MORE SPATIAL GAMES

1994 ◽  
Vol 04 (01) ◽  
pp. 33-56 ◽  
Author(s):  
MARTIN A. NOWAK ◽  
SEBASTIAN BONHOEFFER ◽  
ROBERT M. MAY
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Reproductive Rate ◽  
Spatial Effects ◽  
Random Drift ◽  
Low Frequencies ◽  
Spatial Games

We extend our exploration of the dynamics of spatial evolutionary games [Nowak & May 1992, 1993] in three distinct but related ways. We analyse, first, deterministic versus stochastic rules; second, discrete versus continuous time (see Hubermann & Glance [1993]); and, third, different geometries of interaction in regular and random spatial arrays. We show that spatial effects can change some of the intuitive concepts in evolutionary game theory: (i) equilibria among strategies are no longer necessarily characterised by equal average payoffs; (ii) the strategy with the higher average payoff can steadily converge towards extinction; (iii) strategies can become extinct even though their basic reproductive rate (at very low frequencies) is larger than one. The equilibrium properties of spatial games are instead determined by “local relative payoffs.” We characterise the conditions for coexistence between cooperators and defectors in the spatial prisoner’s dilemma game. We find that cooperation can be maintained if the transition rules give more weight to the most successful neighbours, or if there is a certain probability that cells may remain unoccupied in the next generations when they are surrounded by players with low payoffs. In this second case the cooperators can survive despite a very large payoff advantage to defectors. We also compute average extinction times for random drift in neutral spatial models. Finally we briefly describe the spatial dynamics of an interaction among three species which dominate each other in a cyclic fashion. The emphasis of this paper is presenting a variety of ideas and possibilities for further research in the evolutionary dynamics of spatial games. The overall conclusion is that interactions with local neighbours in 2- or 3-dimensional spatial arrays can promote coexistence of different strategies (such as cooperators and defectors in the Prisoner’s Dilemma), in situations where one strategy would exclude all others if the interactions occurred randomly and homogeneously.

A Strategy with Novel Evolutionary Features for the Iterated Prisoner's Dilemma

2009 ◽  
Vol 17 (2) ◽  
pp. 257-274 ◽  
Author(s):  
Jiawei Li ◽  
Graham Kendall
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Evolution Of Cooperation ◽  
Iterated Prisoner's Dilemma ◽  
Evolutionary Features ◽  
Group Members ◽  
Identification Mechanism ◽  
Iterated Prisoner’S Dilemma

In recent iterated prisoner's dilemma tournaments, the most successful strategies were those that had identification mechanisms. By playing a predetermined sequence of moves and learning from their opponents' responses, these strategies managed to identify their opponents. We believe that these identification mechanisms may be very useful in evolutionary games. In this paper one such strategy, which we call collective strategy, is analyzed. Collective strategies apply a simple but efficient identification mechanism (that just distinguishes themselves from other strategies), and this mechanism allows them to only cooperate with their group members and defect against any others. In this way, collective strategies are able to maintain a stable population in evolutionary iterated prisoner's dilemma. By means of an invasion barrier, this strategy is compared with other strategies in evolutionary dynamics in order to demonstrate its evolutionary features. We also find that this collective behavior assists the evolution of cooperation in specific evolutionary environments.

scholarly journals Evolutionary games and population dynamics: maintenance of cooperation in public goods games

2006 ◽  
Vol 273 (1600) ◽  
pp. 2565-2571 ◽  
Author(s):  
Christoph Hauert ◽  
Miranda Holmes ◽  
Michael Doebeli
Keyword(s):  
Public Goods ◽  
Prisoner's Dilemma ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Natural Extension ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Darwinian Evolution ◽  
Ecological Dynamics ◽  
Public Goods Games

The emergence and abundance of cooperation in nature poses a tenacious and challenging puzzle to evolutionary biology. Cooperative behaviour seems to contradict Darwinian evolution because altruistic individuals increase the fitness of other members of the population at a cost to themselves. Thus, in the absence of supporting mechanisms, cooperation should decrease and vanish, as predicted by classical models for cooperation in evolutionary game theory, such as the Prisoner's Dilemma and public goods games. Traditional approaches to studying the problem of cooperation assume constant population sizes and thus neglect the ecology of the interacting individuals. Here, we incorporate ecological dynamics into evolutionary games and reveal a new mechanism for maintaining cooperation. In public goods games, cooperation can gain a foothold if the population density depends on the average population payoff. Decreasing population densities, due to defection leading to small payoffs, results in smaller interaction group sizes in which cooperation can be favoured. This feedback between ecological dynamics and game dynamics can generate stable coexistence of cooperators and defectors in public goods games. However, this mechanism fails for pairwise Prisoner's Dilemma interactions and the population is driven to extinction. Our model represents natural extension of replicator dynamics to populations of varying densities.

