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In this paper, we give an example of a statement concerning two-player zero-sum games which is undecidable, meaning that it can neither be proven or disproven by the standard axioms of mathematics. Earlier work has shown that there exist "paradoxical" two-player zero-sum games with unbounded payoffs, in which a standard calculation of the two players' expected utilities of a mixed strategy profile yield a positive sum. We show that whether or not a modified version of this paradoxical situation, with bounded payoffs and a weaker measurability requirement, exists is an unanswerable question. Our proof relies on a mixture of techniques from set theory and ergodic theory. [ABSTRACT FROM AUTHOR]

We test the touchstones of economic rationality—utility maximization, stochastic dominance, and expected-utility maximization—of elite students in the U.S. and in Africa. The choices of most students in both samples are generally rationalizable, but the U.S. students' scores are substantially higher. Nevertheless, the development gap in economic rationality in incentivized risk choices between these future elites is much smaller than the difference in performance on a non-incentivized canonical cognitive ability test, often used as a proxy for economic decision-making ability in studies of economic development and growth. We argue for the importance of including consistency with economic rationality in studies of decision-making ability. [ABSTRACT FROM AUTHOR]

Quantiles are used for decision making in investment analysis and in the mining, oil and gas industries. However, it is unknown how common quantile-based decision making actually is among typical individual decision makers. This paper describes an experiment that aims to (1) compare how common is decision making based on quantiles relative to expected utility maximization, and (2) estimate risk attitude parameters under the assumption of quantile preferences. The experiment has two parts. In the first part, individuals make pairwise choices between risky lotteries, and the competing models are fitted to the choice data. In the second part, we directly elicit a decision rule from a menu of alternatives. The results show that a quantile preference model outperforms expected utility for 32%–55%, of participants, depending on the metric. The majority of individuals are risk averse, and women are more risk averse than men, under both models. [ABSTRACT FROM AUTHOR]

This paper studies games when agents have second-order expected utility. It examines the theoretical predictions of the model and compares its performance in explaining behavior in experimental data on games with that of quantal response equilibrium. [ABSTRACT FROM AUTHOR]

The signals used in persuasion mechanisms in practice typically satisfy two well-studied simple properties: (i) they partition an ordered state space into intervals, and (ii) they do not recommend lower actions at higher states. These properties have been studied—often separately—in the Bayesian persuasion literature, where conditions for the optimality of such signals are provided in various settings. The two properties can be defined only when the action and the state space are ordered. Under the proper ordering conditions, we show that the optimal signal features both of these properties, as well as robustness properties, when Receiver is a pessimist. A pessimistic receiver, rather than maximizing expected payoff, takes the action that guarantees the highest level of payoff. Through the notion of maxmin expected utility , our findings explain that simplicity and robustness of optimal signals can emerge from the ambiguity of the prior to Receiver. [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]

Most literature on optimal auctions focuses on optimizing for a risk-neutral seller. We consider risk-averse sellers in a setting of multi-unit auctions with unit-demand bidders. We seek utility-oblivious mechanisms that do not know about the seller's utility function, while still achieving constant factor approximations to the expected utility of the optimal mechanism tailored to the utility function. Our main results are natural hedging-based mechanisms that give such utility-oblivious approximations. Along the way we show that the optimal auction theory of Myerson (1981) extends to risk-averse sellers in the single-unit case, but not in the multi-unit case. [ABSTRACT FROM AUTHOR]

We characterize lexicographic conditional probability systems (LCPSs). Our aim is to address an issue left open in an important contribution by Blume et al. (1991a). They provide a characterization of LCPSs, but one of their axioms quite explicitly imposes disjointness of the supports in an LCPS. The main new axiom is robustness, which is a weak continuity requirement on preferences. It requires preferences between acts x and y to be robust to (unchanged by) small perturbations in payoffs x ω and y ω for some state ω where x and y are different. LCPSs are characterized as the subclass of lexicographic probability systems satisfying robustness. As a corollary we provide an axiomatization of LCPSs in terms of standard properties satisfied by subjective expected utility preferences (as in Anscombe and Aumann (1963)) and robustness. [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]

