Serial Rules in a Multi-Unit Shapley-Scarf Market

We study generalized Shapley-Scarf exchange markets where each agent is endowed with multiple units of an indivisible and agent-specific good and monetary compensations are not possible. An outcome is given by a circulation which consists of a balanced exchange of goods. We focus on circulation rules that only require as input ordinal preference rankings of individual goods, and agents are assumed to have responsive preferences over bundles of goods. We study the properties of serial dictatorship rules which allow agents to choose either a single good or an entire bundle sequentially, according to a fixed ordering of the agents. We also introduce and explore extensions of these serial dictatorship rules that ensure individual rationality. The paper analyzes the normative and incentive properties of these four families of serial dictatorships and also shows that the individually rational extensions can be implemented with efficient graph algorithms.PBiró gratefully acknowledges the financial support by the Hungarian Academy of Sciences, Momentum Grant No. LP2021-2, and by the Hungarian Scientific Research Fund, OTKA, Grant No. K143858. F. Klijn gratefully acknowledges financial support from AGAUR–Generalitat de Catalunya (2017-SGR-1359) and the Spanish Agencia Estatal de Investigación (AEI) through grants ECO2017-88130-P and PID2020-114251GB-I00 (funded by MCIN/ AEI /10.13039/501100011033) and the Severo Ochoa Programme for Centres of Excellence in R&D (Barcelona School of Economics, SEV-2015-0563 and CEX2019-000915-S). S. Pápai gratefully acknowledges financial support from an FRQSC grant titled “Formation des coalitions et des réseaux dans les situations économiques et sociales avec des externalités” (SE-144698

Agreeable sets with matroidal constraints

This article deals with the challenge of reaching an agreement for a group of agents who have heterogeneous preferences over a set of goods. In a recent work, Suksompong (in: Subbarao (ed) Proceedings of the twenty-fifth international joint conference on artificial intelligence, IJCAI 2016, New York, pp 489–495, 2016) models a problem of this kind as the search of an agreeable subset of a given ground set of goods. A subset is agreeable if it is weakly preferred to its complement by every agent of the group. Under natural assumptions on the agents’ preferences such as monotonicity or responsiveness, an agreeable set of small cardinality is guaranteed to exist, and it can be efficiently computed. This article deals with an extension to subsets which must satisfy extra matroidal constraints. Worst case upper bounds on the size of an agreeable set are shown, and algorithms for computing them are given. For the case of two agents having additive preferences, we show that an agreeable solution can also be approximately optimal (up to a multiplicative constant factor) for both agents