Теории индивидуального принятия решений тема диссертации и автореферата по ВАК РФ 00.00.00, доктор наук Эврен Озгур

• Эврен Озгур
• доктор наук
• 2023

Оглавление диссертации доктор наук Эврен Озгур

Contents

1 Introduction

1.1 Indecisiveness and related phenomena

1.2 Other regarding preferences

1.3 Attitudes toward ambiguity and risk

2 Main Results: Short summary

2.1 Findings on indecisiveness and related phenomena

2.2 Findings on other regarding preferences

2.3 Findings on ambiguity and risk attitudes

References

Appendices

Appendix 1 On the multi-utility representation of preference relations

Appendix 2 Extension of monotonic functions and representation of preferences

Appendix 3 On the existence of expected multi-utility representations

Appendix 4 Scalarization methods and expected multi-utility representations

Appendix 5 Preference for flexibility: A continuous representation in an ordinal setup

Appendix 6 Choice overload and asymmetric regret

Appendix 7 Warm-glow giving and freedom to be selfish

Appendix 8 Altruism and voting: A large-turnout result that does not rely on civic duty or cooperative behavior

Appendix 9 Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity

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Введение диссертации (часть автореферата) на тему «Теории индивидуального принятия решений»

1. Introduction

My research belongs to a subfield of microeconomic theory concerned with nonstandard decision making models in individual choice problems. The themes that appear in my work can be divided into three overlapping categories: (i) indecisiveness and related choice anomalies; (ii) other regarding preferences; (iii) attitudes towards ambiguity and risk in decision making problems under uncertainty. In what follows, I briefly describe the research questions that I have studied and their motivation.

1.1. Indecisiveness and related phenomena

In standard models, the preferences of economic agents are assumed to be complete and transitive. While transitivity is a consistency condition, the completeness assumption means that the agent is always decisive: Given two alternatives, she can always identify one that is at least as good as the other.

Starting with Aumann (1962), researchers noted that, unlike transitivity, the completeness axiom cannot really be viewed as a rationality tenet, especially in complex decision problems. Of course, the decision maker (DM) will make a choice, if she has to, but such forced decisions tend to be intransitive (Luce and Raiffa 1957, Mandler 2005, Eliaz and Ok 2006). That is, from a descriptive standpoint, transitivity makes sense only if we relax the completeness axiom.

Early research on representation of incomplete preference relations explored sufficient conditions that allow one to extend a preference relation by a single utility function (e.g., Aumann 1962, Peleg 1970, Levin 1983). The main merit of this approach is that maximization of such a utility function on a set of feasible alternatives always leads to a maximal alternative that the DM can actually select.

However, when studying economic phenomena related to indecisiveness, it becomes often necessary to recover the choice correspondence induced by an incomplete preference relation in its entirety. For example, Rigotti and Shannon (2005) study indeterminacy of equilibria in security markets driven

by multiplicity of choices that are consistent with incomplete preferences. The study of how an agent may or should resolve her indecisiveness is a related area of research.1 Moreover, it has been observed that a variety of behavioral phenomena can be explained by two-stage choice procedures where in the first stage the agent identifies a collection of maximal alternatives in a given choice set (with respect to an endogenously determined incomplete preference relation), and then makes her final choice among these maximal alternatives according to a secondary criterion.2'3

The problem of recovering the choice correspondence induced by an incomplete preference relation gave rise to the literature on multi-utility representations which provide a set of utility functions that fully characterize a given preference relation. Effectively, the preference relation is characterized as a Pareto order associated with a set of utility functions, which can be interpreted as different versions or selves of the DM, each with a complete preference relation.

Of course, just as in Debreu's (1954) theorem on the existence of a continuous utility function for a complete preference relation, the existence of multi-utility representations may require continuity axioms or structural assumptions on the space of all alternatives. In decision problems under uncertainty, one may demand further properties from the utility functions, such as the expected utility form, or risk aversion.

In a seminal paper, Bewley (1986) proved an expected multi-utility theorem for incomplete preference relations under subjective uncertainty. Ok

1For example, Ok, Ortoleva and Riella (2015) propose a model in which the choice between two incomparable alternatives, say x and y, depends on other options in a certain way: the presence of a third alternative z that is asymmetrically dominated by x or y increases the DM's tendency to choose the dominating alternative. In turn, Danan (2010) studies the problem of "how to choose in the absence of preference" from a normative point of view.

2 For instance, some reference-dependent choice models necessitate the use of incomplete preferences in this way (Masatlioglu and Ok 2005, Apesteguia and Ballester 2009). A longer list of indecisiveness-related phenomena includes preference for flexibility and choice deferral (Danan and Ziegelmeyer 2006, Kopylov 2009), as well as preference for commitment (Danan, Guerdjikova and Zimper 2012).

