Uncertainty in Models of Authority and Models of Matching

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

The proposed work consists of two parts: The first part aims to enhance our understanding of the implications of stability of matching outcomes under incomplete information. There is a voluminous literature using matching models to analyze two-sided markets, including problems of matching students to schools, residents to hospitals and workers to firms. The commonly employed solution concept when analyzing matching problems is the core. The use of the core as a solution concept incorporates the stability of a proposed matching between workers and firms: if the proposed outcome is not in the core, we would expect the outcome to be upset by the pair that could jointly improve their circumstances. Matching typically assumes complete information: all parties know exactly what the consequences would be for any possible match. The assumption is crucial because for the standard problems to which these models are applied, participating agents care about the characteristics of their matched party. The PIs propose to extend previous work that defines pairwise stability in incomplete information environments. The main thrust of the proposed work in this area is to investigate how the techniques used can be modified to understand matching in many-to-one environments. The research will provide a better understanding the conditions that assure that there are stable matching of workers to firms and the efficiency properties of such matching. Such an understanding will give insight about possible interventions that will ameliorate inefficiencies in matching problems. The complete information matching theory has had a significant impact on the design of the mechanisms used to assign student to schools and residents to hospitals. This research has the potential of improving the economic performance of these mechanisms. In the second part of the proposal the PIs propose to formally model the process by which laws are, or are not, followed by the agents assumed to be subject to those laws. They suggest that some laws continue to be followed for some time, despite changes in the environment that affect agents' incentives to follow those laws, but then collapse quickly even though there seems to be no dramatic change in the environment. The PIs propose to formalize models of this process of social change that are consistent with such behavior.