While game theory has been transformative for decision-making, the assumptions made can be overly restrictive in certain instances. In this work, we focus on some of the assumptions underlying rationality such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-$k$ reasoning and quantal response equilibrium (QRE) respectively. Specifically, we provide an information-theoretic two-parameter model that can relax both mutual consistency and best response, but can recover approximations of level-$k$, QRE, or typical Nash equilibrium behaviour in the limiting cases. The proposed Quantal Hierarchy model is based on a recursive form of the variational free energy principle, representing self-referential games as (pseudo) sequential decisions. Bounds in player processing abilities are captured as information costs, where future chains of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the applicability of the proposed model to several canonical economic games.
翻译:虽然游戏理论对决策具有变革作用,但在某些情况下,所作的假设可能过于限制性。在这项工作中,我们侧重于一些理性基础的假设,如相互一致和最佳反应,并考虑如何分别利用从水平-美元推理和二次反应平衡(QRE)的概念来放松这些假设。具体地说,我们提供了一种信息理论双参数模型,既可以放松相互一致性,也可以最佳反应,但可以在有限的案例中恢复到1美元、QRE或典型的纳什平衡行为的近似值。拟议的夸特尔分级模型以变异自由能源原则的累进形式为基础,作为(假想)顺序决定,代表自我优惠游戏。玩家的处理能力被记录为信息成本,因为未来的推理链被打折扣,意味着低级玩家的处理资源较少。我们展示了拟议模型对若干明理经济游戏的适用性。