具有任意支付矩阵的2 × 2自适应主体简单博弈模型的自组织
Self-organization in a simple model of adaptive agents playing 2X2 games with arbitrary payoff matrices
摘要：
我们分析，分析和数值，“自私”的自适应代理系统玩一个任意的迭代成对游戏（定义为2X2的支付矩阵）的自组织。可能玩的游戏的例子有：囚徒困境（PD）游戏，鸡游戏，英雄游戏等。代理人没有记忆，使用的策略不是基于直接互惠，也不是“标签”，而是随机选择的，即地理邻近被忽略。他们可以采取两种策略：合作（C）或背叛（D）。参与者通过比较他们的效用与预期收益的估计来衡量他们的成功，并根据一个简单的规则更新他们的策略。研究了模型的两个版本：1）确定性版本（代理人处于确定状态C或D）和2）随机版本（代理人有概率c玩C）。使用一个通用的主方程，我们计算的平衡态，系统自组织，其特征在于他们的平均合作概率c_{eq}。根据支付矩阵，我们表明，c_{eq}可以采取五个不同的值。我们还考虑了使用两个不同的支付矩阵的代理商的混合表明，任何值的c_{eq}可以通过调整使用每个支付矩阵的代理商的比例达到。特别是，这可以被用来作为一种方式来模拟的效果的一小部分d的“反社会”的个人-无法实现任何价值的合作-对合作制度举行的人口中立或“正常”代理。
英文摘要：
We analyze, both analytically and numerically, the self-organization of a system of "selfish" adaptive agents playing an arbitrary iterated pairwise game (defined by a 2X2 payoff matrix). Examples of possible games to play are: the Prisoner's Dilemma (PD) game, the Chicken game, the Hero game, etc. The agents have no memory, use strategies not based on direct reciprocity nor 'tags' and are chosen at random, i.e. geographical vicinity is neglected. They can play two possible strategies: cooperate (C) or defect (D). The players measure their success by comparing their utilities with an estimate for the expected benefits and update their strategy following a simple rule. Two versions of the model are studied: 1) the deterministic version (the agents are either in definite states C or D) and 2) the stochastic version (the agents have a probability c of playing C). Using a general Master Equation we compute the equilibrium states into which the system self-organizes, characterized by their average probability of cooperation c_{eq}. Depending on the payoff matrix, we show that c_{eq} can take five different values. We also consider the mixing of agents using two different payoff matrices an show that any value of c_{eq} can be reached by tunning the proportions of agents using each payoff matrix. In particular, this can be used as a way to simulate the effect a fraction d of "antisocial" individuals -incapable of realizing any value to cooperation- on the cooperative regime hold by a population of neutral or "normal" agents.
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