Bounded rationality for relaxing best response and mutual consistency: An information-theoretic model of partial self-reference

• URL: http://arxiv.org/abs/2106.15844v1
• Date: Wed, 30 Jun 2021 06:56:56 GMT
• Title: Bounded rationality for relaxing best response and mutual consistency: An information-theoretic model of partial self-reference
• Authors: Benjamin Patrick Evans, Mikhail Prokopenko
• Abstract summary: This work focuses on some of the assumptions underlying rationality such as mutual consistency and best-response. We consider ways to relax these assumptions using concepts from level-$k$ reasoning and quantal response equilibrium (QRE) respectively.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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