Scaling Laws for Strategic Interactions

LLM agents increasingly negotiate on behalf of users and firms, often under asymmetries in capability or number. Does a more capable agent grow joint surplus, or extract an unfair share at weaker counterparts' expense? We run scaling-law-style sweeps along three axes---agent capability (LMArena Elo and reasoning-token budget), agent count (up to ), and degree of competition---across three new multi-turn negotiation games: item allocation, treaty bargaining, and participatory budgeting. Across 5{,}000+ games and 30+ models, scaling capability simultaneously increases joint efficiency and the surplus utility stronger agents extract from weaker ones, with the crossover from fair to exploitative play within the current frontier. Game structure mediates these effects: treaty bargaining absorbs capability gaps more stably than the other two. Capability scaling itself becomes non-monotone at high competition, and test-time-compute scaling does not reliably translate into bargaining gains. Selecting a more capable LLM agent does not guarantee a Pareto improvement, with implications for economic deployment and scalable oversight. Our code to reproduce our experiments can be found here: https://anonymous.4open.science/r/bargain/README.md