Critical dynamics in the evolution of stochastic strategies for the iterated Prisoner's Dilemma

Abstract

The observed cooperation on the level of genes, cells, tissues, and individuals has been the object of intense study by evolutionary biologists, mainly because cooperation often flourishes in biological systems in apparent contradiction to the selfish goal of survival inherent in Darwinian evolution. In order to resolve this paradox, evolutionary game theory has focused on the Prisoner's Dilemma (PD), which incorporates the essence of this conflict. Here, we encode strategies for the iterated Prisoner's Dilemma (IPD) in terms of conditional probabilities that represent the response of decision pathways given previous plays. We find that if these stochastic strategies are encoded as genes that undergo Darwinian evolution, the environmental conditions that the strategies are adapting to determine the fixed point of the evolutionary trajectory, which could be either cooperation or defection. A transition between cooperative and defective attractors occurs as a function of different parameters such a mutation rate, replacement rate, and memory, all of which affect a player's ability to predict an opponent's behavior.

27 pages, including supplementary information. 5 figures, 4 suppl. figures. Version accepted for publication in PLoS Comp. Biol

References in corpus (8)

• Coevolutionary games - a mini review
• Evolutionary prisoner's dilemma game on a square lattice
• Social diversity and promotion of cooperation in the spatial prisoner's dilemma game
• Co-evolution of strategy and structure in complex networks with dynamical linking
• Evolution of Biological Complexity
• Evolutionary Games and Computer Simulations
• Mutation-selection equilibrium in games with multiple strategies
• Stochastic gain in population dynamics

Cited by in corpus (15)

• Colloquium: Criticality and dynamical scaling in living systems
• From extortion to generosity, the evolution of zero-determinant strategies in the prisoner's dilemma
• Cooperating with Machines
• Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything
• The use of information theory in evolutionary biology
• What is Information?
• Autocratic strategies for alternating games
• Thermodynamics of Evolutionary Games
• Evolution and stability of altruist strategies in microbial games
• Punishment in Public Goods games leads to meta-stable phase transitions and hysteresis
• Motion, fixation probability and the choice of an evolutionary process
• Topology dependent payoffs can lead to escape from prisoner's dilemma
• Darwinian Evolution of Cooperation via Punishment in the "Public Goods" Game
• Exploitation by asymmetry of information reference in coevolutionary learning in prisoner's dilemma game
• Promoting Cooperation in the Public Goods Game using Artificial Intelligent Agents