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How To Cope With Noise in the Iterated Prisoner's Dilemma

Summary of: How To Cope With Noise in the Iterated Prisoner's Dilemma

Author(s) / Editor(s)

Axelrod, Robert, Wu, Jiangzhong
The Tit-for-Tat strategy is vulnerable to noise – errors in implementing choices – that can lead to echoing defections, but can be made less sensitive by adding generosity (occasionally refraining from punishing defection by opponent) and contrition (refraining from punishing a reaction to accidental defection.)"

Disciplines

Biology, Computer Science, Economics, Political Science

Keywords

agent-based model, complexity, cooperation, game theory, reciprocity, tit-for-tat, prisoners dilemma

Publication Reference

Published in/by
Journal of Conflict Resolution 39, No. 1: 183-189
Date
March 1995

Findings

  • Random errors in implementing strategies is common in the real world ("noise"), and Tit-for-Tat is sensitive to noise because echoes of a mistake (a defection that was meant to be a cooperation) can continue indefinitely.
  • An article in Nature, 1993 (Nowak& Sigmund, "Strategy of Win-Stay, Lose Shift That Outperforms Tit-for-Tat," 364: 56-58) highlighted a strategy that also applies to real-world situations – defectors can shift partners until they find those that are exploitable, and cooperators can shift partners until they find co-cooperators.

Axelrod became concerned with the problem of noise – mistaken defections in Prisoner's Dilemma games that can lead to echoing repetitions – during the Cuban Missile crisis. Adding generosity and contrition to Tit-for-Tat and reimplementing the 63 rules of the original iterated Prisoner's Dilemma tournament proved to be an effective way of coping with noise; Win-Stay, Lose-Shift did not do as well in such an environment. Axelrod was able to put Soviet and US nuclear strategists together to play Prisoner's Dilemma in 1988 for an audience of social scientists -- with noise deliberately introduced. This tournament was the basis for Axelrod's statement that "Noise calls for forgiveness, but too much forgiveness invites exploitation." The authors also noted: "Generosity can correct an error by either player, but contrition can only correct one's own error. Thus, when the population of strategies one is likely to meet has not adapted to the presence of noise, a strategy like Generous Tit-for-Tat is likely to be effective. On the other hand, if the strategies of the other players one is likely to meet have already adapted to noise, then a strategy like Contrite Tit-for-Tat is likely to be even more effective because it can correct its own errors and restore mutual cooperation almost immediately."