On "Indifference" and Backward Induction in Games with Perfect Information

TL;DR

This paper explores the limitations of small perturbations in resolving player indifference in perfect information games and proposes refined rationality concepts like Tit-for-Tat to better handle ties.

Contribution

It introduces a new perspective on resolving indifference in game theory by refining rationality concepts to account for strategic interdependencies.

Findings

Small perturbations cannot handle indifference due to strategic impact.

Refined rationality concepts like Tit-for-Tat can better resolve ties.

Strategic interdependencies influence players' indifference decisions.

Abstract

Indifference of a player with respect to two distinct outcomes of a game cannot be handled by small perturbations, because the actual choice may have significant impact on other players, and cause them to act in a way that has significant impact of the indifferent player. It is argued that ties among rational choices can be resolved by refinements of the concept of rationality based on the utilities of other players. One such refinement is the concept of Tit-for-Tat.