A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game

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@Article{nowak-1993a,
  author         = {Martin Nowak and Karl Sigmund},
  title          = {A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game},
  year           = {1993},
  volume         = {364},
  review-dates   = {2005-02-22},
  value          = {ca},
  month          = {July},
  pages          = {56--58},
  read-status    = {reviewed},
  journal        = {Nature},
  url            = {http://www.ped.fas.harvard.edu/pdf_files/Nature93.pdf},
  hardcopy       = {yes},
  key            = {nowak-1993a}
}

Summary

This is a short work, a letter to Nature, and describes how a win-stay, lose-shift (WSLS)* strategy (aka Pavlov (simple, aka "simpleton") has generally superior performance to TFT (including 'generous' TFT or GTFT, which cooperates after any opponent moves C and some fraction of D actions).

[WSLS is my notation, not paper's]

Problems with TFT:

  1. TFT can allow unconditional cooperators to flourish and allow for later invasion by exploiters of those unconditional cooperators.
  2. Mistakes, noise, or error can elicit retaliation sequences amongst TFT populations, reducing performance.

Nowak and Sigmund had believed GTFT would win out, but Pavlov did much better in the long run.

WSLS-Pavlov distinctions:

Cooperation was only 27.5% (payoff ave>2.95) after t=10^4, but went up to 90% at t=10^7.

"The success of Pavlov-like behaviour does not seem to be restricted to strategies which only remember the last move. In other evolutionary runs, where mutations can extend the memory length, similar strategies have been found: typically they resume cooperation after two rounds of mutual defection." [Axelrod, Lindgren]


Key Factors

Relations to Other Work:

Problem Addressed: Is a WSLS Pavlov or a TFT-variant superior in an evolutionary game with mutation and long-time horizons. How stable are the resulting populations?

Main Claim and Evidence: Pavlov is superior to GTFT and TFT in tournaments with noise over long-term evolutionary simulations. Significant experiments and sufficient analysis confirm this.

The level of stability appears to increase over longer time horizons, but the system may fluctuate from high average scores to low at any time... and the transitions are very quick, only a few generations amongst hundreds of thousands.

Assumptions:

Next Steps:

No future plans of action described.

Remaining Open Questions:

Authors leave some lingering doubt about dominance of win-stay, lose-shift.


Quality

Originality is good.
Contribution/Significance is good.
Quality of organization is excellent.
Quality of writing is outstanding.
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