Abstract
In the one-sided assignment game, any two agents can form a trade; they can decide to form a partnership and agree on how to share the surplus created. Contrary to the two-sided assignment game, stable outcomes often fail to exist in the one-sided assignment game. Hence the core, which coincides with the set of stable payoffs, may be empty. We introduce the idea of tradewise-stable (t-stable) outcomes: they are individually rational outcomes where all trades are stable; that is, no matched agent can form a blocking pair with any other agent, neither matched nor unmatched. We propose the set of constrained-optimal (optimal) t-stable outcomes, the set of the maximal elements of the set of t-stable outcomes, as a natural solution concept for this game. We prove that this set is non-empty, it coincides with the set of stable outcomes when the core is non-empty, and it satisfies similar properties to the set of stable outcomes even when the core is empty. We propose a partnership formation process that starts with the outcome where every player stands alone, goes through steps where the set of active players expands, always forming t-stable outcomes, and ends in an (in any) optimal t-stable outcome. Finally, we also use the new concept to establish conditions under which the core is non-empty.
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We thank Federico Echenique, Jean-Jacques Herings, the associate editor, and two reviewers for their constructive comments. We also thank the suggestions received at SING 15 in Turku, the 30th International Conference on Game Theory at Stony Brook, the ASSET meeting in Athens, the 6th World Congress of the Game Theory Society, and seminars at Aix-Marseille School of Economics, Paris School of Economics, Shanghai University of Finance and Economics, and Universidad Autónoma de Barcelona. Marilda Sotomayor acknowledges financial support from CNPq-Brazil. David Pérez-Castrillo acknowledges financial support from the Ministerio de Ciencia, Innovació n y Universidades and Feder (PGC2018-094348-B-I00), Generalitat de Catalunya (2017SGR-711), ICREA under the ICREA Academia programme, and Severo Ochoa Programme (CEX2019-000915-S). A previous version of this paper has circulated under the title “Conflict-free and Pareto-optimal allocations in the one-sided assignment game: A solution concept weaker than the core”.
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Pérez-Castrillo, D., Sotomayor, M. Constrained-optimal tradewise-stable outcomes in the one-sided assignment game: a solution concept weaker than the core. Econ Theory 76, 963–994 (2023). https://doi.org/10.1007/s00199-022-01483-9
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DOI: https://doi.org/10.1007/s00199-022-01483-9