Can CAs optimize wealth in a Prisoner's Dilemma?
Optimizing Wealth by a Game within Cellular Automata
February 11, 2025
https://arxiv.org/pdf/2502.05246This paper explores using Cellular Automata (CA) to create 2D patterns optimized for a global objective function, defined as the sum of local utilities. A specific utility function based on a spatial Prisoner's Dilemma game is used, where wealth is maximized by balancing cooperators and defectors. A genetic algorithm (GA) finds optimal patterns, from which local matching templates are extracted. These templates are then incorporated into a probabilistic CA rule to generate larger, optimized patterns.
Key points for LLM-based multi-agent systems:
- Emergent Behavior: The CA approach demonstrates how simple local rules (templates) can lead to complex, optimized global patterns (wealth maximization), mirroring how simple agent interactions can achieve complex goals. LLMs could be used to generate more complex templates based on higher-level descriptions of desired outcomes.
- Agent Cooperation and Competition: The Prisoner's Dilemma aspect highlights the interplay of cooperation and competition in multi-agent systems. LLMs can model agent behavior with nuanced strategies beyond simple cooperation or defection.
- Pattern Recognition and Generation: Extracting templates from optimal patterns and using them in the CA rule is analogous to learning successful interaction patterns and applying them. LLMs can accelerate this learning process by analyzing and generalizing successful multi-agent interactions.
- Optimization: The GA-driven optimization process parallels training multi-agent systems. LLMs can act as agents within a similar evolutionary process, learning to optimize their behaviors to achieve a global objective.
- Scalability: The paper shows how the CA framework addresses scalability by using local interactions, an important consideration for complex LLM-based multi-agent systems.