Which Nash Equilibrium? Solver-Dependent Selection on Zero-Sum Nash Polytopes

In competitive games — from poker to cybersecurity — there isn't always a single optimal strategy, but rather a whole family of equally valid equilibria. Which one an AI solver picks can quietly determine how it behaves against opponents who don't play perfectly. This work reveals that the choice of algorithm, not random chance, systematically drives which equilibrium gets selected. Regularized methods like R-NaD tend toward maximum-entropy (most unpredictable) strategies, while regret-averaging methods like CFR drift toward more exploitable ones. This has direct implications for AI agents in auctions, negotiations, multi-agent games, and any setting where strategic robustness against imperfect opponents matters. Authors: Luis Leal Paper: https://arxiv.org/abs/2606.28308v1