Bounded Rationality, Strategy Simplification, and Equilibrium

TL;DR

This paper introduces a new equilibrium concept in game theory where players choose simplified strategies that are stable against deviations, focusing on automata-based strategies in repeated games.

Contribution

It proposes a novel equilibrium notion considering careful strategy simplification that accounts for opponents' responses, extending prior work on bounded rationality.

Findings

Techniques for verifying equilibrium outcomes

Structural results on equilibria in automata-based strategies

Analysis of strategy simplification stability

Abstract

It is frequently suggested that predictions made by game theory could be improved by considering computational restrictions when modeling agents. Under the supposition that players in a game may desire to balance maximization of payoff with minimization of strategy complexity, Rubinstein and co-authors studied forms of Nash equilibrium where strategies are maximally simplified in that no strategy can be further simplified without sacrificing payoff. Inspired by this line of work, we introduce a notion of equilibrium whereby strategies are also maximally simplified, but with respect to a simplification procedure that is more careful in that a player will not simplify if the simplification incents other players to deviate. We study such equilibria in two-player machine games in which players choose finite automata that succinctly represent strategies for repeated games; in this context, we present techniques for establishing that an outcome is at equilibrium and present results on the structure of equilibria.