Dynamic matching and bargaining games are models of decentralized markets with trading frictions. A central objective is to investigate how equilibrium outcomes depend on the level of frictions. In particular, does the trading outcome become Walrasian when frictions become small? Existing specifications of such games provide divergent answers. This paper presents a new characterization result for competitive allocations in quasilinear economies. The characterization result is used to investigate what causes these differences and to generalize insights from the analysis of specific matching and bargaining games. (JEL C73, C78, D82, D83)

This paper studies a first‐price common‐value auction in which bidders do not know the number of their competitors. In contrast to the case of common‐value auctions with a known number of rival bidders, the inference from winning is not monotone, and a “winner's blessing” emerges at low bids. As a result, bidding strategies may not be strictly increasing, but instead may contain atoms. Moreover, an equilibrium fails to exist when the expected number of competitors is large and the bid space is continuous. Therefore, we consider auctions on a grid. On a fine grid, high‐signal bidders follow an essentially strictly increasing strategy, whereas low‐signal bidders pool on two adjacent bids on the grid. The solutions of a “communication extension” based on Jackson, Simon, Swinkels, and Zame (2002) capture the equilibrium bidding behavior in the limit, as the grid becomes arbitrarily fine.

Most of the literature that studies frictional search‐and‐matching models with heterogeneous agents and random search investigates steady state equilibria. Steady state equilibrium requires, in particular, that the flows of agents into and out of the population of unmatched agents balance. We investigate the structure of this balance condition, taking agents' matching behavior as given. Building on the “fundamental matching lemma” for quadratic search technologies in Shimer and Smith (2000), we establish existence, uniqueness, and comparative statics properties of the solution to the balance condition for any search technology satisfying minimal regularity conditions. Implications for the existence and structure of steady state equilibria in the Shimer–Smith model and extensions thereof are noted. These reinforce the point that much of the structure of search‐and‐matching models with quadratic search technologies carries over to more general search technologies.