Decision Theory

(Click titles to expand)

  • Decision-Making under Subjective Risk: Toward a General Theory of Pessimism” (with Anna Gumen and Efe A. Ok) ⟨2014-03-20⟩

    Download: Paper, Bibliographic reference

    Abstract: The primary objective of this paper is to develop a framework in which a decision-maker may have subjective beliefs about the “riskiness” of prospects, even though the risk structure of these prospects is objectively specified. Put differently, we investigate preferences over risky alternatives by postulating that such preferences arise from more basic preferences that act on the subjective transformations of these prospects. This allows us to derive a theory of preferences over lotteries with distorted probabilities and provides information about the structure of such distortions. In addition, we are able to formulate a behavioral trait such as “pessimism” in the context of risk (independently of any sort of utility representation) as a particular manifestation of the uncertainty aversion phenomenon. Our framework also provides a strong connection between the notions of aversion to ambiguity and risk which have so far been regarded as distinct traits in decision theory. In particular, we find that, in the presence of some basic assumptions, the decision-maker distorts probabilities and has non-expected utility preferences if and only if he is not neutral towards ambiguity.

  • Mistake Aversion and a Theory of Robust Decision Making⟨2014-02-21⟩

    Download: Paper, Biblioraphic reference

    Abstract: This paper studies the behavioral trait of aversion to making mistakes in the framework of choice under subjective uncertainty, assuming that the probabilities of outcomes are not exogenously specified. The decision procedure that is proposed to capture mistake aversion follows the general approach of robust decision making: For each probability distribution that may plausibly describe the uncertainty, the decision maker computes his expected utility, and discards the feasible choice options that cannot guarantee a particular level of utility relative to his default option. The paper then follows the revealed preferences approach to study foundations of this procedure and the comparative notion of mistake aversion. As shown in an application, the proposed model is capable of generating higher risk premia and the effects of the volatility of payoffs on asset prices and returns that are different than in the standard models.

  • Preferences With Grades of Indecisiveness” (with Stefania Minardi) ⟨2013-07-31⟩

    Download: Paper, Bibliographic reference

    Abstract: Departing from the traditional approach to modeling an agent who finds it difficult to make clear-cut comparisons between alternatives, we introduce the notion of graded preferences: Given two alternatives, the agent reports a number between 0 and 1, which reflects her inclination to prefer the first option over the second or, put differently, how confident she is about the superiority of the first one. In the classical framework of uncertainty, we derive a representation of a graded preference by a measure of the set of beliefs that rank one option better than the other. Our model is a refinement of Bewley's (1986) model of Knightian uncertainty: It is based on the same object of representation — the set of beliefs — but provides more information about how the agent compares alternatives. We also define and characterize, in terms of the representation, the notion of one agent being “more decisive” than another.

    • A Note on Preferences With Grades of Indecisiveness Without Reciprocity” (with Stefania Minardi) ⟨2013-08-05⟩

      Download: Paper, Bibliographic reference

      Abstract: This note extends the analysis of Minardi and Savochkin (2013) by dropping the Reciprocity axiom. We provide a more general representation result and adapt the related analysis of comparative statics.

  • A Confidence-Based Decision Rule and Ambiguity Attitudes” (with Stefania Minardi) ⟨2013-02-14⟩

    Download: Paper, Bibliographic reference

    Abstract: We propose a decision rule — a procedure that maps incomplete judgements of an agent into final choices — that allows us to link confidence in decision-making under uncertainty to the ambiguity attitude displayed in the choice behavior. If this decision rule is applied to an affine graded preference relation (Minardi and Savochkin, 2013), the emerging choice behavior exhibits sensitivity to ambiguity and it is consistent with the generalized Hurwicz α-pessimism model studied by Ghirardato, Maccheroni, and Marinacci (2004); its famous special case of maxmin preferences of Gilboa and Schmeidler (1989) is obtained by imposing certain additional assumptions. We provide two comparative statics results: First, if the level of tolerance for the lack of confidence in comparisons decreases, the agent becomes more ambiguity averse. Second, a more decisive decision maker displays less ambiguity aversion.

  • An Ordinal Foundation of Preferences With Grades of Indecisiveness” (with Stefania Minardi) ⟨2013-04-12⟩

    Download: Paper, Bibliographic reference

    Abstract: The main objective of this paper is to provide an ordinal foundation to the study of graded preferences in Minardi and Savochkin (2013). More specifically, we show that the analysis of graded preferences can be undertaken in a way that is independent of the scale of the confidence levels that the decision maker reports. As a separate result, we also provide a strengthening of the main representation result of Minardi and Savochkin (2013).

  • Dynamically Stable Preferences” (with Anna Gumen), Journal of Economic Theory 148 (2013) 1487–1508

    Download: Paper, Bibliographic reference
    Working paper version: Paper, Bibliographic reference

    Abstract: In the framework of dynamic choice under uncertainty, we define dynamic stability as a combination of two assumptions prevalent in the literature: dynamic consistency and the requirement that updated preferences have the same “structure” as ex ante ones. Dynamic stability also turns out to be a defining characteristic of the multiplier preferences of Hansen and Sargent (2001) within the scope of variational preferences. Generally, for any class of invariant preferences, dynamic stability is shown to be connected to another independent property — consequentialism.

Mathematical Economics

  • A Functional Characterization of Smooth Ambiguity” (with Stefania Minardi) ⟨2013-11-24⟩

    Download: Paper

    Abstract: In the Anscombe-Aumann framework, we propose a functional characterization of the intersection of the class of variational preferences (Maccheroni, Marinacci, and Rustichini, 2006) and the class of smooth ambiguity preferences (Klibanoff, Marinacci, and Mukerji, 2005).