Using data on one-shot games, we investigate whether players' actions can be viewed as responses to underlying expectations about their opponent's behaviour. In our laboratory experiments, subjects play a set of 14 two-person 3×3 games and state beliefs about which actions they expect their opponents to play. The data sets from the two tasks are largely inconsistent. Rather, we find evidence that the subjects perceive the games differently when they (i) choose actions and (ii) state beliefs—their stated beliefs reveal deeper strategic thinking than their actions. On average, they fail to best respond to their own stated beliefs in almost half of the games. The inconsistency is confirmed by estimates of a unified statistical model that jointly uses the actions and the belief statements. There, we can control for decision noise and formulate a statistical test that rejects consistency. Effects of the belief elicitation procedure on subsequent actions are mostly insignificant.

Ivanov, Levin, and Niederle (2010) use a common-value second-price auction experiment to reject beliefs-based explanations for the winner's curse. ILN's conclusion, however, stems from the misuse of theoretical arguments. Beliefs-based models are even compatible with some observations from ILN's experiment.

This paper reports an experiment that elicits subjects' initial responses to 16 dominance-solvable two-person guessing games. The structure is publicly announced except for varying payoff parameters, to which subjects are given free access. Varying the parameters allows very strong separation of the behavior implied by leading decision rules. Subjects' decisions and searches show that most subjects understood the games and sought to maximize payoffs, but many had simplified models of others' decisions that led to systematic deviations from equilibrium. The predictable component of their deviations is well explained by a structural nonequilibrium model of initial responses based on level-k thinking.

This paper reports experiments designed to measure strategic sophistication, the extent to which players' behavior reflects attempts to predict others' decisions, taking their incentives into account. Subjects played normal-form games with various patterns of iterated dominance and unique pure-strategy equilibria without dominance, using a computer interface that allowed them to look up hidden payoffs as often as desired, one at a time, while automatically recording their look-ups. Monitoring information search allows tests of game theory's implications for cognition as well as decisions, and subjects' deviations from search patterns suggested by equilibrium analysis help to predict their deviations from equilibrium decisions.

Most applications of game theory assume equilibrium, justified by presuming either that learning will have converged to one, or that equilibrium approximates people's strategic thinking even when a learning justification is implausible. Yet several recent experimental and empirical studies suggest that people's initial responses to games often deviate systematically from equilibrium, and that structural nonequilibrium “level-k” or “cognitive hierarchy” models often out-predict equilibrium. Even when learning is possible and converges to equilibrium, such models allow better predictions of history-dependent limiting outcomes. This paper surveys recent theory and evidence on strategic thinking and illustrates the applications of level-k models in economics. (JEL C70, D03, D82, D83)