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

TL;DR

This paper investigates how stochastic strategies in the iterated Prisoner's Dilemma evolve under different environmental conditions, revealing phase transitions between cooperation and defection influenced by mutation, replacement, and memory parameters.

Contribution

It introduces a gene-based encoding of stochastic strategies in the IPD and analyzes how environmental factors drive transitions between cooperative and defective states.

Findings

Environmental conditions determine the fixed point of strategy evolution.

Transitions between cooperation and defection depend on mutation and memory.

Evolutionary trajectories exhibit critical dynamics and phase transitions.

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.