The value of a stochastic information structure

Upon observing a signal, a Bayesian decision maker updates her probability distribution over the state space, chooses an action, and receives a payoff that depends on the state and the action taken. An information structure determines the set of possible signals and the probability of each signal given a state. For a fixed decision problem, the value of an information structure is the maximal expected utility that the decision maker can get when the observed signals are governed by this structure. Thus, every decision problem induces a preference order over information structures according to their value. We characterize preference orders that can be obtained in this way. We also characterize the functions defined over information structures that measure their value.     

Strategic argumentation

I analyze a game between an uninformed decision maker and a possibly biased expert. The expert receives a set of arguments, and each argument favors one of two alternatives. He can disclose each argument credibly, but cannot prove whether he has disclosed everything. In all equilibria, the biased expert sends messages containing arguments both for and against his preferred alternative. However, the decision maker is not influenced by the unfavorable arguments revealed by the biased expert. The latter is able to convince the decision maker to choose the biased expert?s preferred alternative only if he reveals sufficiently many favorable arguments.     

Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice

We develop a model which reflects the tendency of people to simplify the decision problems they face. The decision maker chooses among alternate strategies only on the basis of the payoff she assesses she would obtain from them, and these assessments do not explicitly take into account her subjective judgements regarding the likelihood of alternate states of the world. At each stage, the decision maker chooses the strategy that she assesses to give the highest payoff. She updates her assessments adaptively. We show that such behavior leads to maxmin choices. We also consider the decision maker who experiences shocks. Journal of Economic Literature Classification Numbers: C7, D8.     

PREFERENCES UNDER IGNORANCE

A decision maker (DM) makes choices from different sets of alternatives. The DM is initially ignorant of the payoff associated with each alternative and learns these payoffs only after a large number of choices have been made. We show that, in the presence of an outside option, once payoffs are learned, the optimal choice rule from sets of alternatives can be rationalized by a DM with strict preferences over all alternatives. Under this model, the DM has preferences for preferences while being ignorant of what preferences are “right.”     

Robust estimation and control under commitment

In a Markov decision problem with hidden state variables, a decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby as measured by their expected log likelihood ratios (entropies). Sets of martingales represent alternative models. Within a two-player zero-sum game under commitment, a minimizing player chooses a martingale at time 0. Probability distributions that solve distorted filtering problems serve as state variables, much like the posterior in problems without concerns about misspecification. We state conditions under which an equilibrium of the zero-sum game with commitment has a recursive representation that can be cast in terms of two risk-sensitivity operators. We apply our results to a linear quadratic example that makes contact with findings of T. Ba?ar and P. Bernhard [H^∞-Optimal Control and Related Minimax Design Problems, second ed., Birkhauser, Basel, 1995] and P. Whittle [Risk-sensitive Optimal Control, Wiley, New York, 1990].     

Rationalizability and the savage axioms

Summary. Suppose there is a finite set of acts defined on a finite state space and a decision maker chooses an act from the set. In this setting, the subjective expected utility model is observationally indistinguishable from all models of preference that satisfy Savage's axiom P3. The result has implications also for rationalizability in strategic games. Received: September 18, 1998; revised version: January 29, 1999     

Knightian decision theory and econometric inferences

An uncertainty averse Knightian decision maker has a set of probability distributions over outcomes and chooses something other than the status quo only if the change increases the expected payoff according to all the distributions. It is possible to define a standardized degree of uncertainty aversion. To each such degree, there corresponds a set of prior distributions over the parameters of a Gaussian linear regression model, these priors being centered on a uniform prior. The set of posterior means corresponding to this set of priors has the same properties as a standard confidence region.     

Aggregation of multiple prior opinions

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker?s utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker?s set of priors is precisely all the weighted-averages of priors, where an expert?s prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker?s valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts? valuations.     

Prior symmetry, similarity-based reasoning, and endogenous categorization

This paper presents a rational theory of categorization and similarity-based reasoning. I study a model of sequential learning in which the decision maker infers unknown properties of an object from information about other objects. The decision maker may use the following heuristics: divide objects into categories with similar properties and predict that a member of a category has a property if some other member of this category has this property. The environment is symmetric: the decision maker has no reason to believe that the objects and properties are a priori different. In symmetric environments, categorization is an optimal solution to an inductive inference problem. Any optimal solution looks as if the decision maker categorizes. Various experimental observations about similarity-based reasoning coincide with the optimal behavior in my model.     

A model of boundedly rational “neuro” agents

We consider a model in which each agent in a population chooses one of two options. Each agent does not know what the available options are and can choose an option only after observing another agent who has already chosen that option. In addition, the agents’ preferences over the two options are correlated. An agent can either imitate an observed agent or wait until he meets two agents who made different choices, in which case he can compare their choices and choose accordingly. A novel feature of the model is that agents observe not only the choices made by others, but also some information about the process that led them to those choices. We study two cases: In the first, an agent notes whether the observed agent imitated others or whether he actually compared the available alternatives. In the second, an agent notes whether the observed agent’s decision was hasty or not. It is shown that in equilibrium the probability of making a mistake is higher in the second case and that the existence of these nonstandard “neuro” observations systematically biases the equilibrium distribution of choices.     

Recursive robust estimation and control without commitment

In a Markov decision problem with hidden state variables, a posterior distribution serves as a state variable and Bayes’ law under an approximating model gives its law of motion. A decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby when measured by their expected log likelihood ratios (entropies). Martingales represent alternative models. A decision maker constructs a sequence of robust decision rules by pretending that a sequence of minimizing players choose increments to martingales and distortions to the prior over the hidden state. A risk sensitivity operator induces robustness to perturbations of the approximating model conditioned on the hidden state. Another risk sensitivity operator induces robustness to the prior distribution over the hidden state. We use these operators to extend the approach of Hansen and Sargent [Discounted linear exponential quadratic Gaussian control, IEEE Trans. Automat. Control 40(5) (1995) 968-971] to problems that contain hidden states.     

