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

  title={A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game},
  author={Martin A. Nowak and Karl Sigmund},
THE Prisoner's Dilemma is the leading metaphor for the evolution of cooperative behaviour in populations of selfish agents, especially since the well-known computer tournaments of Axelrod1 and their application to biological communities2,3. In Axelrod's simulations, the simple strategy tit-for-tat did outstandingly well and subsequently became the major paradigm for reciprocal altruism4 12. Here we present extended evolutionary simulations of heterogeneous ensembles of probabilistic strategies… 
Tit-for-tat or win-stay, lose-shift?
A strategy of No-Tricks that sets the stage for unconditional cooperators in Prisoner’s Dilemma
Here it is proposed a promising cooperative strategy of No-Tricks, which wins against WSLS and some other well-known strategies, particularly inhibiting the evolution of ALLD.
Win-Stay-Lose-Learn Promotes Cooperation in the Spatial Prisoner's Dilemma Game
It is shown that even a minute initial fraction of cooperators may be sufficient to eventually secure a highly cooperative final state, and it is found that the proposed win-stay-lose-learn rule promotes the evolution of cooperation very robustly and independently of the initial conditions.
Is Tit-for-Tat the Answer? On the Conclusions Drawn from Axelrod's Tournaments
It is argued that the generality of the results and the policy implications drawn from them are in doubt because the efficacy of tit-for-tat is contingent on the design of the tournament, the criterion used to determine success, and the particular values chosen for the Prisoner’s Dilemma payoff matrix.
Whence tit-for-tat?
T tit-for-tat could be important in nature for cognitively simple organisms of limited memory capacity, in strongly kin-selected or group-selected populations, when interaction sequences between individuals are relatively short, in moderate-sized populations of widely interacting individuals and when defectors appear in the population with moderate frequency.
Win-Stay-Lose-Shift as a self-confirming equilibrium in the iterated Prisoner’s Dilemma
It is argued that players can escape from full defection into a cooperative equilibrium supported by Win-Stay-Lose-Shift in a self-confirming manner, provided that the cost of cooperation is low and the observational learning supplies sufficiently large uncertainty.
Are there really no evolutionarily stable strategies in the iterated prisoner's dilemma?
It is shown that when e is sufficiently small, exactly three one-move memory ESSs exist in S, and it is proved that X is an ESS in S if and only if X is a Nash equilibrium in the set consisting of only S's boundary strategies.
A New Type of Evolutionary Strategy Based on a Multi-player Iterated Prisoner’s Dilemma Game
Abstract According to the philosophy of self-cultivation that “one should refine his personal virtue when in poverty, and help save the world when in success”, a new type of evolutionary strategy,


Tit for tat in heterogeneous populations
It is found that a small fraction of TFT players is essential for the emergence of reciprocation in a heterogeneous population, but only paves the way for a more generous strategy.
TIT FOR TAT in sticklebacks and the evolution of cooperation
Using a system of mirrors, single three-spined sticklebacks approaching a live predator were provided with either a simulated cooperating companion or a simulated defecting one supporting the hypothesis that cooperation can evolve among egoists.
No pure strategy is evolutionarily stable in the repeated Prisoner's Dilemma game
It is argued that no pure strategy can be evolutionarily stable in the repeated Prisoner's Dilemma game, which casts doubt on several of Axelrod's conclusions about the evolution of reciprocity.
Evolutionary games and spatial chaos
MUCH attention has been given to the Prisoners' Dilemma as a metaphor for the problems surrounding the evolution of coopera-tive behaviour1–6. This work has dealt with the relative merits of various
Chaos and the evolution of cooperation.
  • M. Nowak, K. Sigmund
  • Biology
    Proceedings of the National Academy of Sciences of the United States of America
  • 1993
Here it is shown that a heterogeneous population consisting of simple strategies, whose behavior is totally specified by the outcome of the previous round, can lead to persistent periodic or highly irregular oscillations in the frequencies of the strategies and the overall level of cooperation.
Evolution and the Theory of Games
It is beginning to become clear that a range of problems in evolution theory can most appropriately be attacked by a modification of the theory of games, a branch of mathematics first formulated by Von Neumann and Morgenstern in 1944 for the analysis of human conflicts.
Mutual Restraint in Tree Swallows: A Test of the TIT FOR TAT Model of Reciprocity
The TIT FOR TAT model of reciprocity, which is based on a successful program for the game known as the Prisoner's Dilemma, was experimentally tested on a population of tree swallows and found parents behaved as predicted by the model.
The evolution of cooperation.
A model is developed based on the concept of an evolutionarily stable strategy in the context of the Prisoner's Dilemma game to show how cooperation based on reciprocity can get started in an asocial world, can thrive while interacting with a wide range of other strategies, and can resist invasion once fully established.
The Further Evolution of Cooperation
Empirical andoretical work has led to a deeper understanding of the role of other factors in the evolution of cooperation: the number of players, the range of possible choices, variation in the payoff structure, noise, the shadow of the future, population dynamics, and population structure.