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Incentive ratio: a game theoretical analysis of market equilibria

Incentive ratio: a game theoretical analysis of market equilibria
Incentive ratio: a game theoretical analysis of market equilibria

In a Fisher market, the market maker sells m products to n potential agents. The agents submit their utility functions and money endowments to the market maker, who, upon receiving submitted information, derives market equilibrium prices and allocations of the products. Agents are self-interested entities who wish to maximize their utility, and they may misreport their private information for this purpose. The incentive ratio characterizes the extent to which strategic plays can increase an agent's utility. While agents do benefit by misreporting their private information, we show that the ratio of improvement by a unilateral strategic play is no more than two in markets with gross substitute utilities for the agents. Moreover, it can be pinned down to e 1/e≈1.445 in Cobb-Douglas markets. For the Leontief markets in which products are complementary, we show that the incentive ratio is at most two as well.

Fisher market, Incentive ratio, Market equilibrium
0890-5401
Chen, Ning
52f917c7-bcbf-4a36-9a60-d613627972a3
Deng, Xiaotie
772c0705-a735-43dc-8988-f5c527572574
Tang, Bo
9c2ad2f3-dcde-49a2-ba6b-423958b199b3
Zhang, Hongyang
c4c6ac3a-194a-4c01-88b1-a3edeee78535
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a
Chen, Ning
52f917c7-bcbf-4a36-9a60-d613627972a3
Deng, Xiaotie
772c0705-a735-43dc-8988-f5c527572574
Tang, Bo
9c2ad2f3-dcde-49a2-ba6b-423958b199b3
Zhang, Hongyang
c4c6ac3a-194a-4c01-88b1-a3edeee78535
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a

Chen, Ning, Deng, Xiaotie, Tang, Bo, Zhang, Hongyang and Zhang, Jie (2022) Incentive ratio: a game theoretical analysis of market equilibria. Information and Computation, 285 (Part B), [104875]. (doi:10.1016/j.ic.2022.104875).

Record type: Article

Abstract

In a Fisher market, the market maker sells m products to n potential agents. The agents submit their utility functions and money endowments to the market maker, who, upon receiving submitted information, derives market equilibrium prices and allocations of the products. Agents are self-interested entities who wish to maximize their utility, and they may misreport their private information for this purpose. The incentive ratio characterizes the extent to which strategic plays can increase an agent's utility. While agents do benefit by misreporting their private information, we show that the ratio of improvement by a unilateral strategic play is no more than two in markets with gross substitute utilities for the agents. Moreover, it can be pinned down to e 1/e≈1.445 in Cobb-Douglas markets. For the Leontief markets in which products are complementary, we show that the incentive ratio is at most two as well.

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Accepted/In Press date: 6 February 2022
e-pub ahead of print date: 22 February 2022
Published date: 3 June 2022
Additional Information: Funding Information: Xiaotie Deng was partially supported by Science and Technology Innovation 2030 “New Generation Artificial Intelligence” Major Project No. ( 2018AAA0100901 ) and by the NSFC-ISF joint research program (grant No: NSFC-ISF 61761146005 ). Jie Zhang was supported by a Research Project Grant from The Leverhulme Trust . Publisher Copyright: © 2022 The Author(s)
Keywords: Fisher market, Incentive ratio, Market equilibrium

Identifiers

Local EPrints ID: 470388
URI: http://eprints.soton.ac.uk/id/eprint/470388
ISSN: 0890-5401
PURE UUID: 8faaf68b-921a-48d6-a261-baa3c181fdd1

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Date deposited: 07 Oct 2022 16:44
Last modified: 07 Oct 2022 16:46

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Contributors

Author: Ning Chen
Author: Xiaotie Deng
Author: Bo Tang
Author: Hongyang Zhang
Author: Jie Zhang

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