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An axiomatization of expected utility under uncertainty is extended in several steps to characterize more complicated decision models. Central to each step is a bijective mapping that, applied to the set of prospects, changes the framing of the decision problem. Static models of subjective expected utility and reference dependence result from stretch mappings and translations (i.e., shifts), respectively. Dynamic models, such as regret and aspiration learning, involve groups of models each of which applies a translation by a different reference prospect (aspiration). The resulting regret model accommodates preference cycles in a higher-dimensional decision space without violating transitivity. An equilibrium of such a dynamic model is characterized as the prospect that is a maximal element in reference to itself. Under aspiration learning, asymptotic stability thus ensures that the aspiration (eventually) matches the equilibrium prospect. The concepts of regret and aspiration learning are combined to a model of choice acclimatization for the purpose of equilibrium selection. The valuation function of this equilibrium selection model is then further specified to accommodate cumulative regret that accrues during the acclimatization process.

The need for venturing out to distant states is a well-established insight of the behavioral theory of the firm. Previous literature has paid particular attention to the need to complement local experimentation with exploratory search for solutions that involve a multitude of changes, especially when decision problems are complex. Less attention has received the notion that exploration is not a process that occurs instantaneously but rather involves a series of interim steps. An important distinction therefore is to be made between discovery of a distant opportunity and the local learning efforts of the underlying activities that are required. We argue that the discovery of a distant opportunity may serve as a goal that then may inform a firm’s local search. In a computer simulation, we explore how a decision maker’s consideration of a distant goal in local learning shapes a firm’s search path. In particular, we examine how a firm’s level of goal myopia and the goal setting scope affect firm performance. We find that goal myopia to some extent is necessary and helpful in navigating through complex decision problems. We also find that a bounded goal setting scope is preferable in complex environments as firms may in fact reach such goals and more frequently update their goals along the way. In contrast, when firms set very attractive but also very distant goals, they are more likely to get stuck along the way with mediocre strategies.

We generalize Blackwell (1951)'s informativeness order to ambiguous experiments. The ambiguity in experiments is rooted in a lack of understanding about their probabilistic content. Formally, an ambiguous experiment is a mapping from an auxiliary state space to the set of unambiguous experiments. We show that one ambiguous experiment is preferred to another by every decision maker for every decision problem if and only if they are related by a condition called prior-by-prior dominance, which states that for any first-order belief the decision maker entertains on the auxiliary state space, the expected experiment resulting from this belief for the first experiment is Blackwell more informative than that of the second. This equivalence is robust across a wide range of ambiguity preferences. Comparisons of sets of experiments evaluated using the maximin criterion are studied as a special case and are shown to result in a weaker informativeness order.

In this paper, we studied the effect of mobility-on-demand (MoD) services' pricing and matching decisions on mitigating the negative impacts of curbside stopping activities. We first developed a set of macroscopic models of MoD services, curbside stopping systems, road networks, and their interactions. In particular, we generalized an existing queueing model of curbside stopping systems to the multiple-pickup-locations context, and formulated MoD services' demand guidance decision problem as an integer program. We also proposed a novel and efficient numerical method to find the equilibria of the system. Then, we apply simulation optimization methods over the proposed model to search for optimal MoD operations. Our numerical experiments showed that, compared with optimal pricing decisions, optimal matching decisions could better balance the welfare of the MoD service and its negative impact on road network capacities. This observation implied that matching mechanisms could be competitive alternatives to congestion pricing in mitigating the curbside stopping problem.

