Set and revealed preference axioms for multi-valued choice

We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We focus on the relations between several extensions of the condition of independence of irrelevant alternatives on one hand, and conditions on the revealed preference relation on sets, notably the weak axiom of revealed preference, on the other hand. We also establish the connection between the condition of independence of irrelevant alternatives and so-called strong sets; the latter characterize a social choice correspondence satisfying independence of irrelevant alternatives.

Social Image Concern and Reference Point Formation

This paper develops an axiomatic context-dependent model of social image concerns. Allowing for context-dependence based on choice sets, it examines how context-dependence impacts social image concerns, in particular how a decision maker exhibits various social emotions stemming from their intrinsic reference point, which may not be captured by conforming to social norms. To elicit the intrinsic reference point, this paper provides weaker versions of Strategic Rationality and Independence, in addition to the basic axioms, to characterize the model of the Reference-Dependent Image-Conscious utilitarian. This paper also examines how social emotions stemming from the intrinsic reference point are related to preference reversals as violations of the Weak Axiom of Revealed Preference (WARP). Finally, this paper considers the relationship between social image concerns and intrinsic reciprocity. The findings demonstrate that social image plays a large role and the model developed illustrates a condition in which cooperation is sustained in prisoner’s dilemma games.

Revealed Preference Implications of Backward Induction and Subgame Perfection

Consider a decision-maker (DM) who must select an alternative from a set of mutually exclusive alternatives but must take this decision sequentially. If the DM’s choice correspondence over subsets of alternatives satisfies the weak axiom of revealed preference (WARP), then the subgame perfect Nash equilibrium (SPNE) and backward induction (BI) strategies coincide. We study the relation between the SPNE and BI strategies when the DM’s choice correspondence fails to satisfy WARP. First, Sen’s axiom α is necessary and sufficient for the set of SPNE strategies to be a subset of the set of BI strategies; moreover, a mild strengthening of Sen’s axiom β is necessary and sufficient for the set of BI strategies to be a subset of the set of SPNE strategies. These results extend to multiplayer games. (JEL D11, C72, C73)

Expectations-Based Reference-Dependence and Choice Under Risk

This article characterises the behavioural content of a model of choice under risk with reference-dependent preferences and endogenous expectations-based reference points based on the preferred personal equilibrium model of Kőszegi and Rabin (2006). The combination of reference-dependent preferences and endogenous reference points leads to violations of the Independence Axiom and can also lead to violations of the Weak Axiom of Revealed Preference. An axiomatic characterisation shows that the model places testable restrictions on choice under risk.

School choice under partial fairness

We generalize the school choice problem by defining a notion of allowable priority violations. In this setting, a weak axiom of stability (partial stability) allows only certain priority violations. We introduce a class of algorithms called the student exchange under partial fairness (SEPF). Each member of this class gives a partially stable matching that is not Pareto dominated by another partially stable matching (i.e., constrained efficient in the class of partially stable matchings). Moreover, any constrained efficient matching that Pareto improves upon a partially stable matching can be obtained via an algorithm within the SEPF class. We characterize the unique algorithm in the SEPF class that satisfies a desirable incentive property. The extension of the model to an environment with weak priorities enables us to provide a characterization result that proves the counterpart of the main result in Erdil and Ergin (2008).