The computational complexity of rationalizing Pareto optimal choice behavior.

We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with a preference relation such that the observed choices are Pareto efficient. We differentiate between the situation where the choice function is considered to select all Pareto optimal alternatives from a choice set and the situation where it only contains one or several Pareto optimal alternatives. In the former case we find that Pareto rationalizability is an NP-complete problem. For the latter case we demonstrate that, if we have no additional information on the individual preference relations, then all choice behavior is Pareto rationalizable. However, if we have such additional information, then Pareto rationalizability is again NP-complete. Our results are valid for any coalition of size greater or equal than two.

The computational complexity of boundedly rational choice behavior

This research examines the computational complexity of two boundedly rational choice models that use multiple rationales to explain observed choice behavior. First, we show that the notion of rationalizability by K rationales as introduced by Kalai, Rubinstein, and Spiegler (2002) is NP-complete for K greater or equal to two. Second, we show that the question of sequential rationalizability by K rationales, introduced by Manzini and Mariotti (2007), is NP-complete for K greater or equal to three if choices are single valued, and that it is NP-complete for K greater or equal to one if we allow for multi-valued choice correspondences. Motivated by these results, we present two binary integer feasibility programs that characterize the two boundedly rational choice models and we compute their power. Finally, by using results from descriptive complexity theory, we explain why it has been so difficult to obtain `nice' characterizations for these models.

The computational complexity of rationalizing Pareto optimal choice behavior

We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with a preference relation such that the observed choices are Pareto efficient. We differentiate between the situation where the choice function is considered to select all Pareto optimal alternatives from a choice set and the situation where it only contains one or several Pareto optimal alternatives. In the former case we find that Pareto rationalizability is an NP-complete problem. For the latter case we demonstrate that, if we have no additional information on the individual preference relations, then all choice behavior is Pareto rationalizable. However, if we have such additional information, then Pareto rationalizability is again NP-complete. Our results are valid for any coalition of size greater or equal than two.

A revealed preference analysis of the rational addiction model.

We provide a revealed preference analysis of the rational addiction model. The revealed preference approach avoids the need to impose an, a priori unverifiable, functional form on the underlying utility function. Our results extend the previously established revealed preference characterizations for the life cycle model and the one-lag habits model. We show that our characterization is easily testable by means of linear programming methods and we demonstrate its practical usefulness by means of an application to Spanish household consumption data.

A revealed preference analysis of the rational addiction model

We provide a revealed preference analysis of the rational addiction model. The revealed preference approach avoids the need to impose an, a priori unverifiable, functional form on the underlying utility function. Our results extend the previously established revealed preference characterizations for the life cycle model and the one-lag habits model. We show that our characterization is easily testable by means of linear programming methods and we demonstrate its practical usefulness by means of an application to Spanish household consumption data.

Noncooperative household consumption with caring

We present a household consumption model that accounts for caring household members, while allowing for noncooperative behavior in decisions on public goods. The intrahousehold consumption outcome critically depends on the degree of caring between the household members. By varying the degree of intrahousehold caring, the model encompasses a whole continuum of household consumption models that are situated between the fully cooperative model and the noncooperative model without caring. This feature is used to define a measure for the degree of cooperation within the household. We also establish a dual characterization of our noncooperative model with caring preferences: we show that the model is dually equivalent to a noncooperative model with non-caring preferences that is characterized by intrahousehold transfers. Finally, following a revealed preference approach, we derive testable implications of the model for empirical data. We demonstrate the practical usefulness of the model through an illustrative application.

Testable implications of general equilibrium models: an integer programming approach

Focusing on the testable implications on the equilibrium manifold, we show that the rationalizability problem is NP-complete. Subsequently, we present an integer programming (IP) approach to characterizing general equilibrium models. This approach avoids the use of the Tarski-Seidenberg algorithm for quantifier elimination that is commonly used in the literature. The IP approach naturally applies to settings with any number of observations, which is attractive for empirical applications. In addition, it can easily be adjusted to analyze the testable implications of alternative general equilibrium models (that include, e.g., public goods, externalities and/or production). Further, we show that the IP framework can easily address recoverability questions (pertaining to the structural model that underlies the observed equilibrium behavior), and account for empirical issues when bringing the IP methodology to the data (such as goodness-of-fit and power). Finally, we show how to develop easy-to-implement heuristics that give a quick (but possibly inconclusive) answer to whether or not the data satisfy the general equilibrium models.General equilibrium, equilibrium manifold, exchange economies, production economies, NP-completeness, nonparametric restrictions, GARP, integer programming.

Nash bargained consumption decisions: a revealed preference analysis.

We present a revealed preference analysis of the testable implications of the Nash bargaining solution. Our specific focus is on a two-player game involving consumption decisions. We consider a setting in which the empirical analyst has information on both the threat points bundles and the bargaining outcomes. We first establish a revealed preference characterization of the Nash bargaining solution. This characterization implies conditions that are both necessary and sufficient for consistency of observed consumption behavior with the Nash bargaining model. However, these conditions turn out to be nonlinear in unknowns and therefore difficult to verify. Given this, we subsequently present necessary conditions and sufficient conditions that are linear (and thus easily testable). We illustrate the practical usefulness of these conditions by means of an application to experimental data. Such an experimental setting implies a most powerful analysis of the empirical goodness of the Nash bargaining model for describing consumption decisions. To our knowledge, this provides a first empirical test of the Nash bargaining model on consumption data. Finally, we consider the possibility that threat point bundles are not observed. This obtains testable conditions for the Nash bargaining model that can be used in non-experimental (e.g. household consumption) settings, which often do not contain information on individual consumption bundles in threat points.