Abstract In making decisions under risk (i.e., choosing whether to gamble when the outcome probabilities are known), two aspects of decision are of particular concern. The first, if gambling, is how large are potential gains compared to losses? The subjectively larger, the more rewarding to gamble. Thus, this aspect of decision-making, quantified through expected utility (EU), is motivation-related. The second concern is how easy is it to reach the decision? When subjective desirability between gambling and not-gambling is clearly different from each other (regardless of the direction), it is easier to decide. This aspect, quantified through utility distance (UD), is conflict-related. It is unclear how the brain simultaneously processes these two aspects of decision-making. Forty-five participants decided whether to gamble during electroencephalogram (EEG) recording. To compute trial-by-trial variability in EU and UD, we fit participants' choices to models inspired by Expected-Utility and Prospect theories using hierarchical-Bayesian modeling. To examine unique influences of EU and UD, we conducted model-based single-trial EEG analyses with EU and UD as simultaneous regressors. While both EU and UD were positively associated with P3-like activity and delta-band power, the contribution of EU was around 200 ms earlier. Thus, during decision-making under risk, people may allocate their attention to motivation-related aspects before conflict-related aspects. Next, following learning the options and before reporting their decision, higher EU was associated with stronger alpha and beta suppression, while higher UD was associated with a stronger contingent-negativity-variation-like activity. This suggests distinct roles of EU and UD on anticipation-related processes. Overall, we identified time and frequency characteristics of EEG signals that differentially traced motivation-related and conflict-related information during decision-making under risk. Highlights • Model-based EEG teased apart unique influences of motivation & conflict processes. • During risky decisions, both were associated with P3-like and delta-band activity. • The P3-like/delta activity of motivation processes was around 200 ms earlier. • Motivation processes involved stronger alpha and beta suppression. • Conflict processes involved stronger CNV-like activity. [ABSTRACT FROM AUTHOR]

Abstract Optimistic beliefs affect important areas of economic decision making, yet direct knowledge on how belief biases operate remains limited. To better understand these biases I introduce a theoretical framework that trades off anticipatory benefits against two potential costs of forming biased beliefs: (1) material costs which result from poor decisions, of Brunnermeier and Parker (2005) , and (2) direct psychological costs of distorting reality, of Bracha and Brown (2012). The experiment exploits the potential of the BDM elicitation procedure adopted to lotteries to distort beliefs in different directions, depending on which costs are most important. Relative to an elicitation procedure without distortionary incentives, beliefs are biased in the optimistic direction. Increasing payments for accuracy further increases belief reports, in many cases away from the truth, consistent with psychological costs of belief distortion. Yet the overall results suggest that such theories of optimism fail to explain how beliefs respond to financial incentives. [ABSTRACT FROM AUTHOR]

We consider an infinite dimensional optimization problem motivated by mathematical economics. Within the celebrated “Arbitrage Pricing Model”, we use probabilistic and functional analytic techniques to show the existence of optimal strategies for investors who maximize their expected utility. [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]

In the Approval Bargaining game, two players bargain over a finite set of alternatives. To this end, each one simultaneously submits a utility function u jointly with a real number α ; by doing so she approves the lotteries whose expected utility according to u is at least α . The lottery to be implemented is randomly selected among the most approved ones. We first prove that there is an equilibrium where players truthfully reveal their utility function. We also show that, in any equilibrium, the equilibrium outcome is approved by both players. Finally, every equilibrium is sincere and Pareto efficient as long as both players are partially honest. [ABSTRACT FROM AUTHOR]

By extending the equilibrium concepts of Kőszegi and Rabin (2006, 2007) , this paper analyzes the strategic interaction of expectation-based loss-averse players. For loss-averse players with choice-acclimating expectations, the utility from playing a mixed strategy is not linear but convex in the probabilities they assign to their pure strategies. As a consequence, they are generally unwilling to randomize and an equilibrium may fail to exist. For players with choice-unacclimating expectations, by contrast, randomizing over their pure strategies may indeed constitute a credible best response and an equilibrium always exists. Building upon these insights, we delineate how expectation-based loss-averse players differ in their strategic behavior from their counterparts with standard expected-utility preferences, derive novel strategic effects, discuss equilibrium selection, and derive equilibrium play for some simple games. [ABSTRACT FROM AUTHOR]

