# When is tit-for-tat unbeatable?

## Author

Listed:
• Peter Duersch

()

• Jörg Oechssler

()

• Burkhard Schipper

()

## 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 2 $$\times$$ 2 games, and standard examples of Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games. Copyright Springer-Verlag Berlin Heidelberg 2014

## Suggested Citation

• Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2014. "When is tit-for-tat unbeatable?," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 25-36, February.
• Handle: RePEc:spr:jogath:v:43:y:2014:i:1:p:25-36
DOI: 10.1007/s00182-013-0370-1
as

File URL: http://hdl.handle.net/10.1007/s00182-013-0370-1

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## References listed on IDEAS

as
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9. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 553-564, August.
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## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. repec:elg:eechap:15532_7 is not listed on IDEAS
2. Andreas Ortmann & Leonidas Spiliopoulos, 2017. "The beauty of simplicity? (Simple) heuristics and the opportunities yet to be realized," Chapters,in: Handbook of Behavioural Economics and Smart Decision-Making, chapter 7, pages 119-136 Edward Elgar Publishing.
3. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.

### Keywords

Imitation; Tit-for-tat; Decision rules; Learning; Exact potential games; Symmetric games; Repeated games; Relative payoffs; Zero-sum games; C72; C73; D43;

### JEL classification:

• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
• C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
• D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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