In this work, we propose a workflow for quantifying the value of a candidate monitoring strategy for conformance management decisions. A value of information (VOI) analysis framework is constructed by combining a quantitative conformance verification workflow and an economic model via decision tree analysis. The presented workflow is applied to a synthetic case study based on the Smeaheia storage aquifer, where the uncertainty on the transmissibility of an important fault poses a risk to the conformance of the reservoir pressure behaviour. By incorporating information from candidate monitoring configurations to better constrain the forecasts of the ensemble of model realizations used to characterize the inherent geological uncertainties, an assessment of the time-dependent ability of detecting deviations from conforming behaviour is achieved and followed by an economic evaluation of the considered alternatives for pressure control actions. Using data-driven approximations, the analysis can be repeated for several monitoring configurations (type of measurement, location, measurement error and timing of measurement) accounting for plausible outcomes of the analysed measurements. This allows us to determine the expected value of the storage operation for each monitoring configuration, and for possible actions available to the operator for remediating unwanted storage site development. The results obtained show that the value achieved from monitoring depends on both the timing and information content of the measurements. Direct and indirect (imperfect) observations of the quantity of interest for conformance might not always be sufficient to guarantee perfectly accurate conformance statements and conformance management decisions. This highlights the practical value of addressing decision problems in quantitative terms to support the design of CO2 storage systems by gaining insight into the effectiveness of monitoring and corrective actions.

Firms and statistical agencies must protect the privacy of the individuals whose data they collect, analyze, and publish. Increasingly, these organizations do so by using publication mechanisms that satisfy differential privacy. We consider the problem of choosing such a mechanism so as to maximize the value of its output to end users. We show that this is a constrained information design problem, and characterize its solution. When the underlying database is drawn from a symmetric distribution -- for instance, if individuals' data are i.i.d. -- we show that the problem's dimensionality can be reduced, and that its solution belongs to a simpler class of mechanisms. When, in addition, data users have supermodular payoffs, we show that the simple geometric mechanism is always optimal by using a novel comparative static that ranks information structures according to their usefulness in supermodular decision problems.

This paper studies the effects of misspecified boundaries of competition on optimal retail pricing using store-level supermarket scanner data. We focus on two types of misspecification: (i) misspecification of the demand estimation problem, which can arise from either defining the product market to be too narrow or specifying an overly restrictive model of demand; (ii) misspecification of the retailer's decision problem, which can arise from the retailer separately optimizing prices in each category but failing to account for, and thus internalize, cross-category effects. Both sources of misspecification are relevant in differentiated product markets where goods are broadly related but in ways that may not be immediately obvious a priori. Quantifying the costs associated with either form of misspecification is challenging because it requires a flexible yet valid demand system. To this end, we take a nonparametric approach to estimating a multi-category demand system that imposes minimal restrictions on the sign/magnitude of cross-price effects and also satisfies key properties required by economic theory. Our first set of empirical results is descriptive. We use data across nine diverse product groups to show that cross-category effects exists and are often nuanced in their sign and magnitude. That is, many categories are neither "obvious substitutes'" nor "obvious complements." We then zoom in on refrigerated juices and estimate demand nonparametrically across five juice categories where we find empirical support for a flexible model that can accommodate both substitutes and complements. We solve for optimal prices under both sources of misspecification and estimate profit losses to be in the 5-15% range.

The following analysis demonstrates that network efficiency is a very delicate matter. Neither the restriction to suitable core-subnets, nor intelligent enlargements guarantee efficient results in any case. For instance, the numerical example in Myerson (1977) contains a prisoners’ dilemma situation for some agents in the network. Of course, the outcome is inefficient from the perspective of these players – but not for the unrestricted network. Breass’ paradox shows that the enlargement of a network can lead to an inefficient outcome in the Nash equilibrium even if all players are taken into consideration. Restricting the network can create a Pareto efficient outcome. A third model discusses the strategic problem of a cyber network attack in the form of an inspection game. From the defender’s point of view, the question arises which nodes of the network are essential attack targets and thus need special security attention. In principle two types of nodes are critical: important ones and unimportant ones. Important nodes, as they connect to many other essential nodes and are therefore suitable multipliers for network malware and information capture, and unimportant nodes, from the attacker’s point of view, which are, in general, not in the focus of security attention, such that infiltration via them may be undetected for a long time.

