Topics in Market Design
Topics in Market Design
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Date
2008-06-11
Authors
Morrill, Thayer
Advisor
Ausubel, Lawrence
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Abstract
My dissertation consists of two papers covering distinct topics within Microeconomic Theory. The first chapter is drawn from Matching Theory. One of the
oldest but least understood matching problems is Gale and Shapley's (1962) "roommates problem": is there a stable way to assign 2N students into N roommate pairs?
Unlike the classic marriage problem or college admissions problem, there need not
exist a stable solution to the roommates problem. However, the traditional notion
of stability ignores the key physical constraint that roommates require a room, and
it is therefore too restrictive. Recognition of the scarcity of rooms motivates replacing stability with Pareto optimality as the relevant solution concept. This paper
proves that a Pareto optimal assignment always exists in the roommates problem,
and it provides an efficient algorithm for finding a Pareto improvement starting from
any status quo. In this way, the paper reframes a classic matching problem, which
previously had no general solution, to become both solvable and economically more
meaningful.
The second chapter focuses on the role networks play in market and social
organization. In network theory, externalities play a critical role in determining
which networks are optimal. Adding links can create positive externalities, as they
potentially make distant vertices closer. On the other hand, links can result in
negative externalities if they increase congestion or add competition. This paper will
completely characterize the set of optimal and equilibrium networks for a natural
class of negative externalities models where an agent's payoff is a function of the
degree of her neighbors. These results are in sharp contrast to the optimal and
equilibrium networks for the standard class of positive externalities models where
payoff is a function of the distance two agents are apart. This highlights the role
externalities play in optimal and equilibrium network structure.