Real and financial effects of insider trading with correlated signals

Summary. In this paper we study the real and financial effects of insider trading in a Static, Kyle-type model. In our model the insider is also the manager of the firm. Hence the insider chooses both the amount of the real output to be produced and the amount of the stock of the firm to trade. The aim of the paper is to study the relationship between financial decisions and real decisions. In particular, we examine how insider trading on the stock market affects the real output and price and how the real decision making affects the financial variables, such as the extent of insider trading, stock prices, and the stock pricing rule of the market maker. In the model, the market maker observes two correlated signals: the total order flow and the market price of the real good. We study the informativeness of the stock price and the effects on insider's profits. We also construct a compensation scheme that aligns the interests of the insider and the firm. Finally, we generalize the pricing rule set up by a competitive market maker and analyze the comparative statics of the model. Received: October 3, 1999: revised version: December 1, 1999     

Strategy-proof preference aggregation: Possibilities and characterizations

An aggregation rule maps each profile of individual strict preference orderings over a set of alternatives into a social ordering over that set. We call such a rule strategy-proof if misreporting one's preference never produces a different social ordering that is between the original ordering and one's own preference. After describing two examples of manipulable rules, we study in some detail three classes of strategy-proof rules: (i) rules based on a monotonic alteration of the majority relation generated by the preference profile; (ii) rules improving upon a fixed status-quo; and (iii) rules generalizing the Condorcet–Kemeny aggregation method.     

The subjective expected utility hypothesis and revealed preference

Summary A choice behavior of a decision maker is said to satisfy the subjective expected utility hypothesis if there exist a utility and a subjective probability such that a decision maker chooses acts with the highest expected utility. We present a revealed preference characterization of choice behavior that is consistent with the subjective expected utility hypothesis. Our result applies to any state space and compact sets of prizes and observations (either finite or infinite).     

Inter-temporal choices with temporal reference dependence

I develop an intertemporal choice model for rational deviators whose preferences depend not only on their actual consumption but also on comparison to their beliefs about the optimal consumption. The standard decision maker is loss averse with respect to this belief-dependent reference point. When psychologically weighted loss aversion is low, a decision maker deviates from the standard intertemporal choice behavior and over-consumption, as well as the alternative possibility of under-consumption can be rationalized. When the decision maker has time-varying degrees of loss aversion, he re-optimizes the consumption plan through adjusted beliefs as subsequent selves realize that past decision for the present period is no longer optimal. In the dynamic model, I solve for consistent intertemporal optimization rules by which a dynamic deviator should meet rational intertemporal consistency at each point in time. Finally, I demonstrate that the dynamic reference dependent model can solve a puzzling feature in lifecycle consumption data.     

Lexicographic compositions of multiple criteria for decision making

This paper considers two distinct procedures to lexicographically compose multiple criteria for social or individual decision making. The first procedure composes M binary relations into one, and then selects its maximal elements. The second procedure first selects the set of maximal elements of the first binary relation, and then within that set, chooses the maximal elements of the second binary relation, and iterates the procedure until the Mth binary relation. We show several distinct sets of conditions for the choice functions representing these two procedures to satisfy non-emptiness and choice-consistency conditions such as contraction consistency and path independence. We also examine the relationships between the outcomes of the two procedures. Finally we investigate under what conditions the outcomes of each procedure are independent of the order of lexicographic application of the criteria.     

Persuasion,binary choice,and the costs of dishonesty

We study the strategic interaction between a decision maker who needs to take a binary decision but is uncertain about relevant facts and an informed expert who can send a message to the decision maker but has a preference over the decision. We show that the probability that the expert can persuade the decision maker to take the expert’s preferred decision is a hump-shaped function of his costs of sending dishonest messages.     

Unambiguous events and dynamic Choquet preferences

This paper explores the relationship between dynamic consistency and existing notions of unambiguous events for Choquet expected utility preferences. A decision maker is faced with an information structure represented by a filtration. We show that the decision maker’s preferences respect dynamic consistency on a fixed filtration if and only if the last stage of the filtration is composed of unambiguous events in the sense of Nehring (Math Social Sci 38:197–213, 1999). Adopting two axioms, conditional certainty equivalence consistency and constrained dynamic consistency to filtration measurable acts, it is shown that the decision maker respects these two axioms on a fixed filtration if and only if the last stage of the filtration is made up of unambiguous events in the sense of Zhang (Econ Theory 20:159–181, 2002).     

Cognitive constraints, contraction consistency, and the satisficing criterion

A theory of decision making is proposed that offers an axiomatic basis for the notion of “satisficing” postulated by Herbert Simon. The theory relaxes the standard assumption that the decision maker always fully perceives his preferences among the available alternatives, requiring instead that his ability to perceive any given preference be decreasing with respect to the complexity of the choice problem at hand. When complexity is aligned with set inclusion, this exercise is shown to be equivalent to abandoning the contraction consistency axiom of classical choice theory.     

An econometric model of tenure choice and demand for housing as a joint decision

This paper models a household's choice of tenure and demand for housing services as a joint decision imposing the restriction that both discrete and continuous decisions are derived from a single preference ordering. The utility index for households is the translog form of the reciprocal indirect utility function allowing for random preferences. Each household chooses between the two main tenures, the owner-occupied and subsidised rental sectors, but households may be rationed in either or both of these sectors and refused admission, in which case they are assumed to enter the third sector, uncontrolled rental. The model is estimated on UK data for 5895 households.