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Observed individual behavior in the presence of ambiguity shows insufficient responsiveness to changes in subjective likelihoods. Despite being integral to theoretical models and relevant in many domains, evidence on the causes and determining factors of such likelihood insensitive behavior is scarce. This paper investigates the role of beliefs in the form of ambiguity perception – the extent to which a decision-maker has difficulties assigning a single probability to each possible event – as a potential determinant. Using an experiment, I elicit measures of ambiguity perception and likelihood insensitivity and exogenously vary the level of perceived ambiguity. The results provide strong support for a perception-based explanation of likelihood insensitivity. The two measures are highly correlated at the individual level, and exogenously increasing ambiguity perception increases insensitivity, suggesting a causal relationship. In contrast, ambiguity perception is unrelated to ambiguity aversion – the extent to which a decision-maker dislikes the presence of ambiguity. [ABSTRACT FROM AUTHOR]

Although much of the theoretical and applied literature involving decision under ambiguity works under the assumption of uncertainty aversion, experimental evidence suggests that it is not a universal behavioural trait. This paper introduces and axiomatises the family of α -UA (for α -Uncertainty Attitude) preferences: a simple extension of uncertainty averse preferences with a Hurwicz-style mixing coefficient, so as to admit a richer range of uncertainty attitudes. The parameters of the model are uniquely identified in our characterisation. It provides, in the Hurwicz α -maxmin EU special case, a new resolution of a long-standing identification problem. It also yields novel models, including extensions of variational and multiplier preferences. Comparative statics support the interpretation of the mixing coefficient as an index of imprecision aversion. In a standard portfolio problem, the model yields the intuitive relationship between imprecision aversion and investment in an uncertain asset: as the former increases, the latter decreases. [ABSTRACT FROM AUTHOR]

This paper provides a micro-foundation for approximate incentive compatibility using ambiguity aversion. In particular, we propose a novel notion of approximate interim incentive compatibility, approximate local incentive compatibility , and establish an equivalence between approximate local incentive compatibility in a Bayesian environment and exact interim incentive compatibility in the presence of a small degree of ambiguity. We then apply our result to the implementation of efficient allocations. In particular, we identify two economic settings—including ones in which approximately efficient allocations are implementable and ones in which agents are informationally small—in which efficient allocations are approximately locally implementable when agents are Bayesian. Applying our result to those settings, we conclude that efficient allocations are exactly implementable when agents perceive a small degree of ambiguity. [ABSTRACT FROM AUTHOR]

Ambiguous language is ubiquitous and often deliberate. Recent theoretical work (Bose and Renou, 2014 ; Kellner and Le Quement, 2018 ; Beauchêne et al., 2019) has shown how language ambiguation can improve outcomes by mitigating conflict of interest. Our experiment finds a significant effect of language ambiguation on subjects who are proficient at Bayesian updating. For ambiguity averse subjects within this population, a significant part of this effect operates via the channel of subjects' desire to reduce ambiguity. For both ambiguity averse and neutral subjects within this population, an additional behavioral channel is also present. [ABSTRACT FROM AUTHOR]

Semi-consistent conditional preferences are inconsistent enough for different ambiguity attitudes to manifest themselves in different behavior and consistent enough for information to be generically valuable. To simultaneously achieve these two desiderata I assume exactly one type of dynamic inconsistency: agents do not update their preferences upon learning independent randomization outcomes. [ABSTRACT FROM AUTHOR]

This paper explores multi-stage incomplete information games with common ambiguous information about states or types and ambiguity averse players. We characterize a belief formation process that allows players to take their knowledge about the structure of the game into account. This process leads to subjective rectangular ex-ante belief sets for all players. We show that given these sets of beliefs, players behave dynamically consistent. Therefore, using our belief formation process, we can extend the concept of sequential equilibria to multi-stage ambiguous incomplete information games. Furthermore, we characterize assumption under which sequential rationality implies rectangularity. [ABSTRACT FROM AUTHOR]

