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 study a simple model of a decentralized market game in which firms make directed offers to workers. We focus on markets in which agents have aligned preferences. When agents have complete information or when there are no frictions in the economy, there exists an equilibrium that yields the stable match. In the presence of market frictions and preference uncertainty, harsher assumptions on the richness of the economy have to be made in order for decentralized markets to generate stable outcomes in equilibrium.

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.

This thesis studies the importance and implications of information asymmetry in decentralized markets with search frictions. The first chapter provides an introduction and literature review. In the next chapter, I propose a model of the housing market using a search framework in which sellers are unable to commit to asking prices announced ex ante. Relaxing the commitment assumption prevents sellers from using price posting as a signalling device to direct buyers' search. Adverse selection and inefficient entry on the demand side then contribute to housing market illiquidity. Real estate agents that can facilitate the search process can segment the market and alleviate information frictions. In Chapter 3, I further study the importance and implications of the commitment assumptions embedded in directed search models. I eliminate commitment to take-it-or-leave-it trading mechanisms in a model of the labour market with worker heterogeneity and a matching process that allows for multiple firms to match with a single worker. When workers and firms cannot commit to ex ante offers, to an allocation rule, or to an ex post bargaining strategy, the equilibrium is necessarily inefficient. This is true for a broad class of protocols for wage determination, of which bilateral bargaining and Bertrand competition are special cases. Finally, Chapter 4 presents a theory of land market activity for settings where there is uncertainty and private information about the security of land tenure. Land sellers match with buyers in a competitive search environment, and an illiquid land market emerges as a screening mechanism. The implications of the theory are tested using household level data from Indonesia. As predicted, formally titled land is more liquid than untitled land in the sense that ownership rights are more readily transferable.