This paper examines climate-change benefit-cost analysis in the presence of scientific uncertainty in the form of ambiguity. The specific issue addressed is the robustness of benefit-cost analyses of climate-change policy alternatives to relaxation of Savage's original axioms. Two alternatives to subjective expected utility (SEU) are considered: maximin expected utility (MEU) and incomplete expected utility (IEU). Among other results, it is demonstrated that polar opposite recommendations can emerge in an ambiguous decision setting even if all agree on Society's rate of time preference, Society's risk attitudes, the degree of ambiguity faced, and the scientific primitives. We show that, for a simple numerical simulation of our model, an MEU decision maker favors policies which immediately tackle climate change while an IEU decision prefers “business as usual”.“Each agency shall assess the costs and benefits of the intended regulation, and recognizing that some costs and benefits are difficult to quantify, propose or adopt a regulation only upon a reasoned determination that the benefits of the intended regulation justify its cost.” Executive Order 12866 of the US President. [ABSTRACT FROM AUTHOR]

Optimal sensor placement is essentially a decision problem under uncertainty. The maximum expected utility theory and a Bayesian linear model are used in this paper for robust sensor placement aimed at operational modal identification. To avoid nonlinear relations between modal parameters and measured responses, we choose to optimize the sensor locations relative to identifying modal responses. Since the modal responses contain all the information necessary to identify the modal parameters, the optimal sensor locations for modal response estimation provide at least a suboptimal solution for identification of modal parameters. First, a probabilistic model for sensor placement considering model uncertainty, load uncertainty and measurement error is proposed. The maximum expected utility theory is then applied with this model by considering utility functions based on three principles: quadratic loss, Shannon information, and K–L divergence. In addition, the prior covariance of modal responses under band-limited white-noise excitation is derived and the nearest Kronecker product approximation is employed to accelerate evaluation of the utility function. As demonstration and validation examples, sensor placements in a 16-degrees-of-freedom shear-type building and in Guangzhou TV Tower under ground motion and wind load are considered. Placements of individual displacement meter, velocimeter, accelerometer and placement of mixed sensors are illustrated. [ABSTRACT FROM AUTHOR]

Blackwell (1951, 1953) proposes an informativeness ranking of experiments: experiment I is more Blackwell-informative than experiment II if and only if the value of experiment I is higher than that of experiment II for all expected-utility maximizers. Under commitment and reduction, our main theorem shows that Blackwell equivalence holds for all convex and strongly monotone preferences—i.e., uncertainty-averse preferences ( Cerreia-Vioglio et al., 2011b ), which nest most ambiguity-averse preferences commonly used in applications as special cases. [ABSTRACT FROM AUTHOR]

We introduce asymmetric information to games with discontinuous payoffs and prove new equilibrium existence theorems. In particular, the seminal work of Reny (1999) is extended to a Bayesian preferences framework. [ABSTRACT FROM AUTHOR]

We study the role of bush encroachment control for a farmer's income and income risk in a stochastic ecological-economic model of grazing management in semi-arid rangelands. In particular, we study debushing as an instrument of risk management that complements the choice of an adaptive grazing management strategy for that sake. We show that debushing, while being a good practice for increasing the mean pasture productivity and thus expected income, also increases the farmer's income risk. The optimal extent of debushing for a risk-averse farmer is thus determined from balancing the positive and negative consequences of debushing on intertemporal and stochastic farm income.We study the role of bush encroachment control for a farmer's income and income risk in a stochastic ecological-economic model of grazing management in semi-arid rangelands. In particular, we study debushing as an instrument of risk management that complements the choice of an adaptive grazing management strategy for that sake. We show that debushing, while being a good practice for increasing the mean pasture productivity and thus expected income, also increases the farmer's income risk. The optimal extent of debushing for a risk-averse farmer is thus determined from balancing the positive and negative consequences of debushing on intertemporal and stochastic farm income. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a model of choice based on imperfect memory and self-deception. I assume that people have preferences over their own attributes (e.g., skill, knowledge, or competence) and can manipulate their memories. The model provides a prior-dependent theory of regret aversion and allows for prior-dependent information attitudes. It implies that behavior will converge to the one predicted by expected utility theory after a choice has been faced a sufficiently large number of times. [Copyright &y& Elsevier]

