This paper analyzes a multiperiod version of the Spence Job Market Signalling Model in which workers cannot commit to an education choice and firms make wage offers at any point in time. The dynamic competition combined with the incomplete information yield a multiplicity of sequential equilibria, including ones that sustain implicit collusion, even though the length of the game is finite. Emphasis is placed on equilibria that satisfy the “independence of never weak best response” criterion of Kohlberg and Mertens (1986). It is shown that in the limit, as the time between offers tends to zero, any such equilibrium results (in expectation) in the unique stable outcome of the static Spence model.

Conjugate duality relationships are pervasive in matching and implementation problems and provide much of the structure essential for characterizing stable matches and implementable allocations in models with quasilinear (or transferable) utility. In the absence of quasilinearity, a more abstract duality relationship, known as a Galois connection, takes the role of (generalized) conjugate duality. While weaker, this duality relationship still induces substantial structure. We show that this structure can be used to extend existing results for, and gain new insights into, adverse-selection principal-agent problems and two-sided matching problems without quasilinearity.

We study markets in which agents first make investments and are then matched into potentially productive partnerships. Equilibrium investments and the equilibrium matching will be efficient if agents can simultaneously negotiate investments and matches, but we focus on markets in which agents must first sink their investments before matching. Additional equilibria may arise in this sunk-investment setting, even though our matching market is competitive. These equilibria exhibit inefficiencies that we can interpret as coordination failures. All allocations satisfying a constrained efficiency property are equilibria, and the converse holds if preferences satisfy a separability condition. We identify sufficient conditions (most notably, quasiconcave utilities) for the investments of matched agents to satisfy an exchange efficiency property as well as sufficient conditions (most notably, a single crossing property) for agents to be matched positive assortatively, with these conditions then forming the core of sufficient conditions for the efficiency of equilibrium allocations.

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.