Marciano Siniscalchi

Dynamic choice under ambiguity

This paper analyzes sophisticated dynamic choice for ambiguity-sensitive decision makers. It characterizes Consistent Planning via axioms on preferences over decision trees. Furthermore, it shows how to elicit conditional preferences from prior preferences. The key axiom is a weakening of Dynamic Consistency, deemed Sophistication. The analysis accommodates arbitrary decision models and updating rules. Hence, the results indicate that (i) ambiguity attitudes, (ii) updating rules, and (iii) sophisticated dynamic choice are mutually orthogonal aspects of preferences. As an example, a characterization of prior-by-prior Bayesian updating and Consistent Planning for arbitrary maxmin-expected utility preferences is presented. The resulting sophisticated MEU preferences are then used to analyze the value of information under ambiguity; a basic trade-off between information acquisition and commitment is highlighted.

Rationalization and Incomplete Information

We analyze a family of extensive-form solution procedures for games with incomplete information that do not require the specification of an epistemic type space a la Harsanyi, but can accommodate a (commonly known) collection of explicit restrictions D on first-order beliefs. For any fixed D we obtain a solution called D-rationalizability.In static games, D-rationalizability characterizes the set of outcomes (combinations of payoff types and strategies) that may occur in any Bayesian equilibrium model consistent with D; these are precisely the outcomes consistent with common certainty of rationality and of the restrictions D. Hence, our approach to the analysis of incomplete-information games is consistent with Harsanyis, and it may be viewed as capturing the robust implications of Bayesian equilibrium analysis.In dynamic games, D-rationalizability yields a forward-induction refinement of this set of Bayesian equilibrium outcomes. Focusing on the restriction that first-order beliefs be consistent with a given distribution on terminal nodes, we obtain a refinement of self-confirming equilibrium. In signalling games, this refinement coincides with the Iterated Intuitive Criterion.

Vector Expected Utility and Attitudes Toward Variation

This paper proposes a model of decision under ambiguity deemed vector expected utility, or VEU. In this model, an uncertain prospect, or Savage act, is assessed according to (a) a baseline expected-utility evaluation, and (b) an adjustment that reflects the individuals perception of ambiguity and her attitudes toward it. The adjustment is itself a function of the acts exposure to distinct sources of ambiguity, as well as its variability. The key elements of the VEU model are a baseline probability and a collection of random variables, or adjustment factors, which represent acts exposed to distinct ambiguity sources and also reflect complementarities among ambiguous events. The adjustment to the baseline expected-utility evaluation of an act is a function of the covariance of its utility profile with each adjustment factor, which reflects exposure to the corresponding ambiguity source. Copyright 2009 The Econometric Society.

Ambiguity and ambiguity aversion

Abstract The phenomena of ambiguity and ambiguity aversion , introduced in Daniel Ellsberg’s seminal 1961 article, are ubiquitous in the real world and violate both the key rationality axioms and classic models of choice under uncertainty. In particular, they violate the hypothesis that individuals’ uncertain beliefs can be represented by subjective probabilities (sometimes called personal probabilities or priors ). This chapter begins with a review of early notions of subjective probability and Leonard Savage’s joint axiomatic formalization of expected utility and subjective probability. It goes on to describe Ellsberg’s classic urn paradoxes and the extensive experimental literature they have inspired. It continues with analytical descriptions of the numerous (primarily axiomatic) models of ambiguity aversion which have been developed by economic theorists, and concludes with a discussion of some current theoretical topics and newer examples of ambiguity aversion.

A behavioral characterization of plausible priors

Recent theories of choice under uncertainty represent ambiguity via multiple priors, informally interpreted as alternative probabilistic models of the uncertainty that the decision-maker considers equally plausible. This paper provides a robust behavioral foundation for this interpretation. A prior P is deemed “plausible” if (i) preferences over a subset C of acts are consistent with subjective expected utility (SEU), and (ii) jointly with an appropriate utility function, P provides the unique SEU representation of preferences over C. Under appropriate axioms, plausible priors can be elicited from preferences; moreover, if these axioms hold, (i) preferences are probabilistically sophisticated if and only if they are SEU, and (ii) under suitable consequentialism and dynamic consistency axioms, “plausible posteriors” can be derived from plausible priors via Bayes’ rule. Several well-known decision models are consistent with the axioms proposed here.

