Bidding in common value fair division games: The winner's curse or even worse?

A unique indivisible commodity with an unknown common value is owned by group of individuals and should be allocated to one of them while compensating the others monetarily. We study the so-called fair division game (Güth, Ivanova-Stenzel, Königstein, and Strobel (2002, 2005)) theoretically and experimentally for the common value case and compare our results to the corresponding common value auction. Whereas symmetric risk neutral Nash equilibria are rather similar for both games, behavior differs strikingly. Implementing auctions and fair division games in the lab in a repeated setting under first- and second-price rule, we find that overall behavior is much more dispersed for the fair division games than for the auctions. Winners' profit margins and shading rates are on average slightly lower for the fair division game. Moreover, we find that behavior in the fair division game separates into extreme over- and underbidding.common value auction, winner's curse, fair division game

Paradoxes of Fair Division

Two or more players are required to divide up a set of indivisible items that they can rank from best to worst. They may, as well, be able to indicate preferences over subsets, or packages, of items. The main criteria used to assess the fairness of a division are efficiency (Pareto-optimality) and envy-freeness. Other criteria are also suggested, including a Rawlsian criterion that the worst-off player be made as well off as possible and a scoring procedure, based on the Borda count, that helps to render allocations as equal as possible. Eight paradoxes, all of which involve unexpected conflicts among the criteria, are described and classified into three categories, reflecting (1) incompatibilities between efficiency and envy-freeness, (2) the failure of a unique efficient and envy-free division to satisfy other criteria, and (3) the desirability, on occasion, of dividing up items unequally. While troublesome, the paradoxes also indicate opportunities for achieving fair division, which will depend on the fairness criteria one deems important and the trade-offs one considers acceptable.FAIR DIVISION; ALLOCATION OF INDIVISIBLE ITEMS; ENVY-FREENESS; PARETO- OPTIMALITY; RAWLSIAN JUSTICE; BORDA COUNT.

Communication Complexity of Discrete Fair Division

We initiate the study of the communication complexity of fair division with indivisible goods. We focus on some of the most well-studied fairness notions (envy-freeness, proportionality, and approximations thereof) and valuation classes (submodular, subadditive and unrestricted). Within these parameters, our results completely resolve whether the communication complexity of computing a fair allocation (or determining that none exist) is polynomial or exponential (in the number of goods), for every combination of fairness notion, valuation class, and number of players, for both deterministic and randomized protocols.Comment: Accepted to SODA 201