In this paper, we provide an axiomatic foundation of pessimism and optimism towards ambiguity that emerges due to growing awareness. In our setup, this corresponds to a discovery of finer “descriptions” of the original contingencies. A decision-maker can form subjective probabilistic beliefs on the original state space and behaves as an expected utility maximizer. However, as finer contingencies are discovered, he may perceive ambiguity with respect to the newly identified states and thus be unable to extend her initial probabilistic beliefs (...) to the expanded state space in an additive way. As a result, the decision-maker’s new beliefs are now “ambiguous” and represented by a probability distribution combined, for each refinement of an original state, with a degree of confidence in this probability estimate. We provide a parametric representation of preferences, identify the DM’s degree of ambiguity as well as his attitude towards ambiguity as captured by the degree of optimism and pessimism. We illustrate the relation of our model to some well-known capacities, such as the E-capacities introduced by Eichberger and Kelsey, the JP-capacities of Jaffray and Philippe and the NEO-additive capacities developed by Chateauneuf et al.. (shrink)

We study decision under uncertainty in an Anscombe–Aumann framework. Two binary relations characterize a decision-maker: one incomplete relation, reflecting her objective rationality, and a second complete relation, reflecting her subjective rationality. We require the latter to be an extension of the former. Our key axiom is a dominance condition. Our main theorem provides a representation of the two relations. The objectively rational relation has a Bewley-style multiple prior representation. Using this set of priors, we fully characterize the subjectively rational relation (...) in terms of the most optimistic and most pessimistic expected utilities. (shrink)

In Proposition 4, lines 3, 4 and 8, 9 were scrambled by mistake during the pagination process of the online published article.

This paper introduces a receiver who perceives ambiguity in a binary model of Bayesian persuasion. The sender has a well-defined prior, while the receiver considers an interval of priors and maximizes a convex combination of worst and best expected payoffs. We characterize the sender’s optimal signal and find that the receiver’s payoff differences across states given each action, play a fundamental role in the characterization and the comparative statics. If the sender’s preferred action is the least sensitive one, then the (...) sender’s equilibrium payoff, as well as the sender’s preferred degree of receiver ambiguity, is increasing in the receiver’s pessimism. We document a tendency for ambiguity-sensitive receivers to be more difficult to persuade. (shrink)

We study price formulas suited for empirical research in financial markets in which put–call parity is satisfied. We find a connection between risk and the bid–ask spread. We further study the compatibility of the model with market frictions, and determine market subsets where the Fundamental Theorem of Asset Pricing applies. Finally, we characterize the price formula.

The Savage and the Anscombe–Aumann frameworks are the two most popular approaches used when modeling ambiguity. The former is more flexible, but the latter is often preferred for its simplicity. We conduct an experiment where subjects place bets on the joint outcome of an ambiguous urn and a fair coin. We document that more than a third of our subjects make choices that are incompatible with Anscombe–Aumann for any preferences, while the Savage framework is flexible enough to account for subjects’ (...) behaviors. (shrink)

Cultural differences can be a source of ambiguity in coordination games. As players are likely to experience more ambiguity when playing a different culture, we expect players to choose safer strategies. We run experiments with a stag hunt and bargaining coordination game. Using a between-subjects design, we vary the identity of the opponent between someone of the same culture or a different culture. We compare the responses of British and East Asian students at the University of Exeter and show the (...) cultural identity of the opponent by physical appearance. While we find no significant differences between treatments for East Asians, the British choose the safer option in the stag hunt and demand more of the pie in the bargaining game when faced with an opponent from a different culture. (shrink)

The Condorcet Jury Theorem formalises the “wisdom of crowds”: binary decisions made by majority vote are asymptotically correct as the number of voters tends to infinity. This classical result assumes like-minded, expected utility maximising voters who all share a common prior belief about the right decision. Ellis : 865–895, 2016) shows that when voters have ambiguous prior beliefs—a set of priors—and follow maxmin expected utility, such wisdom requires that voters’ beliefs satisfy a “disjoint posteriors” condition: different private signals lead to (...) posterior sets with disjoint interiors. Both the original theorem and Ellis’s generalisation assume symmetric penalties for wrong decisions. If, as in the jury context, errors attract asymmetric penalties then it is natural to consider voting rules that raise the hurdle for the decision carrying the heavier penalty for error. In a classical model, Feddersen and Pesendorfer :23–35, 1998) have shown that, paradoxically, raising this hurdle may actually increase the likelihood of the more serious error. In particular, crowds are not wise under the unanimity rule: the probability of the more serious error does not vanish as the crowd size tends to infinity. We show that this “Jury Paradox” persists in the presence of ambiguity, whether or not juror beliefs satisfy Ellis’s “disjoint posteriors” condition. We also characterise the strictly mixed equilibria of this model and study their properties. Such equilibria cannot exist in the absence of ambiguity but may exist for arbitrarily large jury size when ambiguity is present. In addition to uninformative strictly mixed equilibria, analogous to those exhibited by Ellis : 865–895, 2016), there may also exist strictly mixed equilibria which are informative about voter signals. (shrink)

