Emergence of exploitation as symmetry breaking in iterated prisoner's dilemma
Emergence of exploitation as symmetry breaking in iterated prisoner's dilemma
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DOI：
10.1103/physrevresearch.1.033077
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发表时间：
2019-11-05
影响因子：
4.2
通讯作者：
Kaneko, Kunihiko
中科院分区：
文献类型：
--
作者：
Fujimoto, Yuma;Kaneko, Kunihiko
在社会中，相互合作、背叛和剥削关系是常见的。虽然博弈论的文献对合作和背叛进行了广泛的研究，但玩家之间的剥削关系（游戏邦注：即一方比另一方获得更大的利益，而游戏本身是对称的）却很少被探索。在最近的一项开创性研究中，Press和Dyson证明，如果只有一个玩家可以了解另一个玩家，那么在囚徒困境游戏中就实现了不对称剥削。然而，在他们的研究中，人们之间的决策是不对称的；剥削方单方面地决定和确定策略，被剥削方遵循策略。目前尚不清楚这种剥削是否会出现，是否会稳定建立，即使双方都对称地了解对方，并试图优化他们的收益。在这里，我们首先制定了一个动态系统，该系统描述了玩家概率策略的变化，通过强化学习获得更大的收益，基于其他玩家的识别。通过将此公式应用于标准的囚徒困境博弈，我们用数值和分析的方法证明了在对称策略动态和对称博弈规则下，剥削关系是可以实现的。这种剥削关系被双方所稳定：剥削一方要求另一方进行不公平的合作。即使被剥削的一方获得的收益比被剥削的一方低，也优化了自己的策略，但在某种程度上，被剥削的一方接受了对方的背叛。最终的平衡状态是相互合作、背叛还是剥削，关键取决于初始条件。减少对叛逃者的合作概率的响应导致参与者之间合作概率的振荡，从而导致一个复杂的盆地结构达到最终的平衡。特别是，双方初始策略之间的任何微小差异都可能被放大并固定为合作概率的巨大差异，从而导致剥削的固定。换句话说，剥削者和被剥削者之间的对称性被打破了。考虑到结果的普遍性，本研究提供了另一种视角来研究剥削在社会中的起源。
In society, mutual cooperation, defection, and exploitative relationships are common. Whereas cooperation and defection are studied extensively in the literature on game theory, exploitative relationships between players, in which one receives a larger benefit than the other while the game itself is symmetric, are little explored. In a recent seminal study, Press and Dyson demonstrated that if only one player can learn about the other, asymmetric exploitation is achieved in the prisoner's dilemma game. In their study, however, asymmetry is assumed in decision making between persons; the exploiting player one-sidedly determines and fixes the strategy and the exploited player follows it. It is unknown whether such exploitation emerges and is stably established even when both players learn about each other symmetrically and try to optimize their payoffs. Here, we first formulate a dynamical system that describes the change in a player's probabilistic strategy with reinforcement learning to obtain greater payoffs, based on the recognition of the other player. By applying this formulation to the standard prisoner's dilemma game, we numerically and analytically demonstrate that an exploitative relationship can be achieved despite symmetric strategy dynamics and symmetric rule of games. This exploitative relationship is stabilized by both the players: The exploiting player demands the other's unfair cooperation. Even though the exploited player, who receives a lower payoff than the exploiting player, has optimized the own strategy, the player accepts the other's defection to some degree. Whether the final equilibrium state is mutual cooperation, defection, or exploitation crucially depends on the initial conditions. Response to decrease the cooperation probability against a defector leads to oscillations in the probabilities of cooperation between the players and thus a complicated basin structure to the final equilibrium. In particular, any slight difference between both players' initial strategies can be amplified and fixed as a large difference in the probabilities of cooperation, leading to fixation of exploitation. In other words, symmetry breaking between the exploiting and exploited players results. Considering the generality of the result, this study provides another perspective on the origin of exploitation in society.