Economic decisions are often influenced by "salient cues" that stand out in the choice context and attract attention. Intuitively, through channeling attention to a subset of the relevant information, salience thereby reduces the "dimensionality" of a decision problem. Building on this intuition, we hypothesize that people behave more consistently across differently complex problems if there is a common salient cue that guides their attention and, consequently, behavior. We experimentally test and confirm this hypothesis in the context of choice under risk: while revealed attitudes toward skewed risks — which have extreme and salient outcomes — are consistent across differently complex problems, revealed attitudes toward symmetric risks — where such a salient cue is missing — vary significantly with complexity. We provide suggestive evidence that these findings are driven by the extreme outcomes of skewed risks attracting a subject's attention and guiding choices. To rationalize our experimental results, we propose a variant of Bordalo et al.'s (2012) salience theory.

This paper considers the generation and provision of data products in the markets for information. Buyers face a decision problem with uncertainty of two states. They can purchase experiments to augment their private information. A buyer’s willingness to pay for an experiment depends on his private information. To generate these experiments, sellers have to make an investment, which determines the most informative experiment a seller can provide. Sellers then post menus of experiments and prices. We characterize the optimal menu given any investment level and derive the optimal investment. When two sellers compete with investment, we find an equilibrium in which two sellers split the market. One seller only serves to high belief buyers and the other serves to low beliefs buyers. Each seller specializes in generating a more informative signal about one state. Monopoly seller always provides more informative experiments, and to more buyers, than the case of duopoly competition.

We show that posted prices are the optimal mechanism to sell a durable good to a privately informed buyer when the seller has limited commitment in an infinite- horizon setting. We provide a methodology for mechanism design with limited commitment and transferable utility. Whereas in the case of commitment, subject to the buyer’s truthtelling and participation constraints, the seller’s problem is a decision problem, in the case of limited commitment, the seller’s problem corresponds to an intrapersonal game, where different “incarnations" of the seller represent the different beliefs he may have about the buyer’s valuation.

Over the last two decades the intensity of credit standards’ tightening during economic contractions has exceeded their easing during expansions among euro area banks. This mechanism is fed by the boom-bust cycle of credit that, as much research has shown, is linked to financial instability with large effects on the real economy. We build a small scale nonlinear quadratic (NLQ) model to study how credit feedback can affect the overall adjustment path of the economy towards some steady state, when the central bank solves a finite-horizon decision problem where the policy rate is allowed to also be zero or negative. Then, we estimate local projections for a super- visory shock hitting banks’ credit standards and propose a new external instrument to identify its dynamic causal impact on the real and financial sector. We find that the regime dependence reveals important information to policy makers to implement macroprudential measures.

A major concern with the Bayesian approach is the use of a unique probability measure to quantify all relevant uncertainty. Specifying a unique probability with extreme precision when only vague or fragmentary information is available may not be feasible. This would be less of a concern under a form of prior robustness, i.e. when a minor variation in the prior would lead to decisions with similar value. This paper studies prior robustness as a form of continuity of the value of a decision problem under uncertainty. I show that this notion of robustness can be characterized by a form of stable choice over a sequence of perturbed decision problems, i.e. decision problems in which the available acts are perturbed in a precise fashion. I then study a measure of prior robustness that captures the sensitivity of the value under perturbations of the prior. Finally, I consider applications to portfolio choice and a consumption-savings problem.

This paper examines the robustness of Lehmann's ranking of experiments ( Lehmann, 1988 ) for decisionmakers who are uncertainty averse a la Cerreia-Vioglio et al. (2011) . We show that, assuming commitment, for all uncertainty-averse indices satisfying some mild assumptions, Lehmann's informativeness ranking is equivalent to the induced uncertainty-averse value ranking of experiments for all agents with single-crossing vNM utility indices (Theorem 1). Moreover, Lehmann's ranking can also be detected by varying the uncertainty-averse indices for a fixed finite collection of vNM utility indices (Proposition 1). Our findings suggest that Lehmann's ranking can be a useful enrichment of Blackwell's ranking for monotone decision problems even if ambiguity is present. We apply our results to problems that include social aggregation of information preferences and investment decisions.

