Lucky Numbers in Simple Games

Simple game structures like discoordination, hide-and-seek, or Colonel-Blotto games have been used to model a wide range of economically relevant situations. Yet, Nash-equilibrium and its alternatives notoriously fail to explain observed behaviour in these games when alternatives carry descriptive labels. This paper shows that throughout the different games, behavioural patterns resemble `lucky-number' patterns: the choice patterns in related lotteries. Starting from this observation, I adjust standard models to account for the data. The adjusted models outperform the existing models, but they do not outperform a simple benchmark model. In the benchmark model, agents pick according to the `lucky numbers' or, under certain circumstances, choose any of the other options with equal probabilities. Interestingly, this benchmark model predicts two additional general regularities that bear out on the existing data and new data from two additional games: hide-and-seek seekers rely on `lucky numbers' more heavily than any other player role; and the stronger the `lucky-number' pattern deviates from a uniform distribution, the more likely it is observed also in the game data.