New game theory model optimizes social welfare with rewards and punishments

In a new arXiv preprint, researchers tackle a critical but overlooked aspect of institutional incentives in multi-agent systems: maximizing social welfare rather than simply minimizing institutional cost or maximizing cooperation frequency. The team—spanning Vietnamese universities, Adobe Research, and the University of Birmingham—analyzes finite, well-mixed populations playing classic social dilemmas (Donation Game and Public Goods Game). They consider both reward-based and punishment-based incentive mechanisms, deriving closed-form expressions for expected total population payoff net of institutional expenditure. Their analysis reveals that the relationship between incentive strength and social welfare can be non-monotonic, with single optimal levels in some parameter regimes and qualitative phase transitions leading to multiple local optima in others.

The researchers prove that any welfare-maximizing incentive is either zero or concentrated around a simple closed-form target, and they provide an efficient algorithm to compute these optima. Importantly, they derive conditions under which reward outperforms punishment for any given budget, challenging common assumptions about the relative efficacy of punishment. The results expose a systematic gap between incentives optimized for cost or cooperation frequency and those that truly maximize overall welfare—a finding with direct implications for designing AI systems, governance mechanisms, and economic policies. By shifting the optimization objective to total welfare, the work offers a more rigorous foundation for incentive design in both human and artificial agent societies.