Optimizing Wealth by a Game within Cellular Automata

TL;DR

This paper develops a method to discover cellular automata rules that optimize global social wealth by evolving patterns that maximize collective payoffs in a game-theoretic context, using genetic algorithms and local neighborhood analysis.

Contribution

It introduces a novel approach combining genetic algorithms and cellular automata to optimize social wealth in a game-theoretic setting, specifically for prisoner's dilemma scenarios.

Findings

The constructed CA rule finds optimal patterns for various grid sizes.

Optimal patterns of odd size contain a single 2x2 cooperator block.

The method effectively maximizes collective payoffs in the modeled system.

Abstract

The objective is to find a Cellular Automata (CA) rule that can evolve 2D patterns that are optimal with respect to a global fitness function. The global fitness is defined as the sum of local computed utilities. A utility or value function computes a score depending on the states in the local neighborhood. First the method is explained that was followed to find such a CA rule. Then this method is applied to find a rule that maximizes social wealth. Here wealth is defined as the sum of the payoffs that all players (agents, cells) receive in a prisoner's dilemma game, and then shared equally among them. The problem is solved in four steps: (0) Defining the utility function, (1) Finding optimal master patterns with a Genetic Algorithm, (2) Extracting templates (local neighborhood configurations), (3) Inserting the templates in a general CA rule. The constructed CA rule finds optimal and near-optimal patterns for even and odd grid sizes. Optimal patterns of odd size contain exactly one singularity, a 2 x 2 block of cooperators.