Playing Divide-and-Choose Given Uncertain Preferences

We study the classic divide-and-choose method for equitably allocating divisible goods between two players who are rational, self-interested Bayesian agents. The players have additive private values drawn from common priors. We characterize the structure of optimal divisions in the divide-and-choose game and show how to efficiently compute equilibria. We identify several striking differences between optimal strategies in the cases of known versus unknown preferences. Most notably, the divider has a compelling "diversification" incentive which leads to multiple goods being divided at equilibrium. We show that the relative utilities of the two players depend on their uncertainties about each other's values and the number of goods. We prove that, when values are independently and identically distributed across players and goods, the chooser is strictly better off for a small number of goods, while the divider is strictly better off for a large number of goods.