3Aizerman and Aleskerov (1995) provide a comprehensive study of the analytical features of two stage choice models with multiple criteria.

(2002) and Mandler (2006) studied multi-utility representations for ordinal preferences. Another important contribution is the expected multi-utility theorem of Dubra Maccheroni and Ok (2004) for preferences under objective uncertainty (i.e., risk). These earlier contributions left many questions unanswered. A significant part of my research is dedicated to such questions on multi-utility representations.

Evren and Ok (2011) provides a comprehensive study of ordinal multiutility representations. The paper investigates the cases in which the representing sets of utility functions are either arbitrary or finite, and those cases in which the utility functions are required to be continuous or semi-continuous.

The ordinal representation theorems reported in Evren and Ok (2011) build upon Nachbin's (1965) work on a mathematical problem of extending a weakly monotonic and continuous function defined on a small set to a larger set without violating the continuity and monotonicity conditions. Evren and Husseinov (2021) provide Nachbin-type extension theorems for strictly monotonic functions, and explore their implications for the representation of preferences by means of utility functions that are monotonic with respect to a given dominance relation.

Evren (2008) and Evren (2014) study expected multi-utility representations under risk, in order to understand the roles of compactness assumptions on the prize space and alternative continuity assumptions on preferences, respectively.

In a menu-choice problem, the DM chooses a set of alternatives, such as a restaurant menu or a budget set, which determines her feasible options in a subsequent period. Following Kreps' (1979) seminal work on representation of preference for flexibility, this menu-choice framework proved to be a powerful tool to model a variety of behavioral phenomena.4

In Evren (2020), I study a conjecture of Kreps on a continuous version of his representation, and a further extension that relaxes Kreps' completeness axiom. A Nachbin-type technique for constructing monotonic utility functions

4Such phenomena include preference for freedom of choice (Puppe 1996), temptation and self-control (Gul and Pesendorfer 2001, Dekel Lipman and Rustichini 2009), anticipated regret (Sarver 2008), costly contemplation (Ergin and Sarver 2010), and perfectionism (Kopylov 2012).

lies at the heart of my analysis.

A DM with incomplete preferences may regret choosing any given alternative upon learning more about her tastes. Several researchers advanced this point as a potential explanation of choice overload, a behavioral phenomenon that refers to a stronger tendency to stick to the default option in choice problems that contain many alternatives (see, e.g., Iyengar and Lep-per 2000, Anderson 2003, and Inbar, Botti and Hanko 2011). Buturak and Evren (2017) study this connection for choice problems under risk by using an axiomatic approach.

1.2. Other regarding preferences

Warm-glow refers to other regarding behavior that causes the actor to experience positive feelings, irrespective of the social implications of the actions. For example, it has been argued that social image concerns or a desire for acclaim may drive prosocial behavior (e.g. Becker 1974, Andreoni 1990, Glazer and Konrad 1996). By contrast, an altruistic person only cares about the social allocation. One can also envision a third type of individuals who perceive prosocial behavior as an unpleasant obligation (Dillenberger and Sadowski 2012, Noor and Ren 2015). Roughly, my research is concerned with similarities and distinctions between warm-glow and the other two forms of prosocial behavior.

Evren and Minardi (2017) study behavioral foundations of warm-glow in a menu-choice setup that provides clear-cut distinctions between warm-glow and the competing forms of prosocial behavior.

In an influential paper, Feddersen and Sandroni (2006) have shown that a model of warm-glow can generate large turnout rates that we observe in large elections, as well as a number of other empirical findings on voters' behavior. As a distinctive feature, voters in that model follow an ethical line of thinking: Before choosing an action—abstaining or voting for a particular candidate— they ask themselves what would happen if all other voters with similar characteristics adapted the same action. This is known as rule-utilitarianism. In Evren (2012), I study the connections between this model and a familiar

form of altruism that allows me to use a standard concept of Nash equilibrium in a game-theoretic setup.

1.3. Attitudes toward ambiguity and risk

Ambiguity aversion refers to a tendency to prefer risky bets with objectively defined probabilities to ambiguous bets where the probabilities of events are not so clear. Ellsberg's (1961) classic examples show that this type of behavior is incompatible with the standard expected utility theory.

A reasonable response to Ellsberg-type behavior, first suggested by Segal (1987), is to utilize a second-order belief—a probability measure over possible distributions of the states—with the interpretation that the DM does not know the "correct" distribution of the states, but she can make a probabilistic assessment of it. More recently, Klibanoff, Marinacci and Mukerji (2005), and Seo (2009) proposed an alternative version of this second-order approach, known as the "smooth ambiguity model."

