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 framework for auditing a monitored player relative to known reference strategies in two-player normal-form games. In particular, we introduce $(ϵ,\delta )$-strategic testing, which limits the flag rate under honest reference play to $\delta$ and ensures that no deviating strategy achieves an expected accepted winning payoff more than $ϵ$ above the honest benchmark, uniformly over opponent actions. We characterize the optimal acceptance policy through a linear program, derive a direct threshold rule, and compare it with uniform acceptance. We extend testing to zero-payoff outcomes through separate flag budgets and exposure scores, and connect the framework to deviation costs and incentive compatibility, showing that payoff control alone need not preserve honest play as a best response. We also formulate the auditing problem as an auxiliary zero-sum Stackelberg game. Finally, we evaluate the framework through synthetic experiments comparing optimal and uniform auditing across random games and examining the trade-off between payoff control, incentives, and honest reward retention.