In the context of normal-form games with complete information, we introduce a notion of correlated equilibrium that allows partial delegation to a mediator and ambiguity in the correlation device. Without ambiguity, the sets of equilibrium action distributions are equivalent to those for coarse correlated equilibrium (Moulin and Vial, 1978). With correlation devices that incorporate ambiguity, any action distribution that Pareto dominates a coarse correlated equilibrium or a correlated equilibrium (Aumann, 1974), can be approximated with an arbitrary degree of precision using the proposed equilibrium notion. These approximations are attained in one-shot, static strategic interactions, and do not require repeated play. We also analyze such equilibria when the set of feasible posteriors is exogenously constrained, which yields, as a special case, a definition and characterization of an "ambiguous correlated equilibrium" that does not require delegation to the mediator. [ABSTRACT FROM AUTHOR]

Outsourcing of research is commonly observed in knowledge-intensive industries such as biotech. We model innovation as an ambiguous stochastic process with dynamically consistent updating. We assume that the research labs are less ambiguity averse than the commercial firms. We characterize the optimal sequence of short-term contracts governing innovation, and show how it facilitates ambiguity-sharing. This ambiguity sharing agreement mitigates the dynamic moral hazard problem, resulting in monotonically decreasing investment and preventing equilibrium delay. Compared to an ambiguity-neutral policymaker's benchmark, the research alliances stop experimenting too early, and may liquidate the project even after being patented. The problems are structural, redesigned patent laws cannot solve both of these problems. [ABSTRACT FROM AUTHOR]

This paper studies a multi-state binary choice experiment in which in each state, one alternative has well understood consequences whereas the other alternative has unknown consequences. Subjects repeatedly receive feedback from past choices about the consequences of unfamiliar alternatives but this feedback is aggregated over states. Varying the payoffs attached to the various alternatives in various states allows us to test whether unfamiliar alternatives are discounted and whether subjects' use of feedback is better explained by similarity-based reinforcement learning models (in the spirit of the valuation equilibrium, Jehiel and Samet, 2007) or by some variant of Bayesian learning model. Our experimental data suggest that there is no discount attached to the unfamiliar alternatives and that similarity-based reinforcement learning models have a better explanatory power than their Bayesian counterparts. [ABSTRACT FROM AUTHOR]

We propose a new solution concept, called Context-Dependent Equilibrium Under Ambiguity (CD-EUA), for strategic games where players' beliefs may be influenced by exogenous context-related information. Players' beliefs about the strategic behavior of their opponents are represented by belief functions. The notion of belief functions allows us to combine exogenous context information in the spirit of Schelling (1960) with endogenous equilibrium beliefs about the opponents' behavior in analogy to the standard Nash equilibrium. For any finite strategic game, we prove existence of a CD-EUA for any context information and any degree of confidence in it. Moreover, we show continuity of the equilibrium correspondence. Finally, we illustrate how CD-EUA can be applied to different types of context information in games by explaining some stylized facts from experimental research on coordination. [ABSTRACT FROM AUTHOR]

Neoclassical economic theory assumes that whenever agents tackle dynamic decisions under ambiguity, preferences are represented by the Subjective Expected Utility (SEU) model and prior beliefs are updated according to Bayes rule, upon the arrival of partial information. Nevertheless, when one considers non-neutral ambiguity attitudes, either the axiom of dynamic consistency or of consequentialism should be relaxed. Using data from an economic experiment on dynamic choice under ambiguity, we study which of the two rationality axioms people violate, along with the question of whether this violation is part of a conscious planning strategy or not. The combination of the two, allows us to classify non-SEU subjects to three behavioural types: resolute, naïve and sophisticated. The hypothesis of Bayesian updating is rejected for more than half of the experimental population. For ambiguity non-neutral subjects, we find that the majority are sophisticated, a few are naïve and very few are resolute. [ABSTRACT FROM AUTHOR]

This paper studies minimax regret traders in a sealed bid double auction. Unlike the expected utility maximizers that populate typical market models, these traders do not determine their actions using a single prior. The analysis proves that, with no restrictions on beliefs about others' types and strategies, minimax regret traders will not converge to price-taking as the size of the market increases, contrary to standard economic intuition. In fact, minimax regret traders' bids and asks are invariant to the number of traders in the market. Thus, the robustness of the sealed bid double auction is sensitive to traders' preferences. [ABSTRACT FROM AUTHOR]

