algorithm
67-79
equilibrium price vector
prices
novel aspects
chapter
lattice
limit
Fisher market model
2017-08-19
paper
chapters
spending
social welfare
number
vector
2017-08-19
representation
market equilibrium
function
number of agents
applications
utility
price vector
integers
Fisher markets
variety
market representation
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 \documentclass[12pt]{minimal}
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\begin{document}$$O(n^3\ell \log (\ell + nU))$$\end{document}, where n is the number of agents, \documentclass[12pt]{minimal}
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\begin{document}$$\ell \ge n$$\end{document} 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.
maximal price
central concept
time
https://scigraph.springernature.com/explorer/license/
Earning Limits in Fisher Markets with Spending-Constraint Utilities
indivisible items
false
buyers
copies
polynomial time
such markets
items
equilibrium
model
minimal price
linear
market
allocation
2022-11-24T21:11
supply
multiple copies
https://doi.org/10.1007/978-3-319-66700-3_6
results
large integers
utility function
concept
sellers
computational results
bounds
aspects
market model
income
interesting novel aspect
welfare
multi-unit markets
Nash social welfare
segments
agents
Springer Nature - SN SciGraph project
Jugal
Garg
Hoefer
Martin
Bilò
Vittorio
doi
10.1007/978-3-319-66700-3_6
dimensions_id
pub.1091272448
University of Illinois at Urbana-Champaign, Champaign, USA
University of Illinois at Urbana-Champaign, Champaign, USA
Michele
Flammini
Springer Nature
Goethe University Frankfurt, Frankfurt, Germany
Goethe University Frankfurt, Frankfurt, Germany
Xiaohui
Bei
Kurt
Mehlhorn
Economics
978-3-319-66699-0
Algorithmic Game Theory
978-3-319-66700-3
MPI Informatik, Saarbrücken, Germany
MPI Informatik, Saarbrücken, Germany
Applied Economics
Nanyang Technological University, Singapore, Singapore
Nanyang Technological University, Singapore, Singapore