We study transactions that require investments before trading in a competitive market, when forward contracts fixing the transaction price are absent. We show that, despite the market being perfectly competitive and subject to arbitrarily little uncertainty, the inability to jointly determine investment levels and prices may make it impossible for buyers and sellers to predict the prices at which they will trade, leading to inefficient levels of investment and trade.

We consider a market with “red” and “green” workers, where labels are payoff irrelevant. Workers may acquire skills. Skilled workers search for vacancies, while firms search for workers. A unique symmetric equilibrium exists in which color is irrelevant. There are also asymmetric equilibria in which firms search only for green workers, more green than red workers acquire skills, skilled green workers receive higher wages, and the unemployment rate is higher among skilled red workers. Discrimination between ex ante identical individuals arises in equilibrium, and yet firms have perfect information about their workers, and strictly prefer to hire minority workers. (JEL C70, D40, J30)

We examine an economy in which the cost of consuming some goods can be reduced by making commitments that reduce flexibility. We show that such consumption commitments can induce consumers with risk-neutral underlying utility functions to be risk averse over small variations in income, but sometimes to seek risk over large variations. As a result, optimal employment contracts will smooth wages conditional on being employed, but may incorporate a possibility of unemployment. Copyright 2008, Wiley-Blackwell.

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.

Different extensive form games with the same reduced normal form can have different information sets and subgames. This generates a tension between a belief in the strategic relevance of information sets and subgames and a belief in the sufficiency of the reduced normal form. We identify a property of extensive form information sets and subgames which we term strategic independence. Strategic independence is captured by the reduced normal form, and can be used to define normal form information sets and subgames. We prove a close relationship between these normal form structures and their extensive form namesakes. Using these structures, we are able to motivate and implement solution concepts corresponding to subgame perfection, sequential equilibrium, and forward induction entirely in the reduced normal form, and show close relations between their implications in the normal and extensive form.

We formulate a notion of stable outcomes in matching problems with one-sided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make. We show that the set of stable outcomes is nonempty in incomplete-information environments, and is a superset of the set of complete-information stable outcomes. We then provide sufficient conditions for incomplete-information stable matchings to be efficient. Lastly, we define a notion of price-sustainable allocations and show that the set of incomplete-information stable matchings is a subset of the set of such allocations.

We explore the deliberate infusion of ambiguity into the design of contracts. We show that when the agent is ambiguity‐averse and hence chooses an action that maximizes their minimum utility, the principal can strictly gain from using an ambiguous contract, and this gain can be arbitrarily high. We characterize the structure of optimal ambiguous contracts, showing that ambiguity drives optimal contracts toward simplicity. We also provide a characterization of ambiguity‐proof classes of contracts, where the principal cannot gain by infusing ambiguity. Finally, we show that when the agent can engage in mixed actions, the advantages of ambiguous contracts disappear.