Games of Boldness, Where the Player Performing the Hardest Task Wins

In a game of boldness a player chooses one from a group of tasks, each having a known probability of success. The player attempts the task, and wins if it succeeds and has the lowest probability of any that succeed. Y. Gerchak and M. Henig (1986) showed that sports competitions that take this form and have players perform sequentially with full information are biased, in that the order of play helps later competitors. We discuss six game variants embodying different types of information possessed by the players before they choose, and different rules about the sequence of choice. Our results suggest that contests would be fairer if players were told others' task difficulties but not told their successes. Y. Gerchak and M. Kilgour's proposal to make later players choose tasks no easier than previous ones, also does well in regard to fairness and practicality.