Essays on behavioural economic theory

PhDThe chapters of this work lie at the intersection between classical choice theory and experimental data on decision making. In chapter 21 study necessary and sufficient conditions for a choice function to be rationalized in the following sense: there exists a complete asymmetric relation T (a tournament) such that, for each feasible (finite) set, the choice set coincides with the uncovered set of T restricted to that feasible set. This notion of 'maximization' may offer testable restrictions on observable choice behavior. In chapter 3 Mariotti and I give a group revealed preference interpretation to the concept of uncovered set, and we provide a characterization of uncovered bargaining solutions of a Pareto-consistent tournament. In chapter 41 study the rationalizability of reason-based choice correspondences axiomatically. A reason-based choice correspondence rationalizes choice behaviour in terms of a two stage choice procedure. Given a feasible set S, the individual eliminates in the first step all of the dominated alternatives according to her fixed (not necessarily complete) strict preference relation. In the second step, she first constructs for each maximal alternative identified in the first step its lower contour set, and then she eliminates from the maximal set all of those alternatives so that the following justification holds: there exists another maximal alternative whose lower contour set strictly contains that of another maximal alternative. This procedural model captures the basic idea behind the experimental finding known as "attraction effect". Finally, in chapter 51 build a connection between the behavioral property expressed by the weak axiom of revealed non-inferiority and a new weak notion of rationality. This notion is weaker than that characterized by the weak axiom of revealed preference (WARP)

Reason-Based Choice Correspondences

A reason-based choice correspondence rationalizes choice behaviour in terms of a two-stage choice procedure. Given a feasible set S , the individual eliminates from it all of the dominated alternatives according to her fixed (not necessarily complete) strict preference relation, in the first step. In the second step, first she constructs for each maximal alternative identified in the first step its lower contour set (i.e., the set of alternatives which are dominated by it in S ), and then she eliminates from the maximal set all of those alternatives so that the following justification holds: there exists another maximal alternative whose lower contour set strictly contains that of another maximal alternative. This procedural model captures the basic idea behind the experimental finding known as "attraction effect". We study the rationalizability of reason-based choice correspondences axiomatically. We relate our choice-consistency conditions to standard consistency proprieties. Our characterization result offers testable restrictions on this `choice anomaly' for large (but finite) set of alternatives.Reason-based choice, Revealed preferences

Choice by Lexicographic Semiorders

We propose an extension of Tversky's lexicographic semiorder to a model of boundedly rational choice. We explore the connection with sequential rationalisability of choice, and we provide axiomatic characterisations of both models in terms of observable choice data.lexicographic semiorders, bounded rationality, revealed preference, choice

Choice by lexicographic semiorders

In Tversky's (1969) model of a lexicographic semiorder, preference is generated by the sequential application of numerical criteria, by declaring an alternative x better than an alternative y if the first criterion that distinguishes between x and y ranks x higher than y by an amount exceeding a fixed threshold. We generalize this idea to a fully-fledged model of boundedly rational choice. We explore the connection with sequential rationalizability of choice (Apesteguia and Ballester 2009, Manzini and Mariotti 2007), and we provide axiomatic characterizations of both models in terms of observable choice data.Lexicographic semiorders, bounded rationality, revealed preference, choice

Choosing VNM-stable sets of the revealed dominance digraph

The choice functions that are consistent with selections of VNM-stable sets of an underlying revealed dominance digraph are characterized both under VNM-perfection of the latter and in the general case.VNM-stable sets, kernel-perfect digraphs, choice func-tions 1

Uncovered Bargaining Solutions

An uncovered bargaining solution is a bargaining solution for which there exists a complete and strict relation (tournament) such that, for each feasible set, the bargaining solution set coincides with the uncovered set of the tournament. We provide a characterization of a class of uncovered bargaining solutions.Bargaining, Tournaments, Uncovered set, Non-convex problems

