Standard game-theoretic analysis yields highly incomplete descriptions of behavior in complex games of complete information. A key part of the reason is that standard models do not account for the role of complexity in shaping players' strategic behavior. We investigate the implications of complexity empirically and theoretically, focusing on the game of chess---a good setting for our study because it is a rare example of an extensive-form game that is played by experienced, motivated players, and for which we have vast amounts of data.

The early stages of many careers serve as a trial period where employees seek a high-value reward (e.g., a promotion) while working hard to demonstrate their productivity. A key design component of such jobs is the performance feedback offered to the employee, as it allows them to adjust their behaviors and learn what their future rewards might look like. While some experts argue that a policy of full transparency is best---that is, keeping employees fully apprised of their performance---such practice is far form uniform as employers may see a strategic gain from hiding information or postponing its release.

We derive an optimal dynamic contest for environments where effort can be monitored only through a coarse, binary performance measure and the principal chooses prize-allocation and termination rules together with a real-time feedback policy for the contestants. The optimal contest takes a stark cyclical form: contestants are kept fully apprised of their own successes, and at the end of each fixed-length cycle, if at least one agent has succeeded, the contest ends and the prize is shared equally among all successful agents irrespective of when they succeeded; otherwise, the designer informs all contestants that nobody has yet succeeded and the contest resets. Applications include promotions, innovation contests, and proof-of-work protocols.