scholarly journals Matthew Effect of the Random Drift on the Evolution of Cooperation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chao Liu ◽  
Rong Li
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Prisoner’S Dilemma ◽  
Matthew Effect ◽  
Evolution Of Cooperation ◽  
Random Drift ◽  
Prisoner’S Dilemma Game ◽  
Regular Lattices ◽  
The Matthew Effect ◽  
Pattern Formations

The effect of the random drift on the evolutionary prisoner’s dilemma game is studied on regular lattices. A new evolutionary rule is proposed, which stochastically combines the deterministic rule with the random drift rule. It is found that the random drift has an effect on the evolutionary dynamics depending on the values of the temptation-to-defectband the probabilitypof the random drift. When the random drift occurs with low probabilities, which interests us more, a phenomenon of the Matthew effect on the evolution of cooperation is found. Explanations of this phenomenon are deduced through the analysis on the dynamics and pattern formations of the PDG system.

scholarly journals SATO–CRUTCHFIELD FORMULATION FOR SOME EVOLUTIONARY GAMES

2003 ◽  
Vol 14 (07) ◽  
pp. 963-971 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI ◽  
A. S. ELGAZZAR
Keyword(s):  
Prisoner's Dilemma ◽  
Initial Conditions ◽  
Evolutionarily Stable Strategy ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Theoretical Explanation ◽  
Battle Of The Sexes ◽  
Different Types ◽  
Evolutionarily Stable ◽  
Rules Of The Game

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoner's dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

THE EFFECT OF PINNING CONTROL ON EVOLUTIONARY PRISONER'S DILEMMA GAME

2010 ◽  
Vol 24 (25) ◽  
pp. 2581-2589 ◽  
Author(s):  
WEN-BO DU ◽  
HONG ZHOU ◽  
ZHEN LIU ◽  
XIAN-BIN CAO
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Pinning Control ◽  
Control Mechanisms ◽  
Control Cost ◽  
Prisoner’S Dilemma Game ◽  
Scale Free ◽  
Prisoner's Dilemma Game ◽  
Control Degree

The evolutionary game on graphs provides a natural framework to investigate the cooperation behavior existing in natural and social society. In this paper, degree-based pinning control and random pinning control are introduced into the evolutionary prisoner's dilemma game on scale-free networks, and the effects of control mechanism and control cost on the evolution are studied. Numerical simulation shows that forcing some nodes to cooperate (defect) will increase (decrease) the frequency of cooperators. Compared with random pinning control, degree-based pinning control is more efficient, and degree-based pinning control costs less than random pinning control to achieve the same goal. Numerical results also reveal that the evolutionary time series is more stable under pinning control mechanisms, especially under the degree-based pinning control.

scholarly journals Learning dynamics explains human behaviour in Prisoner's Dilemma on networks

2014 ◽  
Vol 11 (94) ◽  
pp. 20131186 ◽  
Author(s):  
Giulio Cimini ◽  
Angel Sánchez
Keyword(s):  
Social Factors ◽  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Prisoner’S Dilemma ◽  
Conditional Cooperation ◽  
The Past ◽  
Extensive Analysis ◽  
Emergence Of Cooperation ◽  
Experimental Findings ◽  
Evolutionarily Stable

Cooperative behaviour lies at the very basis of human societies, yet its evolutionary origin remains a key unsolved puzzle. Whereas reciprocity or conditional cooperation is one of the most prominent mechanisms proposed to explain the emergence of cooperation in social dilemmas, recent experimental findings on networked Prisoner's Dilemma games suggest that conditional cooperation also depends on the previous action of the player—namely on the ‘mood’ in which the player is currently in. Roughly, a majority of people behave as conditional cooperators if they cooperated in the past, whereas they ignore the context and free ride with high probability if they did not. However, the ultimate origin of this behaviour represents a conundrum itself. Here, we aim specifically to provide an evolutionary explanation of moody conditional cooperation (MCC). To this end, we perform an extensive analysis of different evolutionary dynamics for players' behavioural traits—ranging from standard processes used in game theory based on pay-off comparison to others that include non-economic or social factors. Our results show that only a dynamic built upon reinforcement learning is able to give rise to evolutionarily stable MCC, and at the end to reproduce the human behaviours observed in the experiments.

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