When is Tit-for-Tat Unbeatable?

15 Pages Posted: 24 Jan 2013

See all articles by Peter Dürsch

Peter Dürsch

Heidelberg University - Faculty of Economics and Social Studies

Joerg Oechssler

University of Heidelberg - Alfred Weber Institute for Economics

Burkhard C. Schipper

University of California, Davis - Department of Economics

Date Written: January 22, 2013

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.

Keywords: Imitation, tit-for-tat, decision rules, learning, exact potential games, symmetric games, repeated games, relative payoffs, zero-sum games

JEL Classification: C72, C73, D43

Suggested Citation

Dürsch, Peter and Oechssler, Joerg and Schipper, Burkhard C., When is Tit-for-Tat Unbeatable? (January 22, 2013). Available at SSRN: https://ssrn.com/abstract=2206020 or http://dx.doi.org/10.2139/ssrn.2206020

Peter Dürsch

Heidelberg University - Faculty of Economics and Social Studies ( email )

Grabengasse 14
Heidelberg, D-69117
Germany

Joerg Oechssler

University of Heidelberg - Alfred Weber Institute for Economics ( email )

Grabengasse 14
Heidelberg, D-69117
Germany
+49 6221 54 3548 (Phone)
+49 6221 54 3630 (Fax)

HOME PAGE: http://www.awi.uni-heidelberg.de/with2/theorie2/Team/Oechssler/Oechssler_main.html

Burkhard C. Schipper (Contact Author)

University of California, Davis - Department of Economics ( email )

One Shields Drive
Davis, CA 95616-8578
United States
530-752-6142 (Phone)
530-752-9382 (Fax)

HOME PAGE: http://www.econ.ucdavis.edu/faculty/schipper/

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