Tit-for-Tat or Win-Stay, Lose-Shift?
AbstractThe repeated Prisoner's Dilemma is usually known as a story of tit-for-tat (TFT). This remarkable strategy has won both of Robert Axelrod's tournaments. TFT does whatever the opponent has done in the previous round. It will cooperate if the opponent has cooperated, and it will defect if the opponent has defected. But TFT has two weaknesses: (i) it cannot correct mistakes (erroneous moves) and (ii) a population of TFT players is undermined by random drift when mutant strategies appear which play always-cooperate (ALLC). Another equally simple strategy called â€˜win-stay, lose-shiftâ€™ (WSLS) has neither of these two disadvantages. WSLS repeats the previous move if the resulting payoff has met its aspiration level and changes otherwise. Here, we use a novel approach of stochastic evolutionary game dynamics in finite populations to study mutationâ€“selection dynamics in the presence of erroneous moves. We compare four strategies: always-defect (ALLD), ALLC, TFT and WSLS. There are two possible outcomes: if the benefit of cooperation is below a critical value then ALLD is selected; if the benefit of cooperation is above this critical value then WSLS is selected. TFT is never selected in this evolutionary process, but lowers the selection threshold for WSLS.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3200671.
Date of creation: 2007
Date of revision:
Publication status: Published in Journal of Theoretical Biology
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
- Drew Fudenberg & David K. Levine, 1996.
"The Theory of Learning in Games,"
Levine's Working Paper Archive
624, David K. Levine.
- D. Fudenberg & E. Maskin, 2010.
"Evolution and Cooperation in Noisy Repeated Games,"
Levine's Working Paper Archive
546, David K. Levine.
- Breitmoser, Yves, 2012. "Cooperation, but no reciprocity: Individual strategies in the repeated Prisoner's Dilemma," MPRA Paper 41731, University Library of Munich, Germany.
- Dal Bó, Pedro & Fréchette, Guillaume R., 2013. "Strategy choice in the infinitely repeated prisoners' dilemma," Discussion Papers, Research Unit: Economics of Change SP II 2013-311, Social Science Research Center Berlin (WZB).
- Pedro Dal Bó & Enrique R. Pujals, 2013. "The Evolutionary Robustness of Forgiveness and Cooperation," Working Papers 2013-5, Brown University, Department of Economics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Reinhard Engels).
If references are entirely missing, you can add them using this form.