Decision Theory
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“Dynamic Consistency and Rectangularity for the Smooth Ambiguity Model” (with Alexander Shklyaev and Alexey Galatenko)
Abstract: We study the Smooth Ambiguity decision criterion in the dynamic setting to understand when it can satisfy the Dynamic Consistency and Consequentialism properties. These properties allow one to rewrite the decision criterion recursively and solve for optimal decisions by Dynamic Programming. Our result characterizes the possibility of having these properties through a condition that resembles Epstein and Schneider's (2003) rectangularity condition for the maxmin model. At the same time, we show that Dynamic Consistency and Consequentialism can be achieved for Smooth Ambiguity preferences in a narrower set of scenarios than one would hope for.
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“Time for Memorable Consumption” (with Stefania Minardi), Games and Economic Behavior, 2024, vol. 148, pp. 296–322
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Abstract: A consumption event is memorable if the memory of the event affects well-being at times after the material consumption, as originally introduced by Gilboa et al. (2016). Our main contribution is to develop an axiomatic foundation of memorable consumption in a dynamic setting. Preferences are represented by the present value of the sum of utilities derived at each date from the current consumption and from recollecting the past. Our model accommodates well-known phenomena in psychology, such as the peak-end rule, duration neglect, and adaptation trends. We also provide foundations for a prominent special case of the representation with the Markovian property. The model is illustrated with applications in two different contexts: risk-taking behavior in a principal-agent problem and life-cycle consumption-savings decisions.
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“Believing in Forecasts, Uncertainty, and Rational Expectations” (with Efe A. Ok), Economic Theory, 2022, vol. 74(3), pp. 947–971
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Formerly circulated as: “Choice Under Uncertainty with Initial Information”
Abstract: We model situations of choice under uncertainty where one is exogenously given information about the unknown states as a “suggested prior” (as in weather forecasts, betting odds provided by bookmakers, success likelihoods provided by medical doctors, estimates given by financial analysts, etc.). We wish to understand when a decision maker would adopt the suggested prior as her own subjective beliefs, yielding fully to the power of suggestion. We find that this happens under surprisingly weak conditions: If a preference relation, may it be complete or incomplete, (1) uses the information it is given consistently (in the sense of being state-neutral) and (2) believes that events that are suggested to occur with zero probability will indeed not occur, then it is not only probabilistically sophisticated, but also holds the suggested beliefs as actual beliefs. If the agent is a (subjective) expected utility maximizer, this happens even in the absence of condition (2).
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“Subjective Contingencies and Limited Bayesian Updating” (with Stefania Minardi), Journal of Economic Theory, 2019, vol. 183, pp. 1–45
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Abstract: We depart from Savage’s (1954) common state space assumption and introduce a model that allows for a subjective understanding of uncertainty. Within the revealed preference paradigm, we take the analyst's perspective and uniquely identify the agent's subjective state space via her preferences conditional on incoming information. According to our representation, the agent's subjective contingencies correspond to sets of the analyst's states and, as such, are coarse. The agent uses an additively separable utility with respect to her set of contingencies; and she adopts an updating rule that follows the Bayesian spirit but is limited by her perception of uncertainty. We illustrate the relevance of our theory with applications to the confirmatory bias and correlation neglect, as well as to optimal contract design.
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“Preferences With Grades of Indecisiveness” (with Stefania Minardi), Journal of Economic Theory, 2015, vol. 155, pp. 300–331
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Abstract: Departing from the traditional approach of modeling indecisiveness based on the weakening of the completeness axiom, we introduce the notion of graded preferences: The agent is characterized by a binary relation over (ordered) pairs of alternatives, which allows her to express her inclination to prefer one alternative over another and her confidence in the relative superiority of the indicated alternative. In the classical Anscombe-Aumann framework, 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 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.
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(working paper version following the cardinal approach) ⟨2013-07-31⟩
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“A Note on Preferences With Grades of Indecisiveness Without Reciprocity” (with Stefania Minardi) ⟨2013-08-05⟩
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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.
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“Decision-Making under Subjective Risk: Toward a General Theory of Pessimism” (with Anna Gumen and Efe A. Ok) ⟨2014-03-20⟩
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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.
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“Mistake Aversion and a Theory of Robust Decision Making” ⟨2014-02-21⟩
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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.
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“A Confidence-Based Decision Rule and Ambiguity Attitudes” (with Stefania Minardi) ⟨2013-02-14⟩
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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, 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.
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“Dynamically Stable Preferences” (with Anna Gumen), Journal of Economic Theory, 2013, vol. 148, pp. 1487–1508
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Working paper version: Paper, Bibliographic referenceAbstract: 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
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“Characterizations of Smooth Ambiguity Based on Continuous and Discrete Data” (with Stefania Minardi), Mathematics of Operations Research, 2017, vol. 42(1), pp. 167–178
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This paper is an expanded version of an earlier work circulated under the title “A Functional Characterization of Smooth Ambiguity.”
Abstract: In the Anscombe-Aumann setup, we provide conditions for a collection of observations to be consistent with a well-known class of smooth ambiguity preferences (Klibanoff, Marinacci, Mukerji, 2005). Each observation is assumed to take the form of an equivalence between an uncertain act and a certain outcome. We provide three results that describe these conditions for data sets of different cardinality. Our findings uncover surprising links between the smooth ambiguity model and classic mathematical results in complex and functional analysis.