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arXiv · 2502.05246

Optimizing Wealth by a Game within Cellular Automata

Rolf Hoffmann·Franciszek Seredyński·Dominique Désérable
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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.

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Rolf Hoffmann, Franciszek Seredyński, Dominique Désérable. 2025-02-07. Optimizing Wealth by a Game within Cellular Automata. https://arxiv.org/abs/2502.05246

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