Cadet-Branch Matching in a Quasi-Linear Labor Market

Abstract

Sonmez [2013] and Sonmez and Switzer [2013] used matching theory with unilaterally substitutable preferences [Hatfield and Kojima, 2010] to propose mechanisms to match cadets to military branches. Unilaterally substitutable priorities in general exhibit complementarities. In this paper, I construct the same mechanisms in matching markets with substitutable priorities. My results show that cadet-branch matching does not require weakened substitutes conditions. The cadet-branch matching market with substitutable branch priorities constructed in this paper can be often regarded as a labor market in the model of Kelso and Crawford [1982]. The length of a contract is interpreted as the inverse of a salary, and the branches' priorities can be taken to be quasi-linear. Therefore, the substitutable branch priorities are appealing from a theoretical perspective. My results complement the original constructions of the proposed cadet-branch matching mechanisms. Sonmez and Switzer [2013] showed that the currently-implemented USMA priority structure is compatible with fairness, strategy-proofness, and respect for improvements. My approach to the construction of the proposed mechanisms relies on deviation of the branch priorities from the exact currently-implemented priorities, but this modification does not affect the proposed matching mechanisms. Together, my results and those of Sonmez and Switzer [2013] show that cadet-branch matching can be performed in Kelso-Crawford economies so that the deferred acceptance mechanisms, but not the branch priorities in the economies, are consistent with the currently-implemented USMA priorities.