Prisoner's Dilemma in One-Dimensional Cellular Automata: Visualization of Evolutionary Patterns

TL;DR

This paper explores the evolution of cooperation in a one-dimensional cellular automaton version of the Prisoner's Dilemma, revealing dynamic patterns and offering a new framework for studying cooperative behavior.

Contribution

It introduces a simplified, flexible model of the spatial Prisoner's Dilemma in one-dimensional cellular automata, enabling detailed visualization of evolutionary patterns and faster convergence.

Findings

Reproduces previous lattice results with improved efficiency

Visualizes cooperation and defection clusters as particle-like patterns

Provides insights into the emergence and maintenance of cooperation

Abstract

The spatial Prisoner's Dilemma is a prototype model to show the emergence of cooperation in very competitive environments. It considers players, at site of lattices, that can either cooperate or defect when playing the Prisoner's Dilemma with other z players. This model presents a rich phase diagram. Here we consider players in cells of one-dimensional cellular automata. Each player interacts with other z players. This geometry allows us to vary, in a simple manner, the number of neighbors ranging from one up to the lattice size, including self-interaction. This approach has multiple advantages. It is simple to implement numerically and we are able to retrieve all the previous results found in the previously considered lattices, with a faster convergence to stationary values. More remarkable, it permits us to keep track of the spatio-temporal evolution of each player of the automaton. Giving rise to interesting patterns. These patterns allow the interpretation of cooperation/defection clusters as particles, which can be absorbed and collided among themselves. The presented approach represents a new paradigm to study the emergence and maintenance of cooperation in the spatial Prisoner's Dilemma.