An important application of the theory of choice under uncertainty is to asset markets, and an important property in these markets is a preference for portfolio diversification. If an investor is an expected utility maximizer, then (s)he is risk averse if and only if (s)he exhibits a preference for diversification. This paper examines the relationship between risk aversion and portfolio diversification when preferences over probability distributions of wealth do not have an expected utility representation

We propose a method to test a prediction of the distribution of a stochastic process. In a non-Bayesian, non-parametric setting, a predicted distribution is tested using a realization of the stochastic process. A test associates a set of realizations for each predicted distribution, on which the prediction passes, so that if there are no type I errors, a prediction assigns probability 1 to its test set. Nevertheless, these test sets can be “small”, in the sense that “most” distributions assign it probability 0, and hence there are “few” type II errors. It is also shown that there exists such a test that cannot be manipulated, in the sense that an uninformed predictor, who is pretending to know the true distribution, is guaranteed to fail on an uncountable number of realizations, no matter what randomized prediction he employs. The notion of a small set we use is category I, described in more detail in the paper.

We explore sequential voting in symmetric two‐option environments. We show that the (informative) symmetric equilibria of the simultancous voting game are also equilibria in any sequential voting structure. In unanimity games, (essentially) the whole set of equilibria is the same in all sequential structures. We also explore the relationship between simultaneous and sequential voting in other contexts. We illustrate several instances in which sequential voting does no better at aggregating information than simultaneous voting. The inability of the sequential structure to use additional information in voting models is distinct from that in the herd‐cascade literature.

We endogenize preferences using the “indirect evolutionary approach”. Individuals are randomly matched to play a two-person game. Individual (subjective) preferences determine their behaviour and may differ from the actual (objective) pay-offs that determine fitness. Matched individuals may observe the opponents’ preferences perfectly, not at all, or with some in-between probability. When preferences are observable, a stable outcome must be efficient. When they are not observable, a stable outcome must be a Nash equilibrium and all strict equilibria are stable. We show that, for pure-strategy outcomes, these conclusions are robust to allowing almost perfect, and almost no, observability, with the notable exception that inefficient strict equilibria may fail to be stable with any arbitrarily small degree of observability (despite being stable with no observability).

The authors discuss the unity between the two standard approaches to noncooperative solution concepts for games. The decision-theoretic approach starts from the assumption that the rationality of the players is common knowledge. This leads to the notion of correlated rationalizability. It is shown that correlated rationalizability is e quivalent to a posteriori equilibrium-a refinement of subjective corr elated equilibrium. Hence a decision-theoretic justification for the equilibrium approach to game theory is provided. An analogous equival ence result is proved between independent rationalizability, which is the appropriate concept if each player believes that the others act independently, and conditionally independent a posteriori equilibrium.

We study the random Strotz model, a version of the Strotz (1955) model with uncertainty about the nature of the temptation that will strike. We show that the random Strotz representation is unique and characterize a comparative notion of “more temptation averse.” Also, we demonstrate an unexpected connection between the random Strotz model and a generalization of the Gul–Pesendorfer (GP) (2001) model of temptation which allows for the temptation to be uncertain and which we call random GP. In particular, a preference over menus has a random GP representation if and only if it also has a representation via a random Strotz model with sufficiently smooth uncertainty about the intensity of temptation. We also show that choices of menus combined with choices from menus can distinguish the random GP and random Strotz models.

An agent chooses among projects with random outcomes. His payoff is increasing in the outcome and in an observer's expectation of the outcome. With some probability, the agent can disclose the true outcome to the observer. We show that choice is inefficient: the agent favors riskier projects even with lower expected returns. If information can be disclosed by a challenger who prefers lower beliefs of the observer, the chosen project is excessively risky when the agent has better access to information, excessively risk{averse when the challenger has better access, and efficient otherwise. We also characterize the agent's worst-case equilibrium payoff.

We develop a theory of monotone comparative statics for models with adjustment costs. We show that comparative‐statics conclusions may be drawn under the usual ordinal complementarity assumptions on the objective function, assuming very little about costs: only a mild monotonicity condition is required. We use this insight to prove a general Le Chatelier principle: under the ordinal complementarity assumptions, if short‐run adjustment is subject to a monotone cost, then the long‐run response to a shock is greater than the short‐run response. We extend these results to a fully dynamic model of adjustment over time: the Le Chatelier principle remains valid, and under slightly stronger assumptions, optimal adjustment follows a monotone path. We apply our results to models of saving, production, pricing, labor supply, and investment.