Intermediated matching: Two essays
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This dissertation consists of two essays on two-sided matching. In chapter 2, we consider a model of intermediation wherein an incumbent matchmaker faces the threat of entry from a potential entrant. We model this competition as an entry game where the incumbent moves first and offers a contract to a subset of men and women. The entrant observes the actions of the incumbent and then decides to enter or stay out. If there is entry, then the entrant offers a contract targeted to a subset of men and women. When the payoff from matching is complementary in the types of the agents, we prove that there exists a weak sequential equilibrium either with entry and market segmentation or with entry deterrence. Our model explains the strategic market differentiation by the firms as the creation of a niche market for themselves. The data on the presence of niche dating websites confirms this result. An important finding of our model is that at an equilibrium, each firm offers a different contract to the men and women that they match. In sharp contrast to existing models in the Industrial Organization literature on entry deterrence, we find that accommodating the entrant is an optimal strategy for the incumbent, not entry deterrence. We then compare the duopoly market with a two-price monopoly market and find that the duopoly market has greater coverage than a two-price monopoly market. The model is then extended to allow for sequential entry. When intermediation is costless, allowing for sequential entry yields the socially efficient outcome as the number of entrants tends to infinity. Introducing intermediation costs leads to a welfare loss and a finite number of intermediaries entering. In chapter 3, we extend the model developed in chapter 2 by introducing search in a model of intermediation. It is common that men and women also search by themselves for a suitable partner in addition to using the services of the intermediaries. The entry game is modified by allowing for the possibility that the men and women can search in the decentralized market. The men and women compare the expected value of accepting the match offered by the intermediaries to the expected value of search in the decentralized market. We prove that there exists a weak sequential equilibrium where the incumbent offers a contract to a subset consisting of the highest types of men and women, the entrant enters and offers a contract to a subset of the highest types remaining in the residual market and the men and women not offered any contract by either the incumbent or the entrant search in the decentralized market using a reservation value strategy. Thus in addition to incorporating search in a model of intermediation, our model proves that market segmentation arises due to competition between the intermediaries to create a niche market for themselves. An interesting finding is that the higher types of agents prefer using the services of intermediaries while the lower types search by themselves. We then discuss the issues of entry accommodation and entry deterrence and find that strategic entry accommodation is the optimal strategy for the entrant, not entry deterrence. Thereafter we compare the duopoly model with a two-price monopoly market to ascertain whether the duopoly market has a greater coverage than a two-price monopoly market. Unlike in chapter 2, we do not get a direct answer. Coverage could be higher in either of the two markets. However, as the value of search in the decentralized market decreases (and in the limit reaches zero), the duopoly market has greater coverage than a two-price monopoly market. Finally we extend the model to allow for sequential entry. When intermediation is costless we find that the number of entrants tends to infinity and that matching is socially efficient. However introducing intermediation costs distorts this efficiency result and only a finite number of intermediaries enter the market.