In Evren (2019), I study two issues within Segal's (1987) model. The first issue is the comparative strength of ambiguity aversion and its relation to the level of ambiguity; a problem that needs to be addressed so that we can perform comparative statics exercises within Segal's model. Second, I study when Segal's model is guaranteed to predict ambiguity aversion, irrespective of the specification of the second-order belief, and relate the answer to the specification of risk preferences.

2. Main Results: Short summary

This section contains a brief overview of my findings and some further information about their place in the literature. I will follow the same thematic order as in Section 1.

2.1. Findings on indecisiveness and related phenomena

Evren and Ok (2011) show that sufficient conditions for the existence of ordinal multi-utility representations are surprisingly weak with the exception of two

cases where (i) the representing set is required to be finite, and (ii) utility functions are required to be continuous while the underlying space of alternatives is topologically large. In particular, order-separability assumptions of Ok (2002) and Mandler (2006) prove redundant if one is seeking semicontinuous utility functions, or if no continuity requirement is present. Moreover, a classical closed-continuity axiom suffices for the existence of a continuous multi-utility representation whenever the space of alternatives is locally compact and a-compact,5 as in the case of Euclidean spaces. The paper also provides more demanding sufficient conditions that lead to multi-utility representations in some other cases.

Consider a dominance relation (a preorder) ^ on a topological space X, such as the "greater than or equal to" relation on a function space, or a stochastic dominance relation on a space of probability measures. Inspired by Nachbin's (1965) work on extension of weakly monotonic functions, Evren and Hiisseinov (2021) show that under two sets of assumptions, a continuous real function defined on a compact subset of X that is strictly monotonic with respect to ^ can be extended to X without violating the continuity and mono-tonicity conditions. Their most novel set of assumptions focus on those cases in which X is a topological vector space, and ^ is a (closed) and translation invariant preorder. To illustrate potential uses of the extension theorems, they prove several representation theorems for revealed or exogenously given preferences that are monotonic with respect to a dominance relation. In particular, a generalization of Afriat's (1967) classical theorem on rationalizable choice data is proved for a space X that is not necessarily locally compact. For example, it becomes possible to determine when we can rationalize choice data on monetary lotteries by using a continuous utility function on the space of all monetary lotteries that are strictly monotonic with respect to the first-order stochastic dominance relation.

Evren (2008) shows that the conclusion of the expected multi-utility theo-

5 A topological space X is locally compact if every point in X has an open neighborhood with compact closure. X is said to be ^-compact if it can be written as a union of countably many compact sets.

rem of Dubra, Maccheroni and Ok (2004) fails to hold for preference relations defined on the set of all monetary lotteries because the prize space R is not compact. A positive result is established for the case of the smaller domain that consists of all compactly supported monetary lotteries. The assumption of compact supports become redundant if the preference relation satisfies a classical risk aversion condition, or if it admits a best and a worst prize in the context of non-monetary prizes.

For complete preference relations, it is well-known that the weak (upper and lower) contour sets are topologically closed if and only if the strict contour sets are open. By contrast, these continuity notions become distinct upon relaxation of the completeness axiom, and they are actually incompatible with each other (Schmeidler 1979). In Evren (2014), I replace the closed-continuity axiom of Dubra, Maccheroni and Ok (2004) with the open-continuity axiom, using the same (weak convergence) topology. The resulting representation theorem features a compact set of (continuous) expected utility functions that preserve both indifferences and strict preferences. This finding contrasts with the representation theorem of Dubra et al. which typically delivers some functions that do not respect strict preferences. My representation theorem reduces the problem of recovering the associated choice correspondence on convex sets of lotteries to a scalar-valued, parametric optimization exercise.

Evren (2020) uses Nachbin-type arguments to solve a representation problem that Kreps (1979) has left open. Specifically, the paper shows that given a complete preference relation on closed menus in a compact metric space of alternatives X, a standard continuity property and Kreps' axioms jointly imply the existence of a representation with a collection of continuous (state-dependent) utility functions on X, and a further continuous function, referred to as an aggregator, that determines the overall value of a menu based on the state-dependent functions' maximum values on the menu. The interpretation is that the flexibility offered by a given menu allows the DM to wait and learn more about her tastes, so that ex-post she can select an alternative that maximizes the "correct" utility function over that menu. The state-dependent utility functions do attain their maximum values because they are continuous.

Kreps (1979) were only able to find lower semi-continuous utility functions.6 To the best of my knowledge, Evren (2020) is the first paper that illustrates potential uses of Nachbin-type constructions in the context of menu-preferences. In addition, Kreps' completeness axiom is dropped to let the DM remain indecisive on occasion.

