Strategic Testing in Games

When chess world champion Magnus Carlsen accused Hans Niemann of cheating in September 2022, it spotlighted a challenge that extends well beyond chess: how can one audit a competitor's play while protecting honest players from false accusations? We propose a principled framework for auditing a monitored player relative to a known strategy in two-player normal-form games. In particular, we introduce $(\epsilon, \delta)$-strategic testing which, given a tolerated accusation rate $\delta$, keeps the accepted winning payoff within $\epsilon$ of the honest expected winning payoff. We characterize the optimal acceptance policy by a linear program, compare it with a suboptimal policy, and show why purely distributional criteria can miss or overstate strategically relevant deviations. Finally, we formulate the auditing problem as an auxiliary zero-sum Stackelberg game.