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We analyze maximization of revenue in the dynamic and stochastic knapsack problem where a given capacity needs to be allocated by a given deadline to sequentially arriving agents. Each agent is described by a two-dimensional type that reflects his capacity requirement and his willingness to pay per unit of capacity. Types are private information. We first characterize implementable policies. Then we solve the revenue maximization problem for the special case where there is private information about per-unit values, but capacity needs are observable. After that we derive two sets of additional conditions on the joint distribution of values and weights under which the revenue maximizing policy for the case with observable weights is implementable, and thus optimal also for the case with twodimensional private information. In particular, we investigate the role of concave continuation revenues for implementation. We also construct a simple policy for which per-unit prices vary with requested weight but not with time, and we prove that it is asymptotically revenue maximizing when available capacity and time to the deadline both go to infinity. This highlights the importance of nonlinear as opposed to dynamic pricing.

Heterogeneous buyers and sellers must make investments before entering a continuum assignment market. I show that efficient ex post contracting equilibria (Cole, Mailath, and Postlewaite 2001b) exist in a general assignment game framework. I then shed light on what enables and what precludes coordination failures. A simple condition—absence of technological multiplicity—guarantees efficient investments for each pair, but a mismatch of agents may still occur. However, using optimal transport theory, I also show that mismatch is heavily constrained in certain multidimensional environments with differentiated agents and no technological multiplicity. Under technological multiplicity, even extreme ex ante heterogeneity need not preclude inefficiencies. (JEL C78, D41, D86)

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