Date of Award

Spring 2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Economics

First Advisor

Samuelson, Larry

Abstract

This dissertation studies a range of topics in game and economic theory. Chapter 1 proposes a new solution to the two-player bargaining problem of Nash (1950): The Consensus solution. The Consensus solution maximizes the total amount of options that both players agree are worse than the solution but better than no-cooperation. It can be characterized by a simple equality. It satisfies all the axioms of the Nash solution except Axiom IIA (Independence of Irrelevant Alternatives); the Nash solution satisfies all its axioms except one which says: when both players' utilities of no-cooperation become lower creating additional room for players to cooperate, then as long as options within the additional room are worse than the current solution, the solution shall not change. At the same time, it is the same as the Nash solution in comprehensive bargaining problems, a class of bargaining problems where many good properties of the Nash solution are discovered. We discuss when bargaining problems are non-comprehensive. We conclude that the key difference between the two solutions is that the Consensus solution emphasize what players can achieve via cooperation whereas the Nash solution focus more on the anticipation of no-cooperation. Chapter 2, coauthored with with Treb Allen and Costas Arkolakis, studies a broad class of network models where a large number of heterogeneous agents simultaneously interact in many ways. We provide an iterative algorithm for calculating an equilibrium and offer sufficient and ``globally necessary'' conditions under which the equilibrium is unique. The results arise from a multi-dimensional extension of the contraction mapping theorem which allows for the separate treatment of the different types of interactions. We illustrate that a wide variety of heterogeneous agent economies -- characterized by spatial, production, or social networks -- yield equilibrium representations amenable to our theorem's characterization. Chapter 3, coauthored with with Treb Allen and Costas Arkolakis, develops a quantitative general equilibrium model that incorporates the many economic interactions that occur over the city, including commuting and spatial spillovers of productivities. Despite the many spatial linkages, the model allows for characterizing the existence and efficiency of the spatial equilibrium of the city when there are no spillovers. Additionally, we consider a city planner who can design zoning policy but leave the rest to the market. We show that even with the presence of spillovers, the city planner can still be efficient. We provide an explicit formula to evaluate welfare effects of zoning policies.

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