Sensitivity of fair prices in assignment markets

• Published in: Mathematical social sciences Vol. 126; pp. 1 - 12
• Main Author: Solymosi, Tamás
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2023
• Subjects: Assignment game; Competitive price; Fair price; Sensitivity range; Two-sided matching market; Competitive price; Fair price; Assignment game; Sensitivity range; Two-sided matching market
• ISSN: 0165-4896; 1879-3118
• DOI: 10.1016/j.mathsocsci.2023.09.003

It is well known that in assignment markets competitive prices always exist, but no price mechanism is strategy-proof for all agents. We investigate the extent a single agent can influence three special competitive price vectors by misreporting his/her reservation values. We provide an exact formula how the minimum, the maximum, and the fair competitive price vectors change, and show that at the fair prices no agent can gain more than half of the deviation from the true values. We also derive the analogous results for the corresponding core payoffs of the associated assignment game via graph-theoretic characterizations of the two side-optimal core payoffs. •Sensitivity of competitive equilibrium prices in assignment markets are studied.•Any agent can influence the fair prices by misreporting his/her reservation values.•An exact formula is given how the fair price of a single misreporting agent changes.•Analogous results are given for core payoffs of the associated assignment game.•Graph-theoretic characterizations of the side-optimal core payoffs are used.