Imagine a group of individuals faces a yes-no type question whose answer is logically determined by multiple premises. There are two salient types of procedures to aggregate individual judgments -- the ``premise-based way'' (PBW) and the ``conclusion-based way'' (CBW). We derive necessary and sufficient conditions under which two procedures are universally ordered. If (and only if) a decision problem takes a ``conjunctive'' form, PBW derives a positive collective judgment (i.e., ``yes'') whenever CBW does. Furthermore, if we replace ``conjunctive'' with ``disjunctive'' in the previous line, PBW derives a negative collective judgment (i.e., ``no'') whenever PBW does. These observations highlight the fact that these two procedures are a mathematical dual of each another. Asymptotic properties are also studied. Under classical Condorcetian assumptions, PBW ensures the probability that the voting outcome is correct converges to one as the size of a group tends to infinity, whereas this holds for CBW only if an additional condition is satisfied.

In many delivery and service settings, the customer must be home when the provider arrives. If the customer is not at home, the delivery or service fails and the provider may have to return at a later point, needlessly creating additional vehicle miles and emission. To prevent such missed deliveries, it is increasingly common for providers to let customers choose from a menu of narrow time slots in which the delivery or service will take place. An important decision problem in this setting is which time slots to offer to maximize the expected number of placed orders while guaranteeing a feasible delivery schedule. In this paper, we particularly identify the occurrence of multiple customers simultaneously interact with a booking system. Indeed, customers might arrive while the system is still processing a previous customer, and customers might arrive while another customer is still deciding on his or her preferred time slot. Such simultaneous interactions lead to additional waiting time and invalid service offers, as we demonstrate in this paper. We argue that state-of- the-art procedures are not yet equipped to deal with this and present new approaches for this purpose. We illustrate their performance using real-time experiments with thousands of customers arriving over a small period of time. Our findings provide insights that may help to improve the design of current online booking systems, and opens up new areas of research.

The selection of projects from a set of possible alternatives is a fundamental decision problem for any organization. Governments and businesses that allocate sizeable resource budgets across projects and initiatives face the same fundamental challenge: to select the most valuable projects while respecting budget constraints. The literature proposes efficient algorithms to solve these knapsack problems, but the higher complexity of the real-world selection problems, together with the black-box behavior of these algorithms, make their adoption impractical. Instead, decision makers perform mental searches across the available options, thereby introducing behavioral effects into the knapsack problem. Through a lab experiment, we show that the decision makers’ mental search is biased towards selecting too many small projects compared to the optimal choice. This suggests that selection decisions may lead to inefficient resource allocation in organizations. We provide evidence that this fundamental bias stems from the structure of the search process: decision makers predominantly build up the feasible portfolio of projects (i.e., forward search). We discuss recommendations that could help decision makers reduce this bias and make better project selection decisions.

Should monetary policy be more aggressive or more cautious when facing uncertainty on the relationship between macroeconomic variables? This paper's answer is: “it depends” on the degree of persistence of the shocks that hit the economy. The paper studies optimal monetary policy in a basic (two-equation) forward looking New-Keynesian (NK) framework with random parameters. It relaxes the assumption of full central bank information in two ways: by allowing for uncertainty on the model parameters and by assuming asymmetric information. While the private sector observes the realizations of the random process of the parameters as they occur, the central bank observes them with a one period delay. Compared to the problem with full information, the monetary authority must solve the Bayesian decision problem of minimizing the expected stream of future welfare losses integrating over its prior probability distribution of the unknown parameters. The paper proposes a general method to account for uncertainty on any subset of parameters of the model. As an application, it focuses on two cases: uncertainty on the natural rate of interest and on the slope of the Phillips curve.

