Success on many tasks depends on a trade-off between speed and accuracy. In a novel variant, a speed-accuracy trade-off with sample-based decisions in which both speed and accuracy jointly depend on (self-truncated) sample size, we found strong accuracy biases. On every trial of a sequential investment game, participants chose between 2 investment funds based on binary samples of the funds' past outcomes. Participants could stop sampling and decide whenever they felt sufficiently informed. Total payoff was the product of choice accuracy and number of choices completed within the available time (speed). Participants' failure to understand the dominance of speed over accuracy-that speed decreases more than accuracy improves with increasing sample size-led to dramatic oversampling. Our research aimed to examine to what extent metacognitive functions of monitoring and control could correct for the accuracy bias. Experiments 1a through 1c demonstrated similarly strong accuracy biases and payoff losses in psychology and economics students, depressed, and control patients. In Experiments 2 through 4, the accuracy bias persisted despite several manipulations (feedback, sample limit, choice difficulty, payoff, sampling truncation as default) that underlined the speed advantage, reflecting a conspicuous metacognitive deficit. Even when participants faced no risk of losing on incorrect trials but could still win on correct trials (Experiment 3) and when sampling was contingent on the active solicitation of every new element (Experiment 4), participants continued to sample too much and failed to overcome the accuracy bias. The final discussion focuses on psychological reasons and possible remedies for the metacognitive deficit in trade-off regulation. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

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.

Accounting for ambiguity aversion in dynamic decisions generally implies that either dynamic consistency or consequentialism must be given up. To gain insight into which of these principles better describes people’s preferences, we tested them using a variation of Ellsberg’s three-color urn experiment. Subjects were asked to make a choice both before and after they received a signal. We found that most ambiguity neutral subjects satisfied both dynamic consistency and consequentialism and behaved consistent with subjective expected utility with Bayesian updating. The majority of ambiguity averse subjects satisfied consequentialism, but violated dynamic consistency.

In this paper, we study choice under uncertainty with belief functions. Belief functions can capture partial information by describing what is objectively known about the probabilities of events. State-contingent acts together with a belief function over states induce belief functions over outcomes. We assume that decision makers have preferences over belief functions that reflect both their valuation of outcomes and the information available about the likelihood of outcomes. We provide axioms characterizing a preference representation for belief functions that captures what is (objectively) known about the likelihood of outcomes and combines it with subjective beliefs according to the “principle of insufficient reason” whenever the likelihood of events is unknown. This treatment of partial information yields a natural distinction between ambiguity and ambiguity attitudes. The approach is novel in its treatment of partial information and in its axiomatization of the uniform distribution in case of ignorance.

We propose a solution concept, consistent-planning equilibrium under ambiguity (CP-EUA), for two-player multi-stage games with almost perfect information. Players are neo-expected payo¤ maximizers. The associated (ambiguous) beliefs are revised by Generalized Bayesian Updating. Individuals take account of possible changes in their preferences by using consistent planning. We show that if there is ambiguity in the centipede game and players are su¢ ciently optimistic then it is possible to sustain ‘cooperation’for many periods. Similarly, in a non-cooperative bargaining game we show that there may be delay in agreement being reached. Keywords: optimism, neo-additive capacity, extensive-form games, dynamic consistency, consistent planning, centipede game. JEL classi…cation: D81 For comments and suggestions we would like to thank Pierpaolo Battigalli, Lorenz Hartmann, Philippe Jehiel, David Levine, George Mailath, Larry Samuelson, Marciano Siniscalchi, Rabee Tourky, Qizhi Wang, an anonymous referee as well participants in presentations at Adelaide, ANU, Bristol, Exeter, FUR (Warwick 2016), DTEA (Paris 2017), SAET (Faro 2017), RUD (Heidelberg 2018), and Dynamic Models in Economics Workshop on Game Theory (NUS, Singapore 2018).

Dans les années 1990, David Schmeidler et Itzhak Gilboa ont introduit un nouveau cadre d’analyse des décisions sous incertitude : les bases des données se substituent aux états du monde comme concept primitif du modèle et informent le choix du décideur. Au début, la théorie de la décision au cas par cas était orientée principalement vers des applications économiques, mais ses méthodes se sont avérées également pertinentes pour l’analyse des croyances et des prédictions statistiques. Cela a ouvert de nouvelles perspectives sur des questions classiques en statistique et en intelligence artificielle. Dans cet article, nous passons en revue ces développements et mettons en avant le caractère extrêmement novateur des travaux académiques de David Schmeidler.

We study how ambiguity and ambiguity attitudes affect asset prices when consumers form their expectations based on past observations. In an overlapping generations economy with risk‐neutral yet ambiguity‐sensitive consumers, we describe limiting asset prices depending on the proportion of investor types. We then study the evolution of consumer‐type shares. With long memory, the market does not select for ambiguity neutrality. Whenever perceived ambiguity is sufficiently small, but positive, only pessimists survive and determine prices in the limit. With one‐period memory, equilibrium prices are determined by Bayesians. Yet, the average price of the risky asset is lower than its fundamental value.

