Essays on Matching and Auction Theory
Johnson, Terence R.
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This dissertation uses mechanism design theory to show how a matchmaker should design two-sided matching markets when agents are privately informed about their qualities or characteristics as a partner and can make monetary payments. Chapter Two uses a mechanism design approach to derive sufficient conditions for assortative matching to be profit-maximizing for the matchmaker or maximize social welfare, and then shows how to implement the optimal match and payments through two-sided position auctions as a Bayesian Nash equilibrium. Chapter Three broadens these results by showing how the implementation concept can be relaxed to ex post equilibrium through the use of market designs similar to the Vickrey-Clarke-Groves mechanism, as well as implemented through the use of dynamic games. Chapter Four shows how the ideas used in Chapters Two and Three can be extended to a multi-dimensional type framework, moving away from the supermodular paradigm that is the workhorse of models of matching with incomplete information.