Abstract: Real world tasks involving moving targets, such as driving a vehicle, are performed based on continuous decisions thought to depend upon the temporal derivative of the expected utility (∂V/∂t), where the expected utility (V) is the effective value of a future reward. However, the neural mechanisms that underlie dynamic decision-making are not well understood. This study investigates human neural correlates of both V and ∂V/∂t using fMRI and a novel experimental paradigm based on a pursuit–evasion game optimized to isolate components of dynamic decision processes. Our behavioral data show that players of the pursuit–evasion game adopt an exponential discounting function, supporting the expected utility theory. The continuous functions of V and ∂V/∂t were derived from the behavioral data and applied as regressors in fMRI analysis, enabling temporal resolution that exceeded the sampling rate of image acquisition, hyper-temporal resolution, by taking advantage of numerous trials that provide rich and independent manipulation of those variables. V and ∂V/∂t were each associated with distinct neural activity. Specifically, ∂V/∂t was associated with anterior and posterior cingulate cortices, superior parietal lobule, and ventral pallidum, whereas V was primarily associated with supplementary motor, pre and post central gyri, cerebellum, and thalamus. The association between the ∂V/∂t and brain regions previously related to decision-making is consistent with the primary role of the temporal derivative of expected utility in dynamic decision-making. [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: Optimism bias is inconsistent with the independence of decision weights and payoffs found in models of choice under risk and uncertainty, such as expected utility theory, subjective expected utility, and prospect theory. We therefore propose an alternative model of risky and uncertain choice where decision weights—affective or perceived risk—are endogenous. Affective decision making (ADM) is a strategic model of choice under risk and uncertainty where we posit two cognitive processes—the “rational” and the “emotional” process. The two processes interact in a simultaneous-move intrapersonal potential game, and observed choice is the result of a pure strategy Nash equilibrium in this game. We show that regular ADM potential games have an odd number of locally unique pure strategy Nash equilibria, and demonstrate this finding for affective decision making in insurance markets. We prove that ADM potential games are refutable by axiomatizing the ADM potential maximizers. [Copyright &y& Elsevier]

Abstract: Most welfare models of environmental or mortality risk reductions assume that risks are exogenously determined and known with certainty. However, a growing body of research suggests that uncertainty about risks can affect choices over risky prospects. I present a decision-weighted random-utility model that decomposes welfare losses into those attributable to an increase in the deterministic component of risk and those attributable to uncertainty about risk. I apply the model to an illustrative dataset of subjects'' perceived mortality risk and willingness to accept the risk of nuclear-waste transport. I estimate the model using Lewbel''s (2000) strictly exogenous regressor approach to account for endogeneity bias and measurement error. Subjects display aversion to both risk and uncertainty about the risk of a transport accident, so that increases in either leads to social-welfare losses. Roughly 12% of the external cost of nuclear-waste transport is attributable to the public''s uncertainty about transport risk. [Copyright &y& Elsevier]

Abstract: This paper presents a new iterative procedure for solving finite non-cooperative games, the reasoning-based expected utility procedure (RBEU), and compares this with existing iterative procedures. RBEU deletes more strategies than iterated deletion of strictly dominated strategies, while avoiding the conceptual problems associated with iterated deletion of weakly dominated strategies. It uses a sequence of “accumulation” and “deletion” operations to categorise strategies as permissible and impermissible; strategies may remain uncategorised when the procedure halts. RBEU and related “categorisation procedures” can be interpreted as tracking successive steps in players'' own reasoning. [Copyright &y& Elsevier]

Abstract: The calibration theorem by Rabin [Rabin, M., 2000a. Risk aversion and expected utility theory: A calibration theorem. Econometrica 68, 1281–1292; Rabin, M., 2000b. Diminishing marginal utility of wealth cannot explain risk aversion. In: Kahneman, D., Tversky, A. (Eds.), Choices, Values and Frames. Cambridge University Press] implies that seemingly plausible small-stake choices under risk imply implausible large-stake risk aversion. This theorem is derived based on the expected utility of wealth model. However, Cox and Sadiraj [Cox, J.C., Sadiraj, V., 2006. Small- and large-stakes risk aversion: Implications of concavity calibration for decision theory. Games Econ. Behav. 56, 45–60] show that such implications do not follow from the expected utility of income model. One may then wonder about the implications for more applied consumption analysis. The present paper therefore expresses utility as a function of consumption in a standard life cycle model, and illustrates the implications of this model with experimental small- and intermediate-stake risk data from Holt and Laury [Holt, C.A., Laury, S.K., 2002. Risk aversion and incentive effects. Amer. Econ. Rev. 92, 1644–1655]. The results suggest implausible risk aversion parameters as well as unreasonable implications for long-term risky choices. Thus, the conventional intertemporal consumption model under risk appears to be inconsistent with the data. [Copyright &y& Elsevier]

