Novel Privacy-Preserving Nash Equilibrium Computation with Pointwise Maximal Leakage Guarantees
Guanpu Chen, Zhaoyang Cheng, Tobias J. Oechtering, Mikael Skoglund · 2025
This paper investigates privacy-preserving Nash equilibrium (NE) computation in non-cooperative games where players may have correlated payoff functions with prior knowledge. Although mechanisms with differential privacy (DP) guarantees are widely used to mitigate information leakage, their privacy guarantees are ineffective for correlated datasets. To address this limitation, we are inspired by pointwise maximal leakage (PML), a recently proposed privacy measure that exploits prior knowledge for assessing information leakage. We first revisit the traditional privacy-preserving mechanism and demonstrate that its PML guarantee averaged over players can be bounded by its DP guarantee. On this basis, we propose a novel NE-computing mechanism that integrates prior knowledge of players' payoff datasets into noise design, ensuring the adaptation of existing techniques for convergence guarantees. Furthermore, we show that the proposed mechanism offers a tighter bound with PML guarantees than the traditional mechanism with DP guarantees, which refines the over-conservative assessment of information leakage risks with correlated payoff datasets. Numerical experiments illustrate the effectiveness of our theoretical results.