Essays on decision theory

Tese (doutorado) — Universidade de Brasília, Faculdade de Administração, Contabilidade, Economia e Gestão de Políticas Públicas, Departamento de Economia, Brasília, 2022.Este trabalho é composto de dois capítulos, independentes entre si, que tem como objetivo aprofundar a literatura econômica que versa sobre escolhas individuais e coletivas. O primeiro capítulo versa sobre o processo de racionalização de indivíduos que apresentam um comportamento de escolhas não transitivo. Tomando como dada uma relação de preferências completa, porém não necessariamente transitiva, é proposta uma família de representações de escolha inspirada no procedimento king-chicken, de acordo com o qual uma alternativa x é escolhida do conjunto de alternativas A se, para cada outra alternativa y em A, ou x é preferido a y ou existe uma outra alternativa z em A tal que x é preferido a z e z é preferido a y. Mostra-se que é possível generalizar este processo para permitir um caminho com mais de uma alternativa entre x e y e caracteriza-se todas as correspondências de escolhas que emergem deste processo. Duas das mais proeminentes soluções de torneios, o uncovered set e o top-cycle, são casos especiais deste procedimento de kingchicken generalizado. Este trabalho, portanto, avança resultados anteriores da literatura de teoria da escolha ao apresentar a axiomatização destes modelos em espaços de escolhas genéricos, não necessariamente finitos. O segundo capítulo explora o processo de atualização bayesiana de uma Random Choice Rule com representação por Finite Random Expected Utility. O capítulo apresenta uma condição necessária e suficiente, chamada de Random Consistency, para que uma Random Choice Rule seja a atualização bayesiana de outra após o agente aprender novas informações e contrair ou expandir seu espaço de estados subjetivo. É apresentada uma extensão a trabalhos já publicados através da caracterização da direção oposta da representação por unforeseen contingencies, quando o espaço de estados subjetivos de uma representação por Finite Random Expected Utility está contido no espaço de estados subjetivo da representação de uma preferência sobre menus. O capítulo ainda apresenta uma discussão sobre as condições sob as quais uma coleção de Random Choice Rules representa uma partição de uma Random Choice Rule mais abrangente ou de uma preferência sobre menus.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).This work is composed of two independent chapters that focus on deepening the economic literature on individual and collective choice. The first chapter explores the process of rationalization for agents that reveal a nontransitive behavior. Given a complete, though not necessarily transitive, preference relation, it is proposed a family of choice representations inspired by the king-chicken procedure, according to which an alternative x is chosen among a set of alternatives A if, for every other alternative y in A, either x is preferred to y or there is another alternative z in A such that x is preferred to z, and z is preferred to y. It is shown that it is possible to generalize this process by allowing the path from x to y to include more than one alternative z and to fully characterize the choice correspondences that can be achieved through it. Two of the most relevant tournament solutions, the uncovered set and the top-cycle, are special cases of this generalized king-chicken choice procedure, so this work improves previous results that have appeared in the choice theory literature by delivering axiomatizations for those models in generic (not necessarily finite) choice spaces. The second chapter explores the process of bayesian updating of a Random Choice Rule with a Finite Random Expected Utility representation. This chapter presents the necessary and sufficient condition, which we call Random Consistency, for a Random Choice Rule to be a update of another after the Decision Maker learns new information and contracts or expands her subjective state spaces. It is also presented an extension to previous works by characterizing the opposite direction of the unforeseen contingencies representation, when the subjective states of the Finite Random Expected Utility representation of a Random Choice Rule is contained in the subjective state space of the representation of a Preference Over Menus. This chapter also presents a discussion on the conditions under which a collection of Random Choice Rules represent a partition of a broader Random Choice Rule or of a Preference Over Menus

Uncovered set choice rules

I study necessary and sufficient conditions for a choice function to be rationalized in the following sense: there exists a total asymmetric relation T (a tournament) such that, for each feasible (finite) set, the choice set coincides with the uncovered set of T restricted to that feasible set. This notion of ‘maximization’ offers testable restrictions on observable choice behavior