Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making

TL;DR

This paper introduces the Quantal Hierarchy model, a flexible decision-making framework that relaxes traditional game theory assumptions like mutual consistency and best response, using an information-theoretic approach to better model human-like reasoning.

Contribution

The paper proposes the Quantal Hierarchy model, which unifies and extends level-k reasoning and QRE by incorporating resource-bounded rationality through an information-theoretic recursive structure.

Findings

Effectively models both simultaneous and sequential economic games

Outperforms traditional models in out-of-sample predictions

Captures hierarchical reasoning resource limitations

Abstract

While game theory has been transformative for decision-making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of 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 propose an information-theoretic two-parameter model called the Quantal Hierarchy model, which can relax both mutual consistency and best response while still approximating level-$k$, QRE, or typical Nash equilibrium behaviour in the limiting cases. The model is based on a recursive form of the variational free energy principle, representing higher-order reasoning as (pseudo) sequential decision-making in extensive-form game tree. This representation enables us to treat simultaneous games in a similar manner to sequential games, where reasoning resources deplete throughout the game-tree. Bounds in player processing abilities are captured as information costs, where future branches of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the effectiveness of the Quantal Hierarchy model in several canonical economic games, {both simultaneous and sequential}, using out-of-sample modelling.