Efficient Nash Equilibrium Computation for Cybersecurity Games

2026-09-23T17:51:24.264Z

• summary: Computing Nash equilibria of simulation-based cybersecurity games with policy-space response oracles (PSRO) is bottlenecked by payoff estimation: every payoff-matrix entry costs Monte-Carlo rollouts of a slow simulator, while policies and restricted-game solves are cheap. We introduce Regret-Weighted Payoff Sampling (RWPS), a budgeted estimator that simulates only the cells an equilibrium is sensitive to and fills the rest with a surrogate trained on every entry simulated earlier in the run. The sup-norm error bound cannot evaluate such an estimator, because it is set by the cells left deliber → Game-theoretic analyses of cyber defence often compute equilibria of games whose payoffs exist only as the output of a simulator. Iterative equilibrium-finding methods grow a set of attacker and defender policies and need the payoff of every attacker--defender pair, so they are bottlenecked by payoff estimation: each payoff costs many simulator runs. We introduce Regret-Weighted Payoff Sampling (RWPS), which spends a fixed simulation budget on the payoffs the equilibrium actually depends on and predicts the rest with a model trained on every payoff measured so far. Standard error bounds for es
• url: https://arxiv.org/abs/2609.19399v1 → https://arxiv.org/abs/2609.19399