This paper shows that all perfect Bayesian equilibria of a dynamic matching game with two-sided incomplete information of independent private values variety are asymptotically Walrasian. Buyers purchase a bundle of heterogeneous, indivisible goods and sellers own one unit of an indivisible good. Buyer preferences and endowments as well as seller costs are private information. Agents engage in costly search and meet randomly. The terms of trade are determined through a Bayesian mechanism proposal game. The paper considers a market in steady state. As discounting and the fixed cost of search become small, all trade takes place at a Walrasian price. However, a robust example is presented where the limit price vector is a Walrasian price for an economy where only a strict subsets of the goods in the original economy are traded, i.e, markets are missing at the limit. Nevertheless, there exists a sequence of equilibria that converge to a Walrasian equilibria for the whole economy where all markets are open. -- Matching and Bargaining ; Search ; Foundations for Perfect Competition ; Two-sided Incomplete Information

We consider decentralized matching with frictions in a two-sided market. By frictions, we mean natural refinements that make it hard or even impossible to use the canonical notion of stability. Instead of that, we use non-cooperative game theory tools: a matching process is described as a game where all agents have their own strategies. It allows us to use Nash equilibrium to distinguish "good" and "bad" matchings. Although this approach significantly complicates the model, market frictions (incomplete information, dynamics, and application costs) allow us to get more nuanced results and better understanding of the matching process itself. In Chapter 2, we consider multi-period decentralized matching in a market of universities and students. Because of dynamics, asymmetry, and private information, we always observe delays and coordination failures with nonzero probability. We show that problems of miscoordination and delay may be solved by signaling or by incentivizing immediate response turning a dynamic problem into a static one and make the matching stable. Although implementing signaling or immediate response is always socially beneficial, it is not necessarily beneficial for the best university. We also obtain sufficient conditions for assortative matching to be and not to be in equilibrium. In Chapter 3, we consider decentralized matching in a market of firms and workers with application costs and limited budgets. Workers choose whether they should take the risk of applying to a higher-ranked firm (with some probability of rejection) or make a safe choice. We show that application costs set by firms with uncertain capacity may be treated as a screening instrument in order to attract only strong applicants or avoid the competition. Surprisingly, competition may lead to increasing costs: low-ranked firms may even prefer implementing highest possible costs in equilibrium. We provide economic intuition behind this paradox and find necessary and sufficient conditions that lead to this result. Finally, Chapter 4 is devoted to the difference in results for firms with limited and unlimited capacity. The main insight here is that in order to avoid competition with high-type employees, low-type employees may send applications to higher-ranked firms. This happens when the entire pool of employees is weak enough.

We experimentally study decentralized one-to-one matching markets with transfers. We vary the information available to participants, complete or incomplete, and the surplus structure, supermodular or submodular. Several insights emerge. First, while markets often culminate in efficient matchings, stability is more elusive, reflecting the difficulty of arranging attendant transfers. Second, incomplete information and submodularity present hurdles to efficiency and especially stability; their combination drastically diminishes stability's likelihood. Third, matchings form "from the top down" in complete-information supermodular markets, but exhibit many more and less-obviously ordered offers otherwise. Last, participants' market positions matter far more than their dynamic bargaining styles for outcomes.