On "Indifference" and Backward Induction in Games with Perfect Information
This addresses a theoretical issue in game theory for researchers, but it appears incremental as it builds on existing concepts like Tit-for-Tat without broad empirical validation.
The paper tackles the problem of handling player indifference in perfect-information games, where small perturbations fail due to significant impacts on other players, and proposes resolving ties using rationality refinements based on others' utilities, such as Tit-for-Tat.
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.