This paper examines the difference between strategic ambiguity as in game theory and ambiguity arising in individual decisions. We identify a new, non-strategic component underlying all strategic ambiguities, called social ambiguity. We recommend controlling for it to better identify strategic causes. Thus, we shed new light on Bohnet and Zeckhauser's betrayal aversion in the trust game. We first show theoretically that, contrary to preceding claims in the literature, ambiguity attitudes can play a role here. We then show experimentally that social ambiguity, rather than betrayal aversion, can explain our empirical findings. Using our new control, we identify the unique effect of strategic ambiguity. Strategic complexity increases ambiguity perception and thus increases people's likelihood insensitivity when making decisions under strategic ambiguity. Our results show the usefulness of controlling for ambiguity attitudes before speculating on strategic factors. [ABSTRACT FROM AUTHOR]

The famous conflict between dynamic consistency and ambiguity purportedly undermines these models' normative credibility, and challenges their use in economic applications. Dynamic consistency concerns preferences over contingent plans: so what counts are the contingencies the decision maker envisages – and plans for – rather than independently fixed contingencies, as implicitly assumed in standard formalisations. An appropriate formulation of dynamic consistency resolves the aforementioned conflict, hence undermining the criticisms of ambiguity models based on it. Moreover, it provides a principled justification for the restriction to certain families of beliefs in applications of these models in dynamic choice problems. Finally, it supports a new analysis of the value of information under ambiguity, showing that decision makers may only turn down information if it has an opportunity cost, in terms of the compromising of information they had otherwise expected to receive. [ABSTRACT FROM AUTHOR]

Economic predictions often hinge on two intuitive premises: agents rule out the possibility of others choosing unreasonable strategies ('strategic reasoning'), and prefer strategies that hedge against unexpected behavior ('cautiousness'). These two premises conflict and this undermines the compatibility of usual economic predictions with reasoning-based foundations. This paper proposes a new take on this classical tension by interpreting cautiousness as robustness to ambiguity. We formalize this via a model of incomplete preferences, where (i) each player's strategic uncertainty is represented by a possibly non-singleton set of beliefs and (i i) a rational player chooses a strategy that is a best-reply to every belief in this set. We show that the interplay between these two features precludes the conflict between strategic reasoning and cautiousness and therefore solves the inclusion-exclusion problem raised by Samuelson (1992). Notably, our approach provides a simple foundation for the iterated elimination of weakly dominated strategies. [ABSTRACT FROM AUTHOR]

Proper scoring rules incentivize truthful probability reports from risk-neutral individuals. For individuals with much more general preferences (including risk and ambiguity aversion) we use duality techniques to characterize the optimal report in any proper scoring rule. We apply this characterization to several well-known families of preferences, and provide several applications. In particular, for the case of CARA and CRRA preferences we (1) can back out true beliefs from optimal reports, (2) show that the quadratic scoring rule minimizes deviations from truthfulness, and (3) provide a two-step procedure in which the agent reports her risk aversion parameter and her belief truthfully. [ABSTRACT FROM AUTHOR]

We ran experiments that gave subjects a straight-forward and simple opportunity to hedge away ambiguity in an Ellsberg-style experiment. Subjects had to make bets on the combined outcomes of a fair coin and a draw from an ambiguous urn. By modifying the timing of the draw, coin flip, and decision, we are able to test the reversal-of-order axiom. Our main result is that the reversal-of-order axiom seems to hold. We also confirm low levels of ambiguity hedging despite the relative obviousness of the opportunity. [ABSTRACT FROM AUTHOR]

We study whether the basic tenets of the theory of zero-sum games are still valid when players are uncertainty averse. We focus on games with one-sided information, in which the uninformed player is uncertain about the state of nature. Uncertainty aversion turns the underlying zero-sum game into a many-player, non-zero-sum game. We show that the uninformed player has a unique equilibrium payoff. We provide conditions under which there is a unique equilibrium payoff vector. [ABSTRACT FROM AUTHOR]

