TY - GEN
T1 - Earning limits in fisher markets with spending-constraint utilities
AU - Bei, Xiaohui
AU - Garg, Jugal
AU - Hoefer, Martin
AU - Mehlhorn, Kurt
N1 - Publisher Copyright:
© Springer International Publishing AG 2017.
PY - 2017
Y1 - 2017
N2 - Earning limits are an interesting novel aspect in the classic Fisher market model. Here sellers have bounds on their income and can decide to lower the supply they bring to the market if income exceeds the limit. Beyond several applications, in which earning limits are natural, equilibria of such markets are a central concept in the allocation of indivisible items to maximize Nash social welfare. In this paper, we analyze earning limits in Fisher markets with linear and spending-constraint utilities. We show a variety of structural and computational results about market equilibria. The equilibrium price vectors form a lattice, and the spending of buyers is unique in non-degenerate markets. We provide a scaling-based algorithm that computes an equilibrium in time O(n3ℓlog(ℓ+nU), where n is the number of agents, ℓ≥n a bound on the segments in the utility functions, and U the largest integer in the market representation. Moreover, we show how to refine any equilibrium in polynomial time to one with minimal prices, or one with maximal prices (if it exists). Finally, we discuss how our algorithm can be used to obtain in polynomial time a 2-approximation for Nash social welfare in multi-unit markets with indivisible items that come in multiple copies.
AB - Earning limits are an interesting novel aspect in the classic Fisher market model. Here sellers have bounds on their income and can decide to lower the supply they bring to the market if income exceeds the limit. Beyond several applications, in which earning limits are natural, equilibria of such markets are a central concept in the allocation of indivisible items to maximize Nash social welfare. In this paper, we analyze earning limits in Fisher markets with linear and spending-constraint utilities. We show a variety of structural and computational results about market equilibria. The equilibrium price vectors form a lattice, and the spending of buyers is unique in non-degenerate markets. We provide a scaling-based algorithm that computes an equilibrium in time O(n3ℓlog(ℓ+nU), where n is the number of agents, ℓ≥n a bound on the segments in the utility functions, and U the largest integer in the market representation. Moreover, we show how to refine any equilibrium in polynomial time to one with minimal prices, or one with maximal prices (if it exists). Finally, we discuss how our algorithm can be used to obtain in polynomial time a 2-approximation for Nash social welfare in multi-unit markets with indivisible items that come in multiple copies.
UR - http://www.scopus.com/inward/record.url?scp=85029352669&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85029352669&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-66700-3_6
DO - 10.1007/978-3-319-66700-3_6
M3 - Conference contribution
AN - SCOPUS:85029352669
SN - 9783319666990
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 67
EP - 79
BT - Algorithmic Game Theory - 10th International Symposium, SAGT 2017, Proceedings
A2 - Bilo, Vittorio
A2 - Flammini, Michele
PB - Springer
T2 - 10th International Symposium on Algorithmic Game Theory, SAGT 2017
Y2 - 12 September 2017 through 14 September 2017
ER -