© 2025. All rights reserved.
© 2025. All rights reserved.
An agent employs a stochastic automaton to search for the best alternative drawn randomly with replacement from a menu of unknown composition. In each state, the automaton inquires about some attribute of the currently drawn alternative. I study how the minimum complexity of near-optimal automata depends on the language—collection of binary attributes used to describe alternatives. I show that the tight lower bound on transitional complexity among all languages is 3·⌈log2 (m)⌉, where m is the number of alternatives valued distinctly. I also provide a linear upper bound. If a language facilitates additive utility representation with the smallest possible number of attributes, it reaches the lower complexity bound. This result is if and only if when (3/4)·2n < m ≤ 2n for a natural n. Finally, I drop the assumption that each attribute has 2 values and characterize the lower complexity bound for general languages.
We develop and analyze a model of framing under ambiguity. Frames are circumstances, unobservable to the analyst, that shape the agent’s perception of the relevant ambiguity. The analyst observes a choice correspondence that represents the set of possible choices under the various decision frames. We assume that each frame induces a set of beliefs, while the agent’s utility index remains fixed across frames. We characterize the information about the decision frames that the analyst can identify from the choice behavior. If the collection of sets of beliefs is nested or if all the sets of beliefs are singletons, the collection is uniquely identified. One agent is more consistent than another if the former has a unique choice whenever the latter does. We characterize comparative consistency in terms of the model parameters and apply this result to characterize the aggregation of preferences that satisfy the Unanimity criterion. Finally, we characterize the behavior of agents who recognize that they are subject to different frames and learn by combining their frames into a single model.
Goods and services—public housing, medical appointments, schools—are often allocated to individuals who rank them similarly but differ in their preference intensities. We characterize optimal allocation rules in such settings, considering both the case in which individual preferences are known and ones in which they need to be elicited. Several insights emerge. First-best allocations may involve allocating to some agents lotteries between very high-ranked and very low-ranked goods. When preference intensities are private information, second-best allocations always involve such lotteries and, crucially, may coincide with first-best allocations. Second-best allocations may also entail disposal of services. We also discuss a market-based alternative approach and show how it differs.
An expected utility maximizer learns various aspects of her preferences in different decision frames; each frame is defined as a collection of observable features of the choice environment. We interpret each feature as a Blackwell experiment (signal structure) associated with a state space that describes uncertainty of the agent's preferences, and consider an agent who updates her beliefs using the Bayes rule. An analyst observes the resulting stochastic choice of a population of agents with heterogeneous state-dependent utility functions. We show that almost any stochastic choice that admits a random utility representation within each frame is consistent with such model. However, when the state space has limited cardinality, the resulting stochastic choice should satisfy additional constraints on the sums of Block-Marschak polynomials constructed from choice frequencies under each decision frame.