We study various decision problems regarding short-term investments in risky assets whose returns evolve continuously in time. We show that in each problem, all risk-averse decision makers have the same (problem-dependent) ranking over short- term risky assets. Moreover, in each of these problems, the ranking is represented by the same risk index as in the case of CARA utility agents and normally distributed risky assets.

Keynes developed a number of technical, mathematical tools for dealing with the problems of uncertainty (ambiguity, vagueness, indeterminate probabilities, imprecise probabilities) in his A Treatise on Probability in 1921 (and in his earlier Fellowship Dissertations of 1907 and 1908) that continue to be overlooked by practically all academics in the nearly 100 years since its publication in 1921. Keynes’s technical and mathematical modeling developments took place in chapters 15-17 of Part II of the A Treatise on Probability, chapters 20 and 22 of Part III of the A Treatise on Probability, Chapter 26 of Part IV of the A Treatise on Probability, and chapters 29 and 30 of Part V of the A Treatise on Probability. Part II of the A Treatise on Probability included Keynes’s original work dealing with non –additive probabilities that was based on the original work of George Boole in his 1854 The Laws of Thought. Keynes’s Boolean upper and lower bounded probabilities, which Keynes categorized as inexact measurement and approximation, established his complete grasp of the concept of interval valued probability. The American Theodore Hailperin showed in 1986 that both Boole and Keynes were using early versions of linear programming techniques to solve both linear and non linear systems of equations and inequations. Keynes used the name “non –numerical probability“ when discussing his no additive, non linear interval valued probability approach. Keynes’s approach has been erroneously identified as an ordinal probability approach by all Post Keynesians, Institutional and heterodox economists, who were greatly influenced by the 1975 paper on Keynes and uncertainty in HOPE by E R Weintraub, which misinterpreted Keynes in terms of G L S Shackle’s theory of possibility. Part III of the A Treatise on Probability, building on Part II’s interval valued probability concept, developed the concept of finite probability, applicable to both numerical and non numerical (interval valued) probabilities, in order to deal with applications of probability to Keynes’s concepts of induction, based on degrees of analogy, involving degrees of similarity and dissimilarity using human memory ,intuition and pattern recognition. Part IV of the A Treatise on Probability provided the first decision weight approach to decision making, Keynes’s conventional coefficient of weight and risk, c, that incorporated both non linear probability preferences and non additivity by the use of decision weights .These decision weights incorporated Keynes’s logical analysis, contained in chapter 6 of the A Treatise on Probability of his Evidential weight of the argument approach, V(a/h),which was a logical relation like Keynes P(a/h)=α, 0≤α≤1,but which Keynes waited to provide the comparable mathematical analysis for in chapter 26.In chapter 26,Keynes set V(a/h) equal to w,where w was normalized on the unit interval, so that V(a/h) =w, 0≤w≤1, holds. Keynes then defined uncertainty in the General Theory as an inverse function of V in chapter 12 on page 148 in footnote 1. Keynes then defined his conventional coefficient of weight and risk, c, to equal the standard EMV and SEU rules multiplied by the decision weights [(2w/1+w)] for non additivity and [(1/(1+q)] for non linearity. F Y Edgeworth recognized Keynes’s approach as breaking new ground. However, his plea for reader assistance from subscribers to Mind was ignored. Part V of the A Treatise on Probability provided the first “safety first” approach to decision making. As acknowledged by Edgeworth, Keynes used Chebyshev’s Inequality to establish lower bounds for decision problems in order to minimize risk (Keynes, 1921, pp. 353-358). Samuelson, while analyzing Keynes‘s simplified Least Risk analysis on p. 315 of the A Treatise on Probability, unfortunately overlooked Keynes’s generalized approach using Chebyshev’s Inequality in chapter 29. Samuelson also overlooked on this same page Keynes’s development of the logical and mathematical tools needed to specify the investment multiplier in the General Theory, as well as Kahn’s employment multiplier on p.183 of his June, 1931 article in the Economic Journal.

