Fair Shares: Feasibility, Domination, and Incentives

Moshe Babaioff () and Uriel Feige ()
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Moshe Babaioff: School of Engineering and Computer Science, The Hebrew University of Jerusalem, 9190416 Jerusalem, Israel
Uriel Feige: Department of Computer Science and Applied Mathematics, The Weizmann Institute, 7610001 Rehovot, Israel

Mathematics of Operations Research, 2025, vol. 50, issue 3, 1901-1934

Abstract: We consider fair allocation of indivisible goods to n equally entitled agents. Every agent i has a valuation function v i from some given class of valuation functions. A share s is a function that maps ( v i , n ) to a nonnegative value. A share is feasible if for every allocation instance, there is an allocation that gives every agent i a bundle that is acceptable with respect to v i , one of value at least her share value s ( v i , n ) . We introduce the following concepts. A share is self-maximizing if reporting the true valuation maximizes the minimum true value of a bundle that is acceptable with respect to the report. A share s ρ-dominates another share s ′ if s ( v i , n ) ≥ ρ · s ′ ( v i , n ) for every valuation function. We initiate a systematic study of feasible and self-maximizing shares and a systematic study of ρ -domination relation between shares, presenting both positive and negative results.

Keywords: Primary: 91B32; secondary: 91A68; fair allocation; indivisible goods; maximin share; incentives; feasible share; self-maximizing shares; approximation (search for similar items in EconPapers)
Date: 2025
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