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 approach 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.
翻译:虽然游戏理论对决策具有变革性,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1千元推理和四舍五入反应平衡(QRE)的概念来放松这些假设。具体地说,我们提供了一个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,但在有限情况下可以恢复1千元、QRE或典型的纳什平衡行为的近似。 提议的方法基于变异自由能源原则的累进形式,代表(假想)顺序决定的自我偏好游戏。 玩家处理能力被记录为信息成本,而未来的推理链被打折扣,意味着低级参与者的处理资源较少。