Playing Divide-and-Choose Given Uncertain Preferences
研究了两个理性自利贝叶斯玩家在不确定偏好下通过分与选方法分配可分割物品的均衡策略，发现未知偏好下分割者有强烈的多样化动机，且玩家效用取决于信息水平、价值相关性和物品数量。
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 values for the goods. The prior distributions of those values are common knowledge. We consider both the cases of independent values and values that are correlated across players (as occurs when there is a common-value component). We describe the structure of optimal divisions in the divide-and-choose game and identify several cases where it is possible to efficiently compute equilibria. An approximation algorithm is presented for the case when the distribution over the chooser’s value for each good follows a normal distribution, along with a randomized approximation algorithm for the case of uniform distributions over intervals. A mixture of analytic results and computational simulations illuminates several striking differences between optimal strategies in the cases of known versus unknown preferences. Most notably, given unknown preferences, the divider has a compelling “diversification” incentive in creating the chooser’s two options. This incentive leads to multiple goods being divided at equilibrium, quite contrary to the divider’s optimal strategy when preferences are known. In many contexts, such as buy-and-sell provisions between partners, or in judging fairness, it is important to assess the relative expected utilities of the divider and chooser. Those utilities, we show, depend on the players’ levels of knowledge about each other’s values, the correlations between the players’ values, and the number of goods being divided. Under fairly mild assumptions, we show that the chooser is strictly better off for a small number of goods, whereas the divider is strictly better off for a large number of goods. This paper was accepted by Ilia Tsetlin, behavioral economics and decision analysis. Funding: This work was supported by the Mossavar-Rahmani Center for Business and Government, Harvard University, and the National Science Foundation [Grant DGE1745303]. Any opinions, findings, and conclusions or recommendations expressed in this material reflect the views of the authors and not necessarily those of the National Science Foundation or the Mossavar-Rahmani Center. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.00350 .