We introduce a Bayesian method to infer repeated-game strategies that best describe individuals' observed actions. We apply this method to buyer behavior in posted-offer market experiments. While the strategies of one-quarter of the buyers in our experiments correspond to the game-theoretic prediction of passive price-taking, for three-quarters of the buyers we infer different, non-trivial, repeated-game strategies that condition on time, price, and combinations of the two variables. The strategies are generally effective: the use of strategies and their complexity correlate negatively with market prices and monopolist profits. One strategy is particularly effective: the unconditional and intense forgoing of profitable purchases early in the game is more effective as a counteracting response to monopoly power than punishments that trigger when the market price exceeds a threshold. We propose that strategy inference should at least complement existing methods of statistical inference on observed strategic behavior.