Allocating positions fairly: Auctions and Shapley value

Van Essen, M; Wooders, J

Allocating positions fairly: Auctions and Shapley value

Van Essen, M Wooders, J

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Publisher:: Elsevier BV
Publication Type:: Journal Article
Citation:: Journal of Economic Theory, 2021, 196, pp. 105315-105315
Issue Date:: 2021-09-01

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Field	Value	Language
dc.contributor.author	Van Essen, M
dc.contributor.author	Wooders, J https://orcid.org/0000-0002-4206-7137
dc.date.accessioned	2021-12-06T20:19:27Z
dc.date.available	2021-12-06T20:19:27Z
dc.date.issued	2021-09-01
dc.identifier.citation	Journal of Economic Theory, 2021, 196, pp. 105315-105315
dc.identifier.issn	0022-0531
dc.identifier.issn	1095-7235
dc.identifier.uri	http://hdl.handle.net/10453/152159
dc.description.abstract	We study the problem of fairly allocating heterogenous items, priorities, positions, or property rights to participants with equal claims from three perspectives: cooperative, decision theoretic, and non-cooperative. We characterize the Shapley value of the cooperative game and then introduce a class of auctions for non-cooperatively allocating positions. We show that for any auction in this class, each bidder obtains his Shapley value when every bidder follows the auction's unique maxmin perfect bidding strategy. When information is incomplete we characterize the Bayesian equilibrium of these auctions, and show that equilibrium play converges to maxmin perfect play as bidders become infinitely risk averse. The equilibrium allocations thus converges to the Shapley value allocation as bidders become risk averse. Together these results provide both decision theoretic and non-cooperative equilibrium foundations for the Shapley value in the position allocation problem.
dc.language	en
dc.publisher	Elsevier BV
dc.relation	http://purl.org/au-research/grants/arc/DP140103566
dc.relation.ispartof	Journal of Economic Theory
dc.relation.isbasedon	10.1016/j.jet.2021.105315
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	1401 Economic Theory, 1499 Other Economics
dc.subject.classification	Economic Theory
dc.title	Allocating positions fairly: Auctions and Shapley value
dc.type	Journal Article
utslib.citation.volume	196
utslib.for	1401 Economic Theory
utslib.for	1499 Other Economics
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Business/Economics Discipline
utslib.copyright.status	closed_access	*
dc.date.updated	2021-12-06T20:19:26Z
pubs.publication-status	Published
pubs.volume	196

Abstract:

We study the problem of fairly allocating heterogenous items, priorities, positions, or property rights to participants with equal claims from three perspectives: cooperative, decision theoretic, and non-cooperative. We characterize the Shapley value of the cooperative game and then introduce a class of auctions for non-cooperatively allocating positions. We show that for any auction in this class, each bidder obtains his Shapley value when every bidder follows the auction's unique maxmin perfect bidding strategy. When information is incomplete we characterize the Bayesian equilibrium of these auctions, and show that equilibrium play converges to maxmin perfect play as bidders become infinitely risk averse. The equilibrium allocations thus converges to the Shapley value allocation as bidders become risk averse. Together these results provide both decision theoretic and non-cooperative equilibrium foundations for the Shapley value in the position allocation problem.

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http://hdl.handle.net/10453/152159