We introduce a behavioral model of habit formation, in which habits implicitly serve as heuristics. The agent repeatedly faces a binary-choice problem, whose optimal response is stochastic. At each period, the agent may choose either deliberately or by habit. A choice by habit results from an automatic process and may thus conflict with preferences. The mode of choice is random and its realizations depend on past experience. We define a Markovian representation of this choice behavior and investigate welfare implications. We find that habits inflate the probability of choice for the item that maximizes expected utility, and show that habits are welfare improving if the cognitive costs of deliberate decision making are sufficiently high. A definition and a characterization of a good habit are provided. Also, we address the pricing problem of a monopolist who faces a habitual buyer. We identify the conditions for which the monopolist maximizes profits by charging a fixed (intermediate) price or by applying dynamic pricing. The viability of both strategies is specific to the habit formation model of choice. For some parameter specifications, a habitual consumer yields higher profits than a non-habitual consumer.
We introduce the peer-pressure game, a simultaneous-move binary-action game where players balance intrinsic preferences and conformity pressures. Each player's payoff depends on their choice of action, a mismatch cost proportional to the fraction of opponents choosing a different action, and a player-specific sensitivity parameter that captures heterogeneous responses to peer influence. For games of common interest, we identify conditions under which efficient outcomes emerge as the unique equilibrium and characterize the population-level bound beyond which conformity compromises coordination. In competitive environments, we show how social norms can either be absorbing or dual, and derive the conditions under which agents in the minority play their intrinsically preferred action in equilibrium.
We introduce a novel choice dataset, called joint choice, in which options and menus are multidimensional. In this general setting, we define a notion of choice separability, which requires that selections from some dimensions are never affected by those performed on the remaining dimensions. This generalizes the classical definition of separability for discrete preference relations and utility functions, to encompass a class of choice behaviors that may lack a preference or utility representation. We thoroughly investigate the stability of separability across dimensions, and then suggest effective tests to check whether a joint choice is separable. Upon defining rationalizable joint choices as those explained by the maximization of a relation of revealed preference, we examine the interplay between the notions of rationalizability and separability. Finally, we show that the rationalizability of a separable joint choice can be tested by verifying the rationalizability of some derived joint choices over fewer dimensions.
Categorize and randomize: a permissive model of stochastic choice [pdf]
We model stochastic choices with categorization, resulting from the preliminary step of grouping alternatives in homogenous disjoint classes. The agent randomly chooses one class among those available, then randomly picks an item within the selected class. We give a formal definition of a choice generated by this procedure, and provide a characterization. The characterizing properties allow an external observer to elicit that categorization is applied. In a more general interpretation, the model allows to describe the observed choice as the composition of independent subchoices. This composition preserves rationalizability by random utility maximization. A generalization of the model subsumes Luce model and Nested Logit.
Updating values in a changing environment (with Andrea Gallo)