In the spirit of von Neumann and Morgenstern (1947), this paper provides an axiomatic representation of information. Under the von Neumann-Morgenstern axioms, along with an additional continuity, indifference to randomization, and a Blackwell informativeness axiom, I show that any ordering over information can be essentially uniquely represented as, equivalently: (a) a strictly increasing cost of information acquisition; (b) for a given prior, the expected utility from a decision problem; (c) for a given prior, an additive posterior-separable measure of uncertainty; and (d) a separable cost of signals. I discuss the implications of the results for the rational inattention literature.

I study contests in which each player is ranked by a scoring rule based on both her performance and how close this performance is to a private target, set before the contest. Each player’s decision problem is to choose her target when performance is subject to a random component. I analyse the incentive properties of target setting, derive conditions on the primitives such that equilibria exist and characterise the players’ behaviour. I show that target setting generates outcome uncertainty under a large class of conditions. In particular, neither private abilities nor perfectly correlated states are necessary. Target setting, therefore, has important implications in contest design as outcome uncertainty is a salient determinant of consumers’ demand for contests.

I study the value of information in monotone decision problems where the action spaces are potentially multidimensional. In these general environments, there exist sensible partial orders on actions and higher actions are optimal for higher signal realizations. As a criterion for comparing information structures, I develop a condition called monotone quasi-garbling meaning that an information structure is obtained by adding reversely monotone noise (more noisy in a lower state and less noisy in a higher state) to another. It is shown that monotone quasi-garbling is a sufficient condition for decision makers to get a higher ex-ante expected payoff. This new criterion generally permits more comparisons than the garbling condition by Blackwell (1951, 1953) and the effectiveness condition by Lehmann (1988). To illustrate, I apply the result to an optimal insurance problem and a nonlinear monopoly pricing problem.

This paper experimentally investigates the effect of introducing unavailable alternatives and irrelevant information regarding the alternatives on the optimality of decisions in choice problems. We find that interaction between the unavailable alternatives and irrelevant information regarding the alternatives generates suboptimal decisions. Irrelevant information in any dimension increases the time costs of decisions. We also identify a pure “preference for simplicity” beyond the desire to make optimal decisions or minimize time spent on a decision problem. Our results imply that the presentation set, distinct from the alternative set, needs to be a part of decision making models.

In economic theory, an agent chooses from available alternatives – modelled as a set. In decisions in the field or in the lab, however, agents do not have access to the set of alternatives at once. Instead, alternatives are represented by the outside world in a structured way. Online search results are lists of items, wine menus are often lists of lists (grouped by type or country), and online shopping often involves filtering items which can be viewed as navigating a tree. Representations constrain how an agent can choose. At the same time, an agent can also leverage representations when choosing, simplifying his choice process. For instance, in the case of a list he can use the order in which alternatives are represented to make his choice. In this paper, we model representations and choice procedures operating on them. We ask which properties procedures have to fulfill such that their choices are equivalent to maximizing a strict preference relation. We fully characterize such procedures for general representations including lists, list of lists, trees and other representations.

We propose a dynamic structural model of a loan portfolio, secured by collaterals. Contrary to existing dynamic models, our model takes into account the time-dependence of the debtors' wealth and the fact that, due to defaults, the financial health within the portfolio improves in comparison to the population. As such, the model replicates the empirically observed decrease of loans' default rates in time. In the model, the debtors' resources, insufficiency of which is assumed to cause defaults, and the prices of the collaterals, determining the losses given default (LGD), depend on common and individual factors. The individual factors follow an AR(1) vector process with general residuals, the common factors are general, possibly dependent on exogenous variables. We show that the mapping transforming the common factors into the conditional probabilities of default (PD) and the LGDs is one-to-one monotonous continuously differentiable. As this transformation is not analytically tractable, we propose an approximation technique which is convergent with polynomial complexity. To demonstrate a possible application of our model, we formulate a decision problem for optimal choice of loan candidates. Further, we discuss estimation of the model's parameters, we suggest ways of modelling heterogenous portfolios, and we give arguments supporting empirical validity of the model.

