🤖 AI Summary
In non-cooperative games, Nash equilibrium efficiency is often low due to multiplicity of equilibria and highly sensitive to minor mechanism perturbations, resulting in instability. This paper proposes a lightweight mechanism design framework that introduces a resource-constrained game coordinator. Rather than avoiding such sensitivity, the coordinator actively exploits the inherent instability of efficiency operators via minimal rule adjustments—e.g., localized information interventions or preference shifts. Theoretical analysis and robustness verification demonstrate that, under strict resource constraints, this approach induces stepwise improvements in equilibrium efficiency. We further derive analytical necessary and sufficient conditions for the coordinator’s optimal intervention strategy. To our knowledge, this is the first work to transform the sensitivity of equilibrium efficiency into a design advantage, yielding a novel regulation paradigm for multi-agent systems that jointly ensures feasibility and high efficiency.
📝 Abstract
It is well known that a non-cooperative game may have multiple equilibria. In this paper we consider the efficiency of games, measured by the ratio between the aggregate payoff over all Nash equilibria and that over all admissible controls. Such efficiency operator is typically unstable with respect to small perturbation of the game. This seemingly bad property can actually be a good news in practice: it is possible that a small change of the game mechanism may improve the efficiency of the game dramatically. We shall introduce a game mediator with limited resources and investigate the mechanism designs aiming to improve the efficiency.