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Power indices for networks, with applications to matching markets

Qianqian Kong and Hans Peters

European Journal of Operational Research, 2023, vol. 306, issue 1, 448-456

Abstract: We study situations where agents can form or sever links in a network: what agents can do exactly is described by effectivity functions. A power index assigns to such an effectivity function a number for each agent, measuring the opportunities of that agent. We characterize a class of power indices by four axioms: the Transfer Property, the Dummy Property, Symmetry, and Network Neutrality. As a corollary, we obtain power indices for the case where effectivity functions are induced by preferences of agents about the other agents. Applications include one-to-one, one-to-many, and many-to-many matching markets, as well as roommate problems.

Keywords: Game theory; Power indices; Networks; Matching markets; Roommate problems (search for similar items in EconPapers)
JEL-codes: C71 C78 D71 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.ejor.2022.07.014

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Handle: RePEc:eee:ejores:v:306:y:2023:i:1:p:448-456