynamics and deliver accurate predictions for general parameter configurations.
有条件的分离，即根据对方的行为选择离开互动伙伴的能力，是一种已被证明可以在多种环境中促进合作的机制，但使有条件的分离以这种方式起作用的基本特征尚未得到充分理解。本文确定了一些使有条件的分离导致高水平合作的关键条件，解释了这种机制如何支持在自然界中通常观察到的合作和非合作行为的进化共存，并提供了一个分析公式来估计由此实现的预期合作程度。我们的模型涉及一组配对玩迭代囚徒困境的个体。所有个体都具有相同的能力来对其伙伴之前选择的行为做出反应，并且在没有任何其他先验约束或排除的情况下，他们可以使用任何与这种能力兼容的行为规则。人口的动态演化最终进入非合作或部分合作的状态，这主要取决于个体的预期寿命。只要部分合作的状态实现，其长期稳定性的基石是缺陷者和“以牙还牙”策略者的共存，后者是那些开始合作并通过仅仅离开来回应背叛的策略者。因此，我们发现，有条件的分离是支持合作的必要纪律手段，而其他有条件的策略（如以牙还牙）仅以较小的人口份额存在。这些结论是通过广泛的数值模拟和通过近似随机模拟动力学的解析平均场方法获得的，为一般参数配置提供了准确的预测。