The term "belief function" is generally used to refer to a class of capacities that can be viewed as representing ambiguity averse preferences. This paper introduces a definition of equilibrium for normal-form games with ambiguous beliefs, where belief functions are used to describe strategic uncertainty. To capture independence of strategies and beliefs, a novel notion of a "strategic product integral" is introduced for belief functions, based on their Möbius transforms, and shown to be different from the Choquet integral of an appropriate product capacity. A characterization of the integral in terms of maxmin expected utility expressed relative to elements of the cores of the respective belief functions, is also presented. The resulting equilibrium notion relies on Möbius transforms to embed objectively chosen probabilistic mixed strategies into ambiguous beliefs of opponents about these strategies, while incorporating stronger consistency requirements than those imposed by previous definitions of equilibria under ambiguity. [ABSTRACT FROM AUTHOR]

We consider a game in extensive form recurrently played by agents who are randomly drawn from large populations and matched. We assume that preferences over actions at any information set admit a smooth-ambiguity representation in the sense of Klibanoff et al. (2005) , which may induce dynamic inconsistencies. We take this into account in our analysis of self-confirming equilibrium (SCE) given players' feedback about the path of play. Battigalli et al. (2015) show that the set of SCE's of a simultaneous-move game with feedback expands as ambiguity aversion increases. We show by example that SCE in a sequential game is not equivalent to SCE applied to the strategic form of such game, and that the previous monotonicity result does not extend to general sequential games. Still, we provide sufficient conditions under which the monotonicity result holds for SCE. [ABSTRACT FROM AUTHOR]

Abstract I study how risk preferences and the level of ambiguity influence ambiguity attitudes in Uzi Segal's recursive second-order non-expected utility model. It is shown that the negative certainty independence axiom for risk preferences is equivalent to a global form of ambiguity aversion that entails ambiguity averse behavior irrespective of the state space and the decision maker's second-order belief. Thus, the second-order version of the cautious expected utility model is the only subclass of Segal's theory that robustly predicts ambiguity aversion. Moreover, a mean-preserving spread operation over second-order beliefs, which corresponds to a particular way of increasing the level of ambiguity, is equivalent to increasing the relative strength of ambiguity aversion for each possible specification of risk preferences within the cautious expected utility model. An application of the latter result establishes a negative relation between participation rates in an asset market and the level of ambiguity concerning the distribution of returns. [ABSTRACT FROM AUTHOR]

Abstract I consider static, incomplete information games where players may not be ambiguity neutral. Every player is one of a finite set of types, and each knows her own type but not that of the other players. Ex ante, players differ only in their taste for outcomes. If every player is dynamically consistent with respect to her own information structure and respects Consequentialism, then players act as if expected utility for uncertainty about types. [ABSTRACT FROM AUTHOR]

We introduce linguistic ambiguity into a principal–agent contracting framework. Contracts are drafted in a common language. Nevertheless, the principal and the agent may ultimately disagree about the terms of the contract that apply ex post . We presume that both parties are ambiguity averse and for tractability reasons that their preferences take a recursive constant absolute risk averse (RCARA) form. We consider various dispute resolution regimes and analyze how the optimal dispute resolution regime depends on the ambiguity attitudes of the parties. We also provide an axiomatization of the class of RCARA preferences. [ABSTRACT FROM AUTHOR]

I study the implications of Wald's (1947) complete class theorem for decision making under Knightian uncertainty (or ambiguity). Suppose we call someone who uses Wald's approach to statistical decision making a Waldian. A Waldian may then have preferences over acts that are not in agreement with subjective expected utility but always chooses as if she was a subjective expected utility maximizer. In particular, even Wald's (1945) minmax decision rule is consistent with subjective expected utility. [ABSTRACT FROM AUTHOR]

We study cheap talk communication in a simple two actions-two states model featuring an ambiguous state distribution. Equilibrium behavior of both sender (S) and receiver (R) features mixing and we relate each agent's randomization to a specific mode of ambiguous communication. For sufficiently high ambiguity, implementing the S-optimal decision rule with only two messages is impossible if R has aligned preferences. This may in contrast be possible if R has misaligned preferences. Adding a little ambiguity may generate influential communication that is unambiguously advantageous to S. [ABSTRACT FROM AUTHOR]

