认知层次理论与二人博弈
Cognitive hierarchy theory and two-person games
摘要：
许多社会和经济互动的结果，如股票市场交易，都是由代理人对其他个体行为的预测决定的。认知层次理论提供了一个框架来模拟预测准确性的后果，该框架已被证明适合某些类型的博弈论实验的数据，例如凯恩斯选美比赛和入门游戏。本文以对称两人两行动博弈为研究对象，根据认知层次方法建立了一个求解博弈者策略的算法。我们表明，雪堆游戏表现出的行为模式，其复杂性的增长，随着认知水平的球员的增加。除了找到第三个认知水平的解决方案，我们证明，在这个理论框架中，雪堆游戏的两个新的性质：i）任何雪堆游戏只能由一个参数-它的类，ii）他们是反对称的支付空间的对角线。最后，我们提出了一个模型的基础上，捕获的认知层次理论的主要特征的进化动力学。
英文摘要：
The outcome of many social and economic interactions, such as stock-market transactions, is strongly determined by the predictions that agents make about the behavior of other individuals. Cognitive Hierarchy Theory provides a framework to model the consequences of forecasting accuracy that has proven to fit data from certain types of game theory experiments, such as Keynesian Beauty Contests and Entry Games. Here, we focus on symmetric two-players-two-actions games and establish an algorithm to find the players' strategies according to the Cognitive Hierarchy Approach. We show that the Snowdrift Game exhibits a pattern of behavior whose complexity grows as the cognitive levels of players increases. In addition to finding the solutions up to the third cognitive level, we demonstrate, in this theoretical frame, two new properties of snowdrift games: i) any snowdrift game can be characterized by only a parameter -- its class, ii) they are anti-symmetric with respect to the diagonal of the pay-off's space. Finally, we propose a model based on an evolutionary dynamics that captures the main features of the Cognitive Hierarchy Theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
