The Price of a Chance in Artificial Societies

Rapid advances in large language models (LLMs) have enabled autonomous agents to interact, coordinate, and pursue individual goals in artificial societies. However, our understanding of how reward structures shape their competitive behavior and collective outcomes remains incomplete. We simulate 200 LLM agents competing over 50 rounds to maximize individual wealth. We define overcompetition and lying flat as population investment above and below a Bayesian adaptive baseline, respectively. At the lowest tested reward, populations lie flat; at the two highest, they overcompete, most strongly at intermediate winner coverage. The investment committed to pursuing an uncertain reward constitutes the price of a chance. Agents near the qualification cutoff can invest heavily yet receive no prize, finishing poorer than nonwinners who invest less. Agents' stated rationales link investment decisions to perceived qualification prospects and expected returns. At the collective level, greater investment does not consistently improve ability selection. With a fixed total prize budget, offering smaller prizes to more winners can reduce investment while preserving selection quality relative to the corresponding top-ability target. Further broadening reward coverage yields additional savings but reduces selection quality. These findings show how reward design shapes overcompetition and lying flat, distributes the costs of pursuing opportunity, and influences what competition collectively achieves.