Some Further Properties of the Cumulative Offer Process

27 Pages Posted: 11 Aug 2014 Last revised: 18 Sep 2014

Date Written: August 10, 2014

Abstract

In the matching with contracts framework, we investigate the population/resource monotonicity and respecting improvements properties of the cumulative offer process (COP). Both population and resource monotonicity conditions are solidarity requirements. The former says that no doctor is to be worse off whenever some others leave the market. The latter, on the other hand, requires that no doctor should lose whenever hospitals start hiring more doctors. We first show that the COP separately becomes population and resource monotonic whenever contracts are unilateral substitutes satisfying irrelevance of rejected contracts (IRC). This result along with the stability of the COP ables us to reach the opposite comparative statics results for the hospital side of the market. We then turn to respecting improvements property saying that no doctor should be harmed if some of his contracts become more popular. With an additional law of aggregate demand condition, we show that the COP respects improvements. In a separate independent result, we also show that IRC is very critical for the COP as it may even fail to produce an allocation without it despite contracts being bilateral substitutes.

Suggested Citation

Afacan, Mustafa Oguz, Some Further Properties of the Cumulative Offer Process (August 10, 2014). Available at SSRN: https://ssrn.com/abstract=2478418 or http://dx.doi.org/10.2139/ssrn.2478418

Mustafa Oguz Afacan (Contact Author)

Sabanci University ( email )

Faculty of Art and Social Sciences
Orhanli Tuzla
İstanbul, 34956
Turkey

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