The paper studies the representation and characterization of risks generated by a continuum of random variables. The Main Theorem is a characterization of a broad class of continuum processes in terms of the decomposition of risk into aggregate and idiosyncratic components, and in terms of the approximation of the continuum process by finite collections of random variables. This characterization is used to study decision making problems with anonymous and state-independent payoffs. An Extension Theorem shows that if such a payoff function is defined on simple processes, then it has a unique continuous extension to the class of processes characterized in this paper. This extension is formulated without reference to sample realizations and with minimal restrictions on the patterns of correlation between the random variables. As an application, the theory is used to develop a new model of large games which emphasizes the explicit description of the players' randomizations. This model is used to study the class of environments in which Schmeidler's (1973) representation of strategic uncertainty in large games is valid.

Leading equilibrium concepts require agents’ beliefs to coincide with the model’s true probabilities and thus be free of systematic errors. This implicitly assumes a criterion that tests beliefs against the observed outcomes generated by the model. We formalize this requirement in stationary environments. We show that there is a tension between requiring that beliefs can be tested against systematic errors and allowing agents to disagree or be uncertain about the long-run fundamentals. We discuss the application of our analysis to asset pricing, Markov perfect equilibria, and dynamic games.

I study individuals who use frequentist models to draw uniform inferences from independent and identically distributed data. The main contribution of this paper is to show that distinct models may be consistent with empirical evidence, even in the limit when data increases without bound. Decision makers may then hold different beliefs and interpret their environment differently even though they know each other's model and base their inferences on the same evidence. The behavior modeled here is that of rational individuals confronting an environment in which learning is hard, rather than individuals beset by cognitive limitations or behavioral biases.

Even the simplest of economic transactions can be so complex that it is practically impossible to list the entire range of outcomes and contingencies that might affect contractual performance. Scholars outside the formal economic field of contract theory have long recognized that this complexity implies that real-world contracts will almost never provide an exhaustive description of the rights and obligations of the contracting parties in every possible contingency. The central role of contractual incompleteness in transaction-cost economics, contract law, and the law and economics movement should be contrasted with the minor role it played in the formal theory of contracts developed by economic theorists over the past two decades. The starting point of most formal contracting models (e.g., the principal-agent model with moral hazard) is the feasibility of a complete description of the set of possible contingencies and the ability to write contracts that are sensitive to even the most minute details of the events arising in the course of the transaction. One reason that might help explain this neglect of the role of incomplete contracts is the lack of a well-developed theory of contract enforcement (governance). By focusing on explicit written contracts as the only available method of governance, many models abstract from the role of other instruments such as ownership rights, contract law as interpreted by courts, reputation in long-term relationships, and social conventions that define what constitutes acceptable

We show that a simple "reputation-style" test can always identify which of two experts is informed about the true distribution. The test presumes no prior knowledge of the true distribution, achieves any desired degree of precision in some fixed finite time, and does not use "counterfactual" predictions. Our analysis capitalizes on a result of Fudenberg and Levine (1992) on the rate of convergence of supermartingales. Copyright Copyright 2008 by The Econometric Society.

Hume (1748) challenged the idea that a general claim (e.g., “all swans are white”) can be validated by empirical evidence, no matter how compelling. We examine this issue from the perspective of a tester who must accept or reject the forecasts of a potential expert. If experts can be skeptical about the validity of claims then they can evade rejection strategically. In contrast, if experts are required to conclude that claims backed by sufficient evidence are likely to be true, then they can be tested and rejected. These results provide an economic rationale for claim validation based on incentive problems. (JEL D82)

We develop a model of undescribable events. Examples of events that are well understood by economic agents but are prohibitively difficult to describe in advance abound in real life. This notion has also pervaded a substantial amount of economic literature. Undescribable events in our model are understood by economic agents-their consequences and probabilities are known-but are such that every finite description of such events necessarily leaves out relevant features that have a non-negligible impact on the parties' expected utilities. We illustrate our results using a simple coinsurance problem as a backdrop. When the only uncertainty faced by the two agents is an undescribable event the optimal finite coinsurance contract is no contract at all. Copyright 2006, Wiley-Blackwell.