Adjusted Winner: from Splitting to Selling

Robert Bredereck, Eyal Briman, Bin Sun, Nimrod Talmon

Keywords: Fair Division, Adjusted Winner

Abstract: The Adjusted Winner (AW) method is a fundamental procedure for the fair division of indivisible resources between two agents. However, its reliance on splitting resources can lead to practical complications. To address this limitation, we propose an extension of AW that allows the sale of selected resources under a budget constraint, with the proceeds subsequently redistributed, thereby aiming for allocations that remain as equitable as possible. Alongside developing this extended framework, we provide an axiomatic analysis that examines how equitability and envy-freeness are modified under our model. We then formally define the resulting combinatorial problems, establish their computational complexity, and design a fully polynomial-time approximation scheme (FPTAS) to mitigate their inherent intractability. Finally, we complement our theoretical results with computer-based simulations.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 533