Matching with Slot-Specific Priorities: Theory

Scott Duke Kominers; Tayfun  Sönmez

Article | Theoretical Economics | May 2016

Matching with Slot-Specific Priorities: Theory

by Scott Duke Kominers and Tayfun Sönmez

Abstract

We introduce a two-sided, many-to-one matching with contracts model in which agents with unit demand match to branches that may have multiple slots available to accept contracts. Each slot has its own linear priority order over contracts; a branch chooses contracts by filling its slots sequentially, according to an order of precedence. We demonstrate that in these matching markets with slot-specific priorities, branches’ choice functions may not satisfy the substitutability conditions typically crucial for matching with contracts. Despite this complication, we are able to show that stable outcomes exist in the slot-specific priorities framework and can be found by a cumulative offer mechanism that is strategy proof and respects unambiguous improvements in priority.

Keywords: market design; Matching with Contracts; stability; Strategy-proofness; School Choice; Affirmative Action; Airline Seat Upgrades; Contracts; Market Design; Marketplace Matching; Balance and Stability;

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Citation:

Kominers, Scott Duke, and Tayfun Sönmez. "Matching with Slot-Specific Priorities: Theory." Theoretical Economics 11, no. 2 (May 2016): 683–710.

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We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n ∈{8,24,32,48,56,72,96} every extremal Type II code of length n is generated by its codewords of minimal weight. Where Ozeki and Kominers used spherical harmonics and weighted theta functions, we use discrete harmonic polynomials and harmonic weight enumerators. Along the way we introduce "t12-designs" as a discrete analog of Venkov's spherical designs of the same name.

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Matching with Slot-Specific Priorities: Theory

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