Abstract: If a decision maker whose behavior conforms to the max-min expected utility model is faced with a scoring rule for a subjective expected utility decision maker, she will always announce a probability belonging to her set of priors; moreover, for any prior in the set, there is a scoring rule inducing the agent to announce that prior. We also show that on the domain of Choquet expected utility preferences with risk neutral lottery evaluation and totally monotone capacities, proper scoring rules do not exist. This implies the non-existence of proper scoring rules for any larger class of preferences (CEU with convex capacities, multiple priors). [Copyright &y& Elsevier]

Abstract: We develop an agent-based model for forest harvesting to study how interactions between neighboring land parcels and the degree of information flow among landowners influence harvesting patterns. We assume a forest is composed of a number of land parcels that are individually managed. Each parcel is either mature forested, just-harvested, or immature forested. The state transition of each parcel is described by a Markov chain that incorporates the successional dynamics of the forest ecosystem and landowners’ decisions about harvesting. Landowners decide to cut trees based on the expected discounted utility of forested vs. harvested land. One landowner''s decision to cut trees is assumed to cause the degradation of ecosystem services on the downstream forested parcels. We investigated two different scenarios: in a strongly-connected society, landowners are familiar with each other and have full information regarding the behavior of other landowners. In a weakly-connected society, landowners do not communicate and therefore need to make subjective predictions about the behavior of others without adequate information. Regardless of the type of society, we observed that the spatial interaction between management units caused a chain reaction of tree harvesting in the neighborhood even when healthy forested land provided greater utility than harvested land. The harvest rate was higher in a weakly-connected society than that in a strongly-connected society. If landowners employed a long-term perspective, the harvest rate declined, and a more robust forested landscape emerged. Our results highlight the importance of institutional arrangements that encourage a long-term perspective and increased information flow among landowners in order to achieve successful forest management. [Copyright &y& Elsevier]

Abstract: Tiered testing is an essential part of any resource-efficient strategy for the toxicity testing of a large number of chemicals, which is required for instance in the risk management of general (industrial) chemicals, In spite of this, no general theory seems to be available for the combination of single tests into efficient tiered testing systems. A first outline of such a theory is developed. It is argued that chemical, toxicological, and decision-theoretical knowledge should be combined in the construction of such a theory. A decision-theoretical approach for the optimization of test systems is introduced. It is based on expected utility maximization with simplified assumptions covering factual and value-related information that is usually missing in the development of test systems. [Copyright &y& Elsevier]

Abstract: A bargaining solution based on the Rubinstein–Safra–Thomson ‘ordinal Nash’ outcome is investigated in the Peters–Wakker ‘revealed group preferences’ framework. Assuming non-expected utility preferences, necessary and sufficient conditions are stated on preference pairs in order for the solution to be well-defined and axiomatized uniquely. [Copyright &y& Elsevier]

Abstract: A benchmarking procedure ranks real-valued acts by the probability that they outperform a benchmark β which may itself be a random variable; that is, an act f is evaluated by means of the functional . Expected utility is a special case of benchmarking procedure, where the acts and the benchmark are stochastically independent. This paper provides axiomatic characterizations of preference relations that are representable as benchmarking procedures. The key axiom is the sure-thing principle. When the state space is infinite, different continuity assumptions translate into different properties of the probability P. [Copyright &y& Elsevier]

Abstract: Following Mongin [J. Econ. Theory 66 (1995) 313; J. Math. Econ. 29 (1998) 331], we study social aggregation of subjective expected utility preferences in a Savage framework. We argue that each of Savage''s P3 and P4 are incompatible with the strong Pareto property. A representation theorem for social preferences satisfying Pareto indifference and conforming to the state-dependent expected utility model is provided. [Copyright &y& Elsevier]

