When is tit-for-tat unbeatable?

TL;DR

This paper characterizes the class of symmetric two-player games where tit-for-tat and similar imitation strategies are unbeatable, identifying exact potential games as the key setting where these strategies are effective.

Contribution

It establishes that tit-for-tat and related imitation rules are essentially unbeatable in exact potential games, covering a wide range of common game types.

Findings

Tit-for-tat is unbeatable in exact potential games.

Includes a broad class of imitation rules like imitate-the-best.

Applicable to many standard game models such as Cournot, price competition, and public goods.

Abstract

We characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but also imitate-the-best and imitate-if-better. Every decision rule in this class is essentially unbeatable in exact potential games. Our results apply to many interesting games including all symmetric 2x2 games, and standard examples of Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.