Rationalizable bidding in first-price auctions

Abstract We analyze the consequences of strategically sophisticated bidding without assuming equilibrium behavior. In particular, we characterize interim rationalizable bids in symmetric first-price auctions with interdependent values and affiliated signals. We show that (1) every nonzero bid below the equilibrium is rationalizable, (2) some bids above the equilibrium are rationalizable, (3) the upper bound on rationalizable bids of a given player is a nondecreasing function of her signal. In the special case of independent signals and quasi-linear valuation functions, (i) the least upper bound on rationalizable bids is concave; hence (ii) rationalizability implies substantial proportional shading for high valuations, but is consistent with negligible proportional shading for low valuations. We argue that our theoretical analysis may shed some light on experimental findings about deviations from the risk-neutral Nash equilibrium.

Ambiguity in the Small and in the Large

This paper considers local and global multiple-prior representations of ambiguity for preferences that are (i) monotonic, (ii) Bernoullian, i.e. admit an affine utility representation when restricted to constant acts, and (iii) locally Lipschitz continuous. We do not require either Certainty Independence or Uncertainty Aversion. We show that the set of priors identified by Ghirardato, Maccheroni, and Marinacci (2004)’s ‘unambiguous preference’ relation can be characterized as a union of Clarke differentials. We then introduce a behavioral notion of ‘locally better deviation’ at an act, and show that it characterizes the Clarke differential of the preference representation at that act. These results suggest that the priors identified by these preference statements are directly related to (local) optimizing behavior.

TWO OUT OF THREE AIN'T BAD: A COMMENT ON “THE AMBIGUITY AVERSION LITERATURE: A CRITICAL ASSESSMENT”

Al-Najjar and Weinstein (2009) propose to scrutinize the implications of recent theories of ambiguity in dynamic settings. They conclude that such implications are so unreasonable as to cast doubts on the legitimacy of the theories under consideration. The present paper argues that the seemingly unreasonable implications highlighted by Al-Najjar and Weinstein can be understood as the result of basic trade-offs that arise naturally in the presence of ambiguity. In particular, Al-Najjar and Weinstein are uncomfortable with the possibility that an ambiguity-averse individual may reject freely available information; however, this phenomenon simply reflects a trade-off between the intrinsic value of information, which is positive even in the presence of ambiguity, and the value of commitment.

Introduction to model uncertainty and robustness

Abstract This article introduces the symposium on model uncertainty and robustness.© 2006 Elsevier Inc.All rights reserved. JEL classification: D81; D91 Keywords: Ambiguity; Model uncertainty; Robust control preferences; Robustness; Time consistent preferences This symposium contains four papers about decision making under uncertainty in contexts inwhichadecisionmakercannotordoesnotformulateasingleprobabilitymodel.WaysofthinkingaboutthisproblemsharecommonfeaturesowingtoGliboaandSchmeidler[1],whoaxiomatizeda max–min expected utility theory in which a decision maker chooses an action to maximize anexpected utility function whose probability weights he supposes to be chosen by a malevolentagent. Especially in dynamic settings, we continue to learn how to formulate the set of modelsover which this malevolent agent chooses.Maccheroni,Marinacci,andRustichini[3]extendtomulti-periodproblemsthestatictheoryofvariationalpreferencesthattheyintroducedinanearlierpaper.Apreferenceiscalledvariationalifthe decision maker chooses an act while a malevolent opponent (Nature) chooses the probabilityover states at some cost. Variational preferences include Multiple Priors preferences, RobustControl preferences, and Mean-Variance preferences. In the extension to many periods, bothNature and the decision maker choose in every period. The paper aims to characterize time

Epistemic Game Theory

Epistemic game theory formalizes assumptions about rationality and mutual beliefs in a formal language, then studies their behavioral implications in games. Specifically, it asks: what do different notions of rationality and different assumptions about what players believe about…what others believe about the rationality of players imply regarding play in a game? Being explicit about these assumptions can be important, because solution concepts are often motivated intuitively in terms of players’ beliefs and their rationality; however, the epistemic analysis may show limitations in these intuitions, reveal what additional assumptions are hidden in the informal arguments, clarify the concepts or show how the intuitions can be generalized. A further premise of this chapter is that the primitives of the model— namely, the hierarchies of beliefs—should be elicitable, at least in principle. Building upon explicit assumptions about elicitable primitives, we present classical and recent developments in epistemic game theory and provide characterizations of a nonexhaustive, but wide, range of solution concepts.