In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested by Savage (1954). We will use the Ellsberg (1961) paradox to illustrate the potential of our approach to deal with well-known paradoxes of decision theory.

In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested by Savage. We will use the Ellsberg-paradox to illustrate the potential of our approach to deal with well-known paradoxa of decision theory.

In this paper, we develop an interactive epistemology perspective justifying strategic ambiguity and various equilibrium concepts for games with non-additive beliefs. To accommodate strategic ambiguity in games, we introduce an extended version of interactive belief systems in which some types might not know the action they play. Yet, each type knows his theory, i.e., his probability distribution over the entire state space. It is shown that player’s beliefs about his opponents’ behavior are non-additive if he considers possible that his opponents are undetermined (i.e., his theory assigns a positive probability to opponents’ types who do not know what actions they play). In this framework, we establish epistemic conditions under which beliefs constitute an equilibrium under ambiguity for games with two and more than two players, respectively. Our epistemic conditions for Nash-Equilibrium appear as a special case and thus generalize the celebrated results of Aumann and Brandenburger (1995). JEL Classification: D80, D81, D83.

We propose a solution concept for a class of extensive form games with ambiguity. Specifically we consider multi-stage games. Players have CEU preferences. The associated ambiguous beliefs are revised by Generalized Bayesian Updating. We assume individuals take account of possible changes in their preferences by using consistent planning. We show that if there is ambiguity in the centipede game it is possible to sustain 'cooperation' for many periods as part of a consistent-planning equilibrium under ambiguity. In a non-cooperative bargaining game we show that ambiguity may be a cause of delay in bargaining.

In Lowest-Unmatched Price Auctions (LUPA) all participants pay a bidding fee and the lowest bid placed by only one participant wins. Many LUPAs do not specify what happens with the item on offer if there is no unmatched bid. The item may remain with the auctioneer which may appear unfair given that the auctioneer collects the bidding fees. We show that in a symmetric Nash equilibrium of a LUPA with known prize both players and the auctioneer will have an expected profit of zero. Moreover, LUPAs may be seen as a value-revealing mechanism. (C) 2016 Elsevier B.V. All rights reserved.

We study Equilibria under Ambiguity (EUA) with optimism and pessimism as introduced in Eichberger and Kelsey (2014) for the case of beliefs modelled by belief functions. We show existence of equilibria for …nite games with an arbitrary number of players and both general and speci…c ambiguity about the opponents’strategy choice. We illustrate by examples the potential of this approach to model behavior which cannot be obtained as a Nash equilibrium..

In this note we compare several support notions for capacities and sets of multiple priors. We characterize these support notions in the context of belief functions and show how they affect the analysis of games when players face strategic ambiguity.

As illustrated by the famous Ellsberg paradox, many subjects prefer to bet on events with known rather than with unknown probabilities, i.e., they are ambiguity averse. In an experiment, we examine subjects’ choices when there is an additional source of ambiguity, namely, when they do not know how much money they can win. Using a standard assumption on the joint set of priors, we show that ambiguity-averse subjects should continue to strictly prefer the urn with known probabilities. In contrast, our results show that many subjects no longer exhibit such a strict preference.

Lowest-Unmatched Price Auctions (LUPAs) specify that the lowest bid placed by only one participant wins. They are used in internet trading and TV and radio shows. We model LUPAs as games with minimal restrictions, in particular allowing players to place more than one bid, since multiple bids have been observed in most actual LUPAs. Though LUPAs are games for which a closed-form solution does not seem to exist in general, our model generates several testable implications about the type of strategies played in equilibrium and the highest bid in a given LUPA. Our analysis suggests that players follow strategic considerations and arrive at decisions which, at least in the aggregate, are generally consistent with theoretical predictions, yet there are some remarkable deviations.

This article considers the impact of ambiguity in strategic situations. It extends the existing literature on games with ambiguity‐averse players by allowing for optimistic responses to ambiguity. We use the CEU model of ambiguity with a class of capacities introduced by Jaffrray and Philippe (Mathematics of Operations Research 22 (1997), 165–85), which allows us to distinguish ambiguity from ambiguity‐attitude, and propose a new solution concept, equilibrium under ambiguity (EUA), for players who may be characterized by ambiguity‐preference. Applying EUA, we study comparative statics of changes in ambiguity‐attitude in games with strategic complements. This extends work in Eichberger and Kelsey (Journal of Economic Theory 106 (2002), 436–66) on the effects of increasing ambiguity if players are ambiguity averse.

Raiffa (Q J Econ 75:690–694, 1961) has suggested that ambiguity aversion will cause a strict preference for randomization. We show that dynamic consistency implies that individuals will be indifferent to ex ante randomizations. On the other hand, it is possible for a dynamically consistent ambiguity averse preference relation to exhibit a strict preference for some ex post randomizations. We argue that our analysis throws some light on the recent debate on the status of the smooth model of ambiguity This debate rests on whether the randomizations implicit in the set-up are viewed as being resolved before or after the (ambiguous) uncertainty.