Based on a model where deviations from equilibrium play are assumed to identify irrational players who are characterized by ambiguous set-valued strategies, this paper introduces an equilibrium notion for extensive games with ambiguity averse players that yields a precise interpretation for the counterfactual reasoning usually associated with backward induction. The resulting equilibria are always Nash equilibria, but may not satisfy the conditions required for various refinements of Nash equilibrium, including those for subgame perfection. Existence of such equilibria is proved for all two-player games, and for N -player games with perfect information. [ABSTRACT FROM AUTHOR]

Standard economic models cannot capture the fact that information is often ambiguous , and is interpreted in multiple ways. Using a framework that distinguishes between the language in which statements are made and the interpretation of statements, we demonstrate that, unlike in the case where there is no ambiguity, players may come to have different beliefs starting from a common prior, even if they have received exactly the same information, unless the information is common knowledge. [ABSTRACT FROM AUTHOR]

Abstract: We consider the optimality of liquidated damages contracts in a setting of contractual ambiguity and potential for disputes. We show that when parties are ambiguity averse enough, they will optimally choose liquidated damages contracts and sacrifice risk sharing opportunities. [Copyright &y& Elsevier]

Abstract: Many real-life decisions have to be taken on the basis of probability judgements of which the decision maker is not entirely sure. This paper develops a decision rule for taking such decisions, which incorporates the decision makerʼs confidence in his probability judgements according to the following maxim: the larger the stakes involved in a decision, the more confidence is required in a probability judgement for it to play a role in the decision. A formal representation of the decision makerʼs confidence is proposed and used to formulate a family of decision models conforming to this maxim. A natural member of this family is studied in detail. It is structurally simpler than other recent models of decision under uncertainty, which may make it easier to apply to practical decisions, whilst being axiomatically sound, permitting the separation of beliefs and tastes, and allowing comparative statics analysis of attitudes to choosing in the absence of confidence. [Copyright &y& Elsevier]

Abstract: We model a common pool resource game under environmental uncertainty, where individuals in a symmetric group face the dilemma of sharing a common resource. Each player chooses a consumption level and obtains a corresponding share of that resource, but if total consumption exceeds a sustainable level then the resource deteriorates and all players are worse-off. We consider the effect of uncertainty about the sustainable resource size on the outcome of this game. Assuming a general dynamic for resource deterioration, we study the effect of increased ambiguity (i.e., uncertain probabilities pertaining to the common resourceʼs sustainable size). We show that whereas increased risk may lead to more selfish behavior (i.e., to more consumption), increased ambiguity may have the opposite effect. [Copyright &y& Elsevier]

Highlights: [•] Insurance fraud model with ambiguity-averse policyholders. [•] Insurers can choose between commitment and ambiguity about audits. [•] Insurers avoid commitment and strategically choose ambiguity to fight fraud. [•] Ambiguity about audits deters fraud and yields an ex-ante Pareto improvement. [Copyright &y& Elsevier]

Abstract: Many theories of updating under ambiguity assume either dynamic consistency or consequentialism to underpin behaviorally the link between conditional and unconditional preferences. To test the descriptive validity of these rationality concepts, we conduct a dynamic extension of Ellsbergʼs 3-color experiment. We find that more subjects act in line with consequentialism than with dynamic consistency and that this result is even stronger among ambiguity averse subjects. [Copyright &y& Elsevier]

Abstract: This paper presents a general technique for comparing the concavity of different utility functions when probabilities need not be known. It generalizes: (a) Yaariʼs comparisons of risk aversion by not requiring identical beliefs; (b) Kreps and Porteusʼ information-timing preference by not requiring known probabilities; (c) Klibanoff, Marinacci, and Mukerjiʼs smooth ambiguity aversion by not using subjective probabilities (which are not directly observable) and by not committing to (violations of) dynamic decision principles; (d) comparative smooth ambiguity aversion by not requiring identical second-order subjective probabilities. Our technique completely isolates the empirical meaning of utility. It thus sheds new light on the descriptive appropriateness of utility to model risk and ambiguity attitudes. [Copyright &y& Elsevier]