Buturak and Evren (2017) propose a model of "choice overload" driven by anticipated regret. Their main finding is a behavioral characterization of an asymmetric regret representation for choice correspondences over lotteries. The DM (behaves as if she) is uncertain of her tastes at the time of choice. She anticipates experiencing regret if her choice turns out to be inferior ex post, upon resolution of the uncertainty. Thus, an ordinary alternative (a lottery) is evaluated with its expected utility minus a regret term. By contrast, when evaluating the default option, the DM does not consider the possibility of experiencing regret, leading to a bias towards the default option. Moreover, this bias is stronger in larger choice sets because the regret term for ordinary alternatives increases when additional alternatives become available.

2.2. Findings on other regarding preferences

Evren and Minardi (2017) provide behavioral foundations for a warm-glow model in a menu-choice setup. In the first stage, the DM chooses a set of social allocations (i.e. a menu) from which she will select an element in the second stage. The recipient observes the DM's choice of an allocation in the second stage, but not the earlier choice of a menu. The DM experiences warm-glow to the extent she appears generous in the eyes of the recipient. Thus, the DM enjoys the presence of self-serving options even if she does not plan to select them. Indeed, selecting an other-serving option acts as a signal of generosity only if the DM has the freedom to select a more selfish option. By contrast, other regarding behavior driven by social pressure and the associated

6"If ... >3 is represented ... with U(•, s) continuous for each s ..., then >3 is continuous on Xc. The converse seems reasonable: If 33 is continuous on Xc, then a representation with continuous U(•, s) and u is possible. But I am unable to supply a proof of the converse—U as constructed in the proof of the theorem will be lower semi-continuous only" (Kreps 1979).

negative feelings, such as shame or guilt, entail preference for smaller menus: Removal of prosocial allocations makes the DM better off by enabling her to behave selfishly, as she actually wishes. In turn, a purely altruistic DM cares only about the final allocation, and hence, is neutral against the size of the menus.

Evren and Minardi's (2017) main behavioral axioms are inspired by the literature on "motivation crowding out," which document instances where rewards and restrictive mechanisms to foster prosocial behavior often backfire (see, e.g., Gneezy and Rustichini 2000, Falk and Kosfeld 2006, Mellstrom and Johannesson 2008).

Millions of people vote in large elections despite the fact that voting is a costly activity. This does not make much sense from the perspective of a rational individual who is trying to maximize her material payoff because the probability of being decisive (pivotal) for a single voter is very small in a large election. But how small is it? If there is a second-order uncertainty about the fraction of altruistic voters, then pivot probabilities converge to zero at a linear rate, as the number of voters converge to infinity. This makes it possible to generate significant turnout rates with reasonable levels of altruism. Equiva-lently, the voters may be experiencing a warm-glow payoff when they take the "right" action from a utilitarian perspective. Evren (2012) constructs such a model, and shows that its asymptotic predictions coincide with Feddersen and Sandroni's (2006) rule-utilitarian voter model, up to potential differences due to the interpretation of the parameters. Evren's model uses a standard game-theoretic solution concept, unlike Feddersen and Sandroni's (2006) solution concept that has a cooperative nature.

2.3. Findings on ambiguity and risk attitudes

In Segal's (1987) theory, the DM converts subjective acts into compound lotteries with the help of her second-order belief. She then uses a non-expected utility function on simple lotteries in a recursive fashion to evaluate the compound-lotteries. Segal shows that if this non-expected utility function belongs to Quiggin's (1982) rank dependent utility (RDU) model, then the theory can

generate ambiguity averse behavior. Only "can," because Segal's result requires several further assumptions. Most importantly, the choice problem is assumed to involve only binary bets which return at most two distinct prizes. On the other hand, Artstein-Avidan and Dillenberger (2011) pointed out that Dillenberger's (2010) negative certainty independence axiom (NCI) on risk preferences implies a global ambiguity aversion property: The behavior is guaranteed to be ambiguity averse irrespective of the DM's second-order belief or the state space. It should also be noted that the RDU model generically violates NCI (Dillenberger 2010).

The first result of Evren (2019) establishes the converse of Artstein-Avidan and Dillenberger's (2011) observation: Global ambiguity aversion implies NCI. This finding is somewhat surprising because NCI is not necessary for ambiguity aversion at a local level, given a specific second-order belief, but it is necessary for the global ambiguity aversion property.

In any economic model concerned with ambiguity, comparative statics of the model with respect to the level of ambiguity is of natural interest. Inspired by the classical concept of "increasing risk," Evren (2019) proposes a definition of "increasing ambiguity" that has clear-cut implications on ambiguity attitudes in Segal's (1987) model. Specifically, the paper shows that a mean-preserving spread operation over second-order beliefs characterizes an increase in the strength of ambiguity aversion for the class of globally ambiguity averse preferences.