A composite discrete traction vector.

Tesis (Maestría en Ciencias con Orientación en Ingeniería Estructural) UANL, 2013.

Sharing a River

A group of agents located along a river have quasi-linear preferences over water and money. We ask how the water should be allocated and what money transfers should be performed. We are interested in efficiency, stability (in the sense of the core), and fairness (in a sense to be defined). We first show that the cooperative game associated with our problem is convex : its core is therefore large and easily described. Next, we propose the following fairness requirement : no group of agents should enjoy a welfare higher than what it could achieve in the absence of the remaining agents. We prove that only one welfare vector in the core satisfies this condition : it is the marginal contribution vector corresponding to the ordering of the agents along the river. We discuss how it could be decentralized or implemented.

Non-Deteriorating Choice

We analyze an alternative to the standard rationalizability requirement for observed choices by considering non-deteriorating selections. A selection function is a generalization of a choice function where selected alternatives may depend on a reference (or status quo) alternative in addition to the set of feasible options. A selection function is non-deteriorating if there exists an ordering over the universal set of alternatives such that the selected alternatives are at least as good as the reference option. We characterize non-deteriorating selection functions in an abstract framework and in an economic environment.

Rationalizability of Choice Functions on General Domains without Full Transitivity

The rationalizability of a choice function by means of a transitive relation has been analyzed thoroughly in the literature. However, not much seems to be known when transitivity is weakened to quasi-transitivity or acyclicity. We describe the logical relationships between the different notions of rationalizability involving, for example, the transitivity, quasi-transitivity, or acyclicity of the rationalizing relation. Furthermore, we discuss sufficient conditions and necessary conditions for rational choice on arbitrary domains. Transitive, quasi-transitive, and acyclical rationalizability are fully characterized for domains that contain all singletons and all two-element subsets of the universal set.

A Representation Theorem for Domains with Discrete and Continuous Variables.

This paper proves a new representation theorem for domains with both discrete and continuous variables. The result generalizes Debreu's well-known representation theorem on connected domains. A strengthening of the standard continuity axiom is used in order to guarantee the existence of a representation. A generalization of the main theorem and an application of the more general result are also presented.

Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions.

In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three others on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. We also propose a combined test procedure, whose level is again perfectly controlled through the Monte Carlo test technique and has better power properties than the individual tests that are combined. Finally, in a simulation experiment, we show that the technique suggested provides perfect control of test size and that the new tests proposed can yield sizeable power improvements.

Efficient and Non-Deteriorating Choice

We analyze collective choice procedures with respect to their rationalizability by means of profiles of individual preference orderings. A selection function is a generalization of a choice function where selected alternatives may depend on a reference (or status quo) alternative in addition to the set of feasible options. Given the number of agents n, a selection function satisfies efficient and non-deteriorating n-rationalizability if there exists a profile of n orderings on the universal set of alternatives such that the selected alternatives are (i) efficient for that profile, and (ii) at least as good as the reference option according to each individual preference. We analyze efficient and non-deteriorating collective choice in a general abstract framework and provide a characterization result given a universal set domain.

Candidate Stability and Nonbinary Social Choice

A desirable property of a voting procedure is that it be immune to the strategic withdrawal of a candidate for election. Dutta, Jackson, and Le Breton (Econometrica, 2001) have established a number of theorems that demonstrate that this condition is incompatible with some other desirable properties of voting procedures. This article shows that Grether and Plott's nonbinary generalization of Arrow's Theorem can be used to provide simple proofs of two of these impossibility theorems.

Bureaucratic Corruption As a Constraint on Voter Choice

It Has Often Been Assumed That a Country's Tax Level, Tax Structure Progressivity and After-Tax Income Distribution Are Chosen by Voters Subject Only to Their Budget Constraints. This Paper Argues That At Certain Income Levels Voters' Decisions May Be Constrained by Bureaucratic Corruption. the Theoretical Arguments Are Developed in Asymmetry Limits the Capacity of the Fiscal System to Generate Revenues by Means of Direct Taxes. This Hypothesis Is Tested Witha Sample of International Data by Means of a Simultaneous Equation Model. the Distortions Resulting From Corruption Ar Captured Through Their Effects on a Latent Variable Defined As the Overall Fiscal Structure. Evidence Is Found of Causality Running From This Latent Variable to the Level of Taxes and the Degree of After Tax Inequality.

Aumann-Shapley Pricing : A Reconsideration of the Discrete Case

We reconsider the following cost-sharing problem: agent i = 1,...,n demands a quantity xi of good i; the corresponding total cost C(x1,...,xn) must be shared among the n agents. The Aumann-Shapley prices (p1,...,pn) are given by the Shapley value of the game where each unit of each good is regarded as a distinct player. The Aumann-Shapley cost-sharing method assigns the cost share pixi to agent i. When goods come in indivisible units, we show that this method is characterized by the two standard axioms of Additivity and Dummy, and the property of No Merging or Splitting: agents never find it profitable to split or merge their demands.

The Ghost in the Machine: Inferring Machine-Based Strategies from Observed Behavior

We introduce a procedure to infer the repeated-game strategies that generate actions in experimental choice data. We apply the technique to set of experiments where human subjects play a repeated Prisoner's Dilemma. The technique suggests that two types of strategies underly the data.

First-Degree Discrimination in a Competitive Setting: Pricing and Quality Choice

The paper investigates competition in price schedules among vertically differentiated dupolists. First order price discrimination is the unique Nash equilibrium of a sequential game in which firms determine first whether or not to commit to a uniform price, and then simultaneously choose either a single price of a price schedule. Whether the profits earned by both firms are larger or smaller under discrimination than under uniform pricing depends on the quality gap between firms, and on the disparity of consumer preferences. Firms engaged in first degree discrimination choose quality levels that are optimal from a welfare perspective. The paper also reflects on implications of these findings for pricing policies of an incumbent threatened by entry.

Rational Choice on Arbitrary Domains: A Comprehensive Treatment

The rationalizability of a choice function on arbitrary domains by means of a transitive relation has been analyzed thoroughly in the literature. Moreover, characterizations of various versions of consistent rationalizability have appeared in recent contributions. However, not much seems to be known when the coherence property of quasi-transitivity or that of P-acyclicity is imposed on a rationalization. The purpose of this paper is to fill this significant gap. We provide characterizations of all forms of rationalizability involving quasi-transitive or P-acyclical rationalizations on arbitrary domains.

Domain Closedness Conditions and Rational Choice

The rationalizability of a choice function on an arbitrary domain under various coherence properties has received a considerable amount of attention both in the long-established and in the recent literature. Because domain closedness conditions play an important role in much of rational choice theory, we examine the consequences of these requirements on the logical relationships among different versions of rationalizability. It turns out that closedness under intersection does not lead to any results differing from those obtained on arbitrary domains. In contrast, closedness under union allows us to prove an additional implication.

Social Choice: Recent Developments

In the past quarter century, there has been a dramatic shift of focus in social choice theory, with structured sets of alternatives and restricted domains of the sort encountered in economic problems coming to the fore. This article provides an overview of some of the recent contributions to four topics in normative social choice theory in which economic modelling has played a prominent role: Arrovian social choice theory on economic domains, variable-population social choice, strategy-proof social choice, and axiomatic models of resource allocation.