Social welfare optimisation in well-mixed and structured populations

Research on promoting cooperation among autonomous, self-regarding agents has often focused on the bi-objective optimisation problem: minimising the total incentive cost while maximising the frequency of cooperation. However, the optimal value of social welfare under such constraints remains largely unexplored. In this work, we hypothesise that achieving maximal social welfare is not guaranteed at the minimal incentive cost required to drive agents to a desired cooperative state. To address this gap, we adopt to a single-objective approach focused on maximising social welfare, building upon foundational evolutionary game theory models that examined cost efficiency in finite populations, in both well-mixed and structured population settings. Our analytical model and agent-based simulations show how different interference strategies, including rewarding local versus global behavioural patterns, affect social welfare and dynamics of cooperation. Our results reveal a significant gap in the per-individual incentive cost between optimising for pure cost efficiency or cooperation frequency and optimising for maximal social welfare. Overall, our findings indicate that incentive design, policy, and benchmarking in multi-agent systems and human societies should prioritise welfare-centric objectives over proxy targets of cost or cooperation frequency.