Research

We consider a broad class of spatial models where there are many types of interactions across a large number of locations. We provide a new theorem that offers an iterative algorithm for calculating an equilibrium and sufficient and “globally necessary” conditions under which the equilibrium is unique. We show how this theorem enables the characterization of equilibrium properties for two important spatial systems: an urban model with spillovers across a large number of different types of agents and a dynamic migration model with forward looking agents. An Online Appendix provides eleven additional examples of both spatial and non-spatial economic frameworks for which our theorem provides new equilibrium characterizations. 

Two solutions are proposed to Nash (1950)'s bargaining problem: the Consensus and Compromise solutions. They present a gradual divergence away from the Nash solution. In terms of axioms, the Nash solution's Axiom IIA (Independence of Irrelevant Alternatives) is decomposed into several parts, the controversial ones of which are identified and gradually replaced giving rise to the Consensus and Compromise solutions. The two replacement parts are: 1). if the additional room for cooperation induced by the worsening no-cooperation are, for both players, no better than the solution, the solution shall not change; 2). a solution shall not be the best only for one player i.e. each player should make at least some concession, no matter how small.

We consider a pure model of cooperation where players can choose nothing but cooperation: the cooperation problem. With the help of an axiomatic approach, we use sentiments to understand the cooperation problem in contrast with rationality used to understand non-cooperative games. Applications of the cooperation problem includes the bargaining problem, the selection of solutions (equilibria) of both non-cooperative and cooperative games, and the extensive-form games to allow for explicit cooperation (in addition to no-cooperation).

In this paper, we develop a quantitative general equilibrium model of a city that incorporates the many economic interactions that occur over the space of the city, including commuting, trade, and personal interactions. We show that, despite the many spatial linkages, in the absence of externalities the competitive equilibrium is efficient; conversely, in the presence of spillovers, there exists opportunities for a city planner to increase the welfare of the city inhabitants by restricting the use of land (“zoning”). We provide sufficient conditions for the optimal zoning policy that depend solely on observables and several key model parameters. Finally, we illustrate the flexibility of the model by applying it to study the observed zoning policy of the city of Chicago. Preliminary results suggest that the welfare if residents of Chicago would increase if more area in the central business was allocated to residents district and more area in the outlying neighborhoods was allocated to businesses.