@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

[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:

• - doesn't do well against All-D, as every other round Pavlov switches. Pavlov itself can't invade All-D, requires something like TFT to first invade.
• + Pavlov gracefully recovers from noise or errors resulting in D, whereas TFT will continue titting and tatting. "..Pavlov is fairly tolerant, like GTFT, and can correct mistakes."
• + Pavlov can exploit a sucker, given an error in which it can discover defection leads to success.
• Has best advantage among nicest strategies [can exploit suckers and cooperate with tat-capable cooperators].

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

• kraines-1989a
• Win-stay, lose-shift is a widespread rule according to M. Domjan and B. Burkhart in "The Principles of Learning and Behavior" (Brooks/Cole, Monterey, 1986)
• "simpleton" which is same as Pavlov goes back to 1965 and Rapaport
• Axelrod's GA and simulated annealing

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:

• Stochastic strategies considered, using probabilities (p1,p2,p3,p4) corresponding to cooperation next round based on whether the result was (R,S,T,or P) respectively. TFT=(1,0,1,0) and WSLS-Pavlov=(1,0,0,1).
• Many generations in simulations 10^4 considered short-term, 10^7 considered long-term (end of game).
• Mutation

No future plans of action described.

Remaining Open Questions:

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

Quality