Symmetric divide-and-choose

Abstract

In the United States, a version of divide-and-choose known as the "Texas Shootout" is commonly employed to dissolve partnerships. The Texas Shootout treats symmetric players asymmetrically, with one player designated to be the Divider and the other designated the Chooser. This asymmetry leads to inequitable and inefficient outcomes. This paper introduces a symmetric form of divide-and-choose. Like classical divide-and-choose, the mechanism generates envy-free and proportionally fair outcomes. Unlike classical divide-and-choose, the mechanism treats identical claimants identically and its equilibrium is efficient. Finally, the outcome under maxmin play is closely related to the Shapley value of an associated cooperative game.