Strategic Behavior in Contested-Pile Methods for Fair Division of Indivisible Items

Abstract

Most fair-division procedures are modeled on cake-cutting procedures such as “I cut, you choose”. The inputs are players’ choices, which are assumed to reflect preferences but not fully reveal them; the output is a division that is in some sense fair. However, it seems likely that decision makers sometimes behave insincerely, that is, they make choices that are not consistent with their true preferences. For example, strategic—as opposed to sincere—behavior may be aimed at taking advantage of information about an opponent’s preferences, which most fair-division procedures assume is not available. We focus on contested-pile procedures, a class of procedures for the fair division of indivisible items between two players, related to the alternation procedures proposed by Brams and Taylor (The win-win solution: guaranteeing fair shares to everybody. W. W. Norton, New York, 1999). We use computational models to assess the performance of these procedures under both sincere and strategic behavior. We show how available information about preferences can interact with strategy to shape outcomes. Our results indicate that strategic behavior, although it often changes outcomes, may not make them less efficient or less fair. Furthermore, our investigation suggests that how information about the opponents preference is processed does not have a strong impact, in that a conceptually simple strategy often outperforms a more elaborate one.