Matching Issues: An auction with externalities and unraveling matching markets
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This dissertation examines two problems that may arise in matching problems. The first two chapters deal with auctions for multiple units where bidders exhibit externalities. The third chapter links risk aversion and information to unraveling in labor markets. Auctions can lead to efficient allocations in a wide class of assignment problems. In the presence of externalities, however, efficiency may no longer be guaranteed. This dissertation shows that a modification of Ausubel & Milgrom (2002)'s generalized ascending price auction can be used to allocate multiple items to bidders in this case. Despite the presence of externalities, the resulting auction possesses an efficient Nash equilibrium in pure strategies leading to a core allocation. Furthermore, under certain restrictions on bidder valuations, truthful revelation of valuations is found to a dominant strategy. The auction is augmented to include explicitly the auctioneer's preferences over final outcomes. Externalities affecting non-participants can thus be accounted for straightforwardly. In Cournot game where capacity constraints are determined in an auction prior to the market interaction, the valuations for capacity in the auction will exhibit externalities. Using the generalized ascending price auction allows the bidding firms to reach a joint profit maximizing capacity allocation below the Cournot equilibrium level. Since this comes at the expense of consumer surplus the auctioneer may have an incentive to specify its own valuation taking into account total surplus maximization. Then, the final capacity allocation is bounded by the profit maximizing and the Cournot equilibrium level. Unraveling labor markets, that is periodic labor markets where appointments are made earlier and earlier often leading to a break-down of the market, have been linked to risk-averse workers attempting to reduce the variability of the outcome. In many cases, early contracts are used to fix a wage when the relative supply and demand of workers in the market and hence the division of surplus is uncertain. This chapter represents a different approach. Both workers and firms have preferences over matchings and uncertainty is introduced through the quality of workers. Risk averse workers or risk-loving firms are found to be necessary for early contracting. Further research strategies are suggested.