We seek an evolutionary explanation for why in some situations humans maintain either optimistic or pessimistic attitudes toward uncertainty and are ignorant to relevant aspects of their environment. Players in strategic games face Knightian uncertainty about opponents’ actions and maximize individually their Choquet expected utility with respect to neo-additive capacities allowing for both an optimistic or pessimistic attitude toward uncertainty as well as ignorance to strategic dependencies. An optimist overweighs good outcomes. A complete ignorant never reacts to opponents’ changes of (...) actions. We focus on sub- and supermodular aggregative games and provide monotone comparative statics w.r.t. optimism/pessimism. With qualifications, we show that in finite populations, optimistic complete ignorance is evolutionary stable and yields a strategic advantage in submodular games with aggregate externalities. Moreover, this evolutionary stable preference leads to Walrasian behavior in these classes of games. (shrink)

Ambiguity affects decisions of people who exhibit a distaste of and require a premium for dealing with it. Do ambiguity-neutral subjects completely disregard ambiguity and react to any vague news? Online vending platforms often attempt to affect buyer’s decisions by messages like “20 people are looking at this item right now” or “The average score based on 567 reviews is 7.9/10”. We augment the two-color Ellsberg experiment with similarly worded signals about the unknown probability of success. All decision-makers, including ambiguity-neutral, (...) recognize and account for ambiguity; ambiguity-neutral subjects are less likely to respond to vague signals. The difference between decisions of ambiguity-neutral and non-neutral subjects vanishes for high precision signals; still less than 60% subjects choose the ambiguous urn, even for high communicated probabilities of success. We conjecture participants may discard information, if they see no contradiction between it and their prior beliefs, hence the latter are not updated. Higher confidence makes subjects more likely to discard the news, and empirically ambiguity-neutral subjects appear more confident than those ambiguity-averse. (shrink)

This paper is about participation in efficient risk sharing among agents who have ambiguous beliefs about uncertain states of nature. The question we ask is whether and how can ambiguous beliefs give rise to some agents not participating in efficient risk sharing. Ambiguity of beliefs is described by the multiple-prior expected utility of Gilboa and Schmeidler, or the variational preferences of Maccheroni et al. :1447–1498, 2006). The main result says that if the aggregate risk is relatively small, then the agents (...) whose beliefs are the most ambiguous do not participate in risk sharing. The higher the ambiguity of those agents’ beliefs, the more likely is their non-participation. Another factor making non-participation more likely is low risk aversion of agents whose beliefs are less ambiguous. We discuss implications of our results on agents’ participation in trade in equilibrium in assets markets. (shrink)

We propose an axiomatization of aversion to incomplete preferences. Some prevailing models of incomplete preferences rely on the hypothesis that incompleteness is temporary and that by keeping their opportunity set open individuals reveal a preference for flexibility. We consider that the maintenance of incomplete preference is also aversive. Our model allows us to show how incompleteness induces an aversive attitude in two different ways: intrinsic and instrumental. Intrinsic aversion holds when one instance of incomplete preference in the set suffices to (...) decrease its utility. Instrumental aversion holds only insofar dominating options are affected by incompleteness. Given two partially overlapping sets of axioms on the binary relation over sets we formalize their consistency with the two types of aversion to incompleteness. Finally, we relate our model to the classical Sen’s distinction between tentative and assertive incompleteness. The spelling out of this distinction in the terms of our approach uncovers to what extent aversion to incompleteness may be compatible with a preference for flexibility. (shrink)

We report on an experiment examining whether individuals can solve a simple signal extraction problem of the type found in models with imperfect information. In one treatment, subjects must form point predictions based on observing both public and private signals, while in another they receive the same information but must decide on the weight to attach to each signal, which then determines their point prediction. We find that, at the aggregate level, signal extraction provides a good characterization of subjects’ behavior (...) in both treatments, but at the individual level, there is considerable heterogeneity in subjects’ ability to perform signal extraction. (shrink)

