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 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.

Pareto-Optimal Matching Allocation Mechanisms for Boundedly Rational Agents

This article is concerned with the welfare properties of trade when the behavior of agents cannot be rationalized by preferences. I investigate this question in an environment of matching allocation problems. There are two reasons for doing so: rstly, the niteness of such problems entails that the domain of the agents' choice behavior does not need to be restricted in any which way to obtain results on the welfare properties of trade. Secondly, some matching allocation mechanisms have been designed for non-market environments in which we would typically expect boundedly rational behavior. I nd qualied support for the statements that all outcomes of trade are Pareto-optimal and all Pareto optima are reachable through trade. Contrary to the standard case, dierent trading mechanisms lead to dierent outcome sets when the agents' behavior is not rationalizable. These results remain valid when restricting attention to \minimally irrational" behavior.Bounded Rationality, House Allocation Problems, Fundamental Theorems of Welfare, Multiple Rationales

Computable Rationality, NUTS, and the Nuclear Leviathan

This paper explores how the Leviathan that projects power through nuclear arms exercises a unique nuclearized sovereignty. In the case of nuclear superpowers, this sovereignty extends to wielding the power to destroy human civilization as we know it across the globe. Nuclearized sovereignty depends on a hybrid form of power encompassing human decision-makers in a hierarchical chain of command, and all of the technical and computerized functions necessary to maintain command and control at every moment of the sovereign's existence: this sovereign power cannot sleep. This article analyzes how the form of rationality that informs this hybrid exercise of power historically developed to be computable. By definition, computable rationality must be able to function without any intelligible grasp of the context or the comprehensive significance of decision-making outcomes. Thus, maintaining nuclearized sovereignty necessarily must be able to execute momentous life and death decisions without the type of sentience we usually associate with ethical individual and collective decisions

An iterative method for selecting decision variables in analytical optimization problem

In this paper, we present an iterative method to assist the designer in the setting of decision variables in an optimization problem with analytical models. This method is based on the Design Structure Matrix (DSM) which allows a clear representation of interactions between variables. Such a process becomes particularly useful for complex optimal design for which choosing the right decision variables to efficiently solve the problem is not so trivial. This approach is applied to the geometrical model of a High Speed Permanent Magnet Synchronous Machine (HSPMSM

Nonparametric Tests of Collectively Rational Consumption Behavior: An Integer Programming Procedure

We present an IP-based nonparametric (revealed preference) testing proce- dure for rational consumption behavior in terms of general collective models, which include consumption externalities and public consumption. An empiri- cal application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the practical usefulness of the procedure. Finally, we present extensions of the testing procedure to evaluate the goodness-of-fit of the collective model subject to testing, and to quantify and improve the power of the corresponding collective rationality tests.collective consumption model;revealed preferences;nonparametric rationality tests;integer programming (IP)

Sequential rationalization of multivalued choice

[EN]This paper contributes to the theory of rational choice under sequential criteria. Following the approach initiated by Manzini and Mariotti (2007) for single-valued choice functions, we characterize choice correspondences that are rational by two sequential criteria under a mild consistency axiom. Rationales ensuring the sequential rationalization are explicitly constructed and a uniquely determined, canonical solution is provided

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.

Endogeneous Household Interaction

Most econometric models of intrahousehold behavior assume that household decision-making is efficient, i.e., utility realizations lie on the Pareto frontier. In this paper we investigate this claim by adding a number of participation constraints to the household allocation problem. Short-run constraints ensure that each spouse obtains a utility level at least equal to what they would realize under (inefficient) Nash equilibrium. Long-run constraints ensure that each spouse obtains a utility level equal to a least what they would realize by cheating on the efficient allocation and receiving Nash equilibrium payoffs in all successive periods. Given household characteristics and the (common) discount factor of the spouses, not all households may be able to attain payoffs on the Pareto frontier. We estimate these models using a Method of Simulated Moments estimator and data from one wave of the Panel Study of Income Dynamics. We find that the model with long-run participation constraint fits the data best, and that 6 percent of sample households are not able to attain efficient outcomes. To meet the long-run participation constraint, over 90 percent of "efficient" households are required to modify the ex ante Pareto weight of 0.5 for each spouse assumed to apply to all households.household time allocation, grim trigger strategy, household production, method of simulated moments