  How and why do incentive levels affect strategic behavior? This paper
examines an experiment designed to identify the causal effect of scaling up
incentives on choices and beliefs in strategic settings by holding fixed
opponents' actions. In dominance-solvable games, higher incentives increase
action sophistication and best-response rates and decrease mistake propensity.
Beliefs tend to become more accurate with higher own incentives in simple
games. However, opponents with higher incentive levels are harder to predict:
while beliefs track opponents' behavior when they have higher incentive levels,
beliefs about opponents also become more biased. We provide evidence that
incentives affect cognitive effort and that greater effort increases
performance and predicts choice and belief sophistication. Overall, the data
lends support to combining both payoff-dependent mistakes and costly reasoning.