We generalize a previous result about dynamically consistent menu preferences to the case where preferences are not necessarily complete. We show that, as it is the case when preferences are complete, a subjective state space version of dynamic consistency is linked to a comparative theory of preference for flexibility. In words, an objective signal is interpreted as an event in the agent’s subjective state space and the agent acts in a dynamically consistent way after that if and only if we (...) can attribute all the differences between the agent’s preferences before and after the signal to the fact that the agent values flexibility more before the signal than after. (shrink)

We design an experiment to study investment behavior in different repeated contest settings, varying the uncertainty of the outcomes and the number of participants in contests. We find decreasing over-expenditures and a higher rate of ‘dropout’ in contests with high uncertainty over outcomes, while we detect a quick convergence toward equilibrium predictions and a near to full participation when this type of uncertainty vanishes. These results are robust to changes in the number of contestants. A learning parameter estimation using the (...) experience-weighted attraction model suggests that subjects adopt different learning modes across different contest structures and helps to explain expenditure patterns deviating from theoretical predictions. (shrink)

We propose a new game to strategically justify the constrained equal awards rule in claims problems. Our game is “procedurally fair” and “multilateral”. In addition, even if claimants cannot reach an agreement in any period, they can renegotiate in the next period. We show that, for each claims problem, the awards vector chosen by the constrained equal awards rule achieved at period 1 is the unique subgame perfect equilibrium outcome of the game.

This paper investigates how communication influences people’s judgment quality in simple estimation tasks. Except for an exchange of estimates, our design also allows the exchange of supportive evidence underlying the estimates in a controlled manner. Compared with the control treatment, the exchange of estimates and supportive evidence together improves judgment quality at both the individual level and the crowd level. On the other hand, the exchange of estimates or supportive evidence separately has no impact.

This paper proffers a dialogical theory of decision-making: decision-makers are engaged in two modes of rational decisions, instrumental and existential. Instrumental rational decisions take place when the DM views the self externally to the objects, whether goods or animate beings. Existential rational decisions take place when the DM views the self in union with such objects. While the dialogical theory differs from Max Weber’s distinction between two kinds of rationality, it follows Martin Buber’s philosophical anthropology. The paper expounds the ramifications (...) of the dialogical theory in understanding structures of exchange considering assessments of diverse thinkers. (shrink)

We document outcome bias in situations where an agent makes risky financial decisions for a principal. In three experiments, we show that the principal’s evaluations and financial rewards for the agent are strongly affected by the random outcome of the risky investment. This happens despite her exact knowledge of the investment strategy, which can, therefore, be assessed independently of the outcome. The principal thus judges the same decision by the agent differently, depending on factors that the agent has no influence (...) on. The effect of outcomes persists in a setting where principals communicate a preferred investment level. Principals are more satisfied with the agent after a random success when the agent did not follow the requested investment level, than after a failed investment that followed their explicit request. (shrink)

This study proposes a model of non-unitary time discounting and examines its welfare implications. A key feature of our model lies in the disparity of time discounting between multiple distinct goods, which induces an individual’s preference reversals even though she normally discounts her future utilities for each good. After characterizing the time-consistent decision-making by such an individual, we compare welfare achieved in the market economy and welfare in the planner’s allocation from the perspective of all selves across time. Under certain (...) situations, the selves in early periods strictly prefer the social planner’s allocation, whereas the selves in future periods strictly prefer the market equilibrium. Therefore, the welfare implications of our model are quite different from those in the canonical discounting model and in models of other time-inconsistent preferences. (shrink)

This study considers a voting rule wherein each player sincerely votes when he/she has no information about the preferences of the other players. We introduce the concept of rank-dominant strategies to discuss the situation where a player is completely ignorant in the preferences of the other players and decision theoretic justification of the concept. We show that under the plurality voting rule with the equal probability random tie-breaking, sincere voting is always the rank-dominant strategy of each voter. We also discuss (...) other scoring rules and show that sincere voting may not be a rank-dominant strategy of a voter even with the equal probability random tie-breaking. (shrink)

We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We focus on the relations between several extensions of the condition of independence of irrelevant alternatives on one hand, and conditions on the revealed preference relation on sets, notably the weak axiom of revealed preference, on the other hand. We also establish the connection between the condition of independence of irrelevant alternatives and so-called (...) strong sets; the latter characterize a social choice correspondence satisfying independence of irrelevant alternatives. (shrink)

What does it mean for an agent faced with choice under uncertainty to “know” something? While a variety of mathematical methods are available to construct formal models to answer this question, the combination of different approaches may lead to unsettling paradoxes. I propose a unified theory that eliminates such inconsistencies by relying on a sharp conceptual distinction between information the decision-maker observes and how much of that information she can cognitively process. The resulting model allows for natural decision-theoretic characterizations of (...) comparing different amounts of information. (shrink)