Abstract: A game-theoretic framework that allows for explicitly randomized strategies is used to study the effect of ambiguity aversion on equilibrium outcomes. The notions of “independent strategies” as well as of “common priors” are amended to render them applicable to games in which players lack probabilistic sophistication. Within this framework the equilibrium predictions of two-player games with ambiguity-averse and with ambiguity-neutral players are observationally equivalent. This equivalence result does not extend to the case of games with more than two players. A translation of the concept of equilibrium in beliefs to the context of ambiguity aversion yields substantially different predictions – even for the case with just two players. [Copyright &y& Elsevier]

Abstract: Based on an experiment in the lab, we classify behavior in one-shot normal-form games along three important dimensions. The first dimension, which is of main interest, is about whether subjects are ambiguity-loving, ambiguity-neutral, or ambiguity-averse. The second dimension is about whether subjects are risk-loving, risk-neutral, or risk-averse. The third dimension is about whether subjects are naive or strategic. Our main result is that, in our main treatment, percent of subjects are classified as ambiguity-loving/ambiguity-neutral/ambiguity-averse. [Copyright &y& Elsevier]

Abstract: We demonstrate that people can adopt a favorable view of ambiguous risks relative to ones with known probabilities, contrary to the usual attitude of ambiguity aversion, when doing so permits justification for unfair behavior. We use binary dictator games involving a choice between a relatively equitable allocation and an “unfair” allocation that is both less generous and makes the recipient''s payment dependent on a lottery. Dictators choose the unfair option more frequently when the recipient''s allocation depends on an ambiguous lottery than on a lottery with a known probability — even though the objective distributions of outcomes are identical under the two kinds of lotteries. Dictators'' estimates of the expected value of the recipients'' allocations are inflated under ambiguity, indicating that dictators form self-serving beliefs about ambiguity. Finally, increased unfair behavior under ambiguity is extinguished when dictators are constrained by their own initial unmotivated, and negative, attitudes towards ambiguity. [Copyright &y& Elsevier]

Abstract: Several papers, adopting an axiomatic approach to study decision making under ambiguity aversion, have produced conflicting predictions about how decision makers would behave in simple dynamic urn problems. We explore the concepts of ambiguity aversion and dynamic consistency, with examples of dynamic games against nature. Basically, a malevolent nature puts balls into the urn, and a fair nature draws them out. Depending on the game, various choices that seem inconsistent with static notions of ambiguity aversion or dynamic consistency are consistent with subgame perfection. In the dynamic 3-color Ellsberg urn problem with 30 red balls and 60 blue or green balls, the decision maker could strictly prefer to bet on blue–green at time 0, and to switch to red–green after learning that the ball is not green. [Copyright &y& Elsevier]

Abstract: The robustness of the Bayes–Nash equilibrium prediction for seller revenue in auctions is investigated. In a framework of interdependent valuations generated from independent signals, seller expected revenue may fall well below the equilibrium prediction, even though the individual payoff consequences of suboptimal bidding may be small for each individual bidder. This possibility would be relevant to a seller who models strategic uncertainty as ambiguity, and who is ambiguity-averse in the sense of Gilboa and Schmeidler. It is shown that the second-price auction is more exposed than the first-price auction to lost revenue from the introduction of bidder behavior with small payoff errors. [Copyright &y& Elsevier]

Abstract: We study the behavior of subjects facing choices between certain, risky, and ambiguous lotteries. Subjects'' choices are consistent with the economic theories modeling ambiguity aversion. Our results support the conjecture that subjects face choice tasks as an estimation of the value of the lotteries, and that the difficulty of the choice is an important explanatory variable (in addition to risk and ambiguity aversion). The brain imaging data suggest that such estimation is of an approximate nature when the choices involve ambiguous and risky lotteries, as the regions in the brain that are activated are typically located in parietal lobes. Thus such choices require mental faculties that are shared by all mammals, and in particular are independent of language. In contrast, choices involving partial ambiguous lotteries additionally produce an activation of the frontal region, which indicates a different, more sophisticated cognitive process. [Copyright &y& Elsevier]