This paper characterizes properties of chance attitudes (nonadditive measures). It does so for decision under uncertainty (unknown probabilities), where it assumes Choquet expected utility, and for decision under risk (known probabilities), where it assumes rank-dependent utility. It analyzes chance attitude independently from utility. All preference conditions concern simple violations of the sure-thing principle. Earlier results along these lines assumed richness of both outcomes and events. This paper generalizes such results to general state spaces as in Schmeidler''s model of Choquet expected utility, and to general outcome spaces as in Gilboa''s model of Choquet expected utility. [Copyright &y& Elsevier]

We revisit the well-known result that asserts that an increase in the degree of one''s risk aversion improves the position of one''s opponents. To this end, we apply Yaari''s dual theory of choice under risk both to Nash''s bargaining problem and to Rubinstein''s game of alternating offers. Under this theory, unlike under expected utility, risk aversion influences the bargaining outcome only when this outcome is random, namely, when the players are risk lovers. In this case, an increase in one''s degree of risk aversion increases one''s share of the pie. [Copyright &y& Elsevier]

Belief persistence is a standard rationality axiom in formal models of belief change. It requires that new information be accommodated with the smallest possible change to existing beliefs. This note shows that violations of belief persistence are possible in J. Eichberger and D. Kelsey''s (1999a, “Signalling Games with Uncertainty,” unpublished, University of Birmingham; 1999b, in Beliefs, Interactions and Preferences in Decision Making (M. J. Machina and B. Munier, Eds.), pp. 135–157. Dordrecht: Kluwer Academic) Dempster–Shafer equilibrium (DSE), a solution concept for signaling games based on Choquet expected utility. Such violations may lead to implausible equilibria, so a refinement of DSE is proposed. Journal of Economic Literature Classification Numbers: C72, D81. [Copyright &y& Elsevier]

We study a multiperson bargaining problem with general risk preferences through the use of Shaked''s game of cycling offers with exogenous breakdown. If preferences are “smooth,” then as the risk of breakdown vanishes, the limiting outcome is one in which bargainers are equally marginally bold; where a bargainer''s marginal boldness measures his willingness to risk disagreement in return for a marginal improvement in his position. Under smoothness, any (ordinal-)Nash solution is an equally marginally bold outcome. However, unlike the concept of the (ordinal-)Nash solution, a unique equally marginally bold outcome exists in natural cases—in particular, if all bargainers have risk-averse preferences of the rank-dependent expected utility type. For these preferences, the equally marginally bold outcome maximizes a “bargaining power”-adjusted (asymmetric) Nash product where the degree of asymmetry is determined by the disparity in the marginal valuation of certainty among bargainers. Journal of Economic Literature Classification Numbers: C72, C78, D81. [Copyright &y& Elsevier]

• The method is proposed for optimal selection of master DOFs in dynamic model reduction-based SHM. • Bayesian experimental design is employed for handling the optimal master-DOF selection problem. • Information from the calibration stage is introduced by the ARD likelihood. • Mode pairing between the measured and model predicted modes is avoided. The structural damage identification based on the dynamic condensation of finite element (FE) model can effectively deal with the mismatching between the measured degree of freedom (DOF) and the total DOFs of the entire FE model, and avoid the issues of mode pairing and repeated solution of the generalized eigenvalue problem of large-scale FE models. The proper configuration of master DOFs is essential for the successful application of the model reduction-based damage identification method, which determines the position of the sensors, the rearrangement of system matrices of the FE model according to the master/slave DOFs, and the specific form of the transformation matrix for the dynamic reduction method at the same time. The main purpose of this paper is to investigate the optimized choice of the master DOFs specifically for the dynamic reduction-based damage identification method through Bayesian experimental design, which is based on the Bayesian inference to interpret the data measured during the experiment. In the terminology of Bayesian experimental design, considering the configuration of master DOFs as a design of experiment, the utility function is defined through the Kullback–Leibler divergence, or relative entropy, which is employed as a scalar measure to quantitatively characterize the information gain caused by the measurement data between the prior and posterior probability distribution over the uncertain model parameters. By maximizing the expected utility under the marginal distribution for the data, the optimal experimental design, which is taken as the optimal configuration of the master DOFs, can be achieved. The proposed methodology for the optimal selection of master DOFs relevant to the dynamic reduction-based damage identification method is verified through both numerical case studies on a 40-DOF truss and experimental research on a real-life pedestrian bridge. [ABSTRACT FROM AUTHOR]