Metric-Based Equilibrium Selection in Noncooperative Differentiable Games
This study addresses the problem of selectively attracting specific equilibria in non-cooperative differentiable games without altering their equilibrium locations. To this end, it proposes a conditioning framework based on state-dependent symmetric positive-definite metrics, which achieves targeted equilibrium control by smoothly interpolating between stabilizing and destabilizing strategies. The authors demonstrate that player-independent metrics fail to preserve the stability of differential Nash equilibria, and accordingly construct a unified single metric field that retains all equilibria while prescribing their local stability types. The effectiveness of this approach is successfully validated through experiments on a continuous-commitment Stag Hunt game and an entropy-regularized Iterated Prisoner’s Dilemma.