The paper studies a model in which in period 1, a decision-maker chooses a set of lotteries; and in period 2, Nature chooses a lottery from the set chosen by the decision-maker and the decision-maker consumes the lottery chosen by Nature. Larger sets are interpreted as representing more ambiguous objective information about the lottery that will be consumed. The axioms imposed on preferences over sets of lotteries generalize those often imposed on preferences over single lotteries in the existing literature. A decision-maker who satisfies these axioms evaluates sets of lotteries according to a weighted average of the expected utilities of the best and the worst lottery in a set, with the weights interpreted as a measure of (comparative) attitude to objective ambiguity. ∗I am grateful to Walter Bossert and Peter Klibanoff for their remarks and suggestions regarding related literature. The paper has been presented at Northwestern University, Princeton University,

The folk theorem of repeated games has established that cooperative behavior can be sustained as an equilibrium in repeated settings. Early papers on private monitoring and a recent paper of Cole and Kocherlakota (Games and Economic Behavior, 53 [2005], 59–72) challenge the robustness of this result by providing examples in which cooperation breaks down when players observe only imperfect private signals about other players' actions, or when attention is restricted to strategies with finite memory. This paper shows that Cole and Kocherlakota's result is an artefact of a further restriction that they impose. We prove that the folk theorem with imperfect public monitoring holds with strategies with finite memory. As a corollary, we establish that the folk theorem extends to environments in which monitoring is close to public, yet private.

The difficulties in properly anticipating key economic variables may encourage decision makers to rely on experts' forecasts. Professional forecasters, however, may not be reliable and so their forecasts must be empirically tested. This may induce experts to forecast strategically in order to pass the test. A test can be ignorantly passed if a false expert, with no knowledge of the data-generating process, can pass the test. Many tests that are unlikely to reject correct forecasts can be ignorantly passed. Tests that cannot be ignorantly passed do exist, but these tests must make use of predictions contingent on data not yet observed at the time the forecasts are rejected. Such tests cannot be run if forecasters report only the probability of the next period's events on the basis of the actually observed data. This result shows that it is difficult to dismiss false, but strategic, experts who know how theories are tested. This result also shows an important role that can be played by predictions contingent on data not yet observed.

We prove the folk theorem for discounted repeated games under private, almost-perfect monitoring. Our result covers all finite, n-player games that satisfy the usual full-dimensionality condition. Mixed strategies are allowed in determining the individually rational payoffs. We assume no cheap-talk communication between players and no public randomization device. Copyright The Econometric Society 2006.

We examine Popper's falsifiability within an economic model in which a tester hires a potential expert to produce a theory. Payments are contingent on the performance of the theory vis-à-vis data. We show that if experts are strategic, falsifiability has no power to distinguish scientific theories from worthless theories. The failure of falsification in screening informed and uninformed experts motivates questions on the broader concepts of refutation and verification. We demonstrate an asymmetry between the two concepts. Like falsification, verification contracts have no power to distinguish between informed and uninformed experts, but some refutation contracts are capable of screening experts.

We introduce a class of strategies that generalizes examples constructed in two-player games under imperfect private monitoring. A sequential equilibrium is belief-free if, after every private history, each player's continuation strategy is optimal independently of his belief about his opponents' private histories. We provide a simple and sharp characterization of equilibrium payoffs using those strategies. While such strategies support a large set of payoffs, they are not rich enough to generate a folk theorem in most games besides the prisoner's dilemma, even when noise vanishes.

We consider contests with many, possibly heterogeneous, players and prizes, and show that the equilibrium outcomes of such contests are approximated by the outcomes of mechanisms that implement the assortative allocation in an environment with a single agent that has a continuum of possible types. This makes it possible to easily approximate the equilibria of contests whose exact equilibrium characterization is complicated, as well as the equilibria of contests for which there is no existing equilibrium characterization.

We provide sufficient conditions for equilibrium existence in first‐price auctions with private values that accommodate non quasi‐linear utilities and value‐distributions that contain atoms and exhibit positive or negative correlation. These conditions show that equilibrium existence often turns on properties of a single statistic of the joint distribution of values, namely, the minimum value in the support of the high‐value distribution (the mHV). We also show that modifying the standard tie‐breaking rule only at the mHV is enough to guarantee equilibrium existence without our sufficient conditions. Our results also apply to Bertrand price competition when each firm's constant marginal cost is private information.

Many countries base college admissions on a centrally administered test. Students invest a great deal of resources to improve their performance on the test, and there is growing concern about the high costs associated with these activities. We consider modifying the test by introducing performance-disclosure policies that pool intervals of performance rankings. Pooling affects the equilibrium allocation of students to colleges, which hurts some students and benefits others, but also affects students’ effort. We investigate how such policies can improve students’ welfare in a Pareto sense, study the Pareto frontier of pooling policies, and identify improvements that are robust to the distribution of college seats. We illustrate the potential applicability of our results with an empirical estimation that uses data on college admissions in Turkey. We find that a policy that pools a large fraction of the lowest-performing students leads to a Pareto improvement in a contest based on the estimated parameters. A laboratory experiment based on the estimated parameters generally supports our theoretical predictions.