Two-Sided Matchings: An Algorithm for Ensuring They Are Minimax and Pareto-Optimal
Gale and Shapley (1962) proposed the deferred-acceptance algorithm for matching (i) college applicants and colleges and (ii) men and women. In the case of the latter, it produces either one or two stable matches whereby no man and woman would prefer to be matched with each other rather than with their present partners. But stable matches can give one or both players in a pair their worst match, whereas the minimax algorithm that we propose, which finds all assignments that minimize the maximum rank of players in matches, avoids such assignments. Although minimax matches may not be stable, at least one is always Pareto-optimal: No other matching is at least as good for all the players and better for one or more. If there are multiple minimax matches, we propose criteria for choosing the most desirable among them and also discuss the settings in which minimax matches seem more compelling than deferred-acceptance matches when they differ. Finally, we calculate the probability that minimax matches differ from deferred-acceptance matches in a simple case.
|Date of creation:||07 Jul 2013|
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- Alvin Roth, 2008.
"Deferred acceptance algorithms: history, theory, practice, and open questions,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
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- Alvin E. Roth, 2007. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions," NBER Working Papers 13225, National Bureau of Economic Research, Inc.
- James Boudreau & Vicki Knoblauch, 2013. "Preferences and the price of stability in matching markets," Theory and Decision, Springer, vol. 74(4), pages 565-589, April.
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