A consistent planner evaluates a dynamic decision problem by considering the changes she expects in her future tastes (or rankings), and how these changes will affect her decision making over time. Using preferences today over decision problems tomorrow, we provide an elicitation method that uniquely identifies a consistent planner's expected future rankings. The elicitation method reflects the idea that future rankings should be monotone with respect to a strict partial order defined in a general choice framework, and we argue that this condition naturally arises in many applications. Moreover, we discuss that a test for the agent's sophistication and naivety can be given by comparing elicited rankings with tomorrow's actual rankings. We also identify the conditions that reveal the agent's optimism and pessimism on how indifferences will be resolved in the future. In particular, we show that a Strotzian consistent planner is the most optimistic, and a cautiously consistent planner is the most pessimistic one.

We study the identification and estimation of structural parameters in dynamic panel data logit models where decisions are forward-looking and the joint distribution of unobserved heterogeneity and observable state variables is nonparametric, i.e., fixed-effects model. We consider models with two endogenous state variables: the lagged decision variable, and the time duration in the last choice. This class of models includes as particular cases important economic applications such as models of market entry-exit, occupational choice, machine replacement, inventory and investment decisions, or dynamic demand of differentiated products. The identification of structural parameters requires a sufficient statistic that controls for unobserved heterogeneity not only in current utility but also in the continuation value of the forward-looking decision problem. We obtain the minimal sufficient statistic and prove identification of some structural parameters using a conditional likelihood approach. We apply this estimator to a machine replacement model., Comment: 57 pages

This work focuses on two-step decision problem through a biform game. At the first, in an uncertain environment, each distribution center must define the quantities to be ordered from the production units in order to maximize its own gain. This requires a good forecast of demand. When the demand is deterministic, the centers collaborate to meet their local demand. In this case, it is necessary to define the appropriate cost allocation method, especially since no method guarantees all the properties defined by the literature. This paper proposes an application case of bottling company in morocco. We use neural networks to forecast demand. In the phase of collaboration, we split cost using different methods and analyze results.

G L S Shackle and Joan Robinson both adopted the Neoclassical position that there could only be one theoretical equilibrium position in either the short run or long run. They combined this supposition with their own redefinition of the concept of uncertainty to mean complete, total, fundamental and radical uncertainty or ignorance of the future. They then claimed that it was impossible to use formal mathematical models in macroeconomics that incorporated the concept of equilibrium if there was complete and total uncertainty of the future. Pace Shackle and Robinson, Keynes never defined uncertainty as Ignorance. Keynes recognized that it was mainly only investment projects in long lived, fixed, durable, capital, producer goods that faced the problem of ignorance. Keynes explicitly dealt with this issue in his two 1937 contributions to the Quarterly Journal of Economics and the Eugenics Review if one was dealing with decision problems dealing with the very distant future. An example of such a decision problem would be deciding to invest in a new technology today, given the great uncertainty generated by technological change, advance and innovation, plus the constant threat of technological obsolescence. In general, Keynes dealt with uncertainty as a range. Ignorance was one extreme. This was done by Keynes in the A Treatise on Probability through the use of his logical relation V, where the evidential weight of the argument is defined by V(a/h) = degree w, where 0≤w≤1 and w measures the degree of the completeness of the relevant information, knowledge, data or evidence. Keynes then defined uncertainty, U, to be an inverse function of w in the General Theory in chapter 12 on page 148. Again, Keynes never defined uncertainty as ignorance. It is Shackle and Robinson who claimed that uncertainty meant ignorance. Keynes introduced multiple equilibria into macroeconomics with his creation of the Aggregate Supply Curve, a locus of all D=Z intersections. Uncertainty is thus dealt with by multiple equilibria. There is no evidence that either Shackle or Robinson ever grasped any of Keynes’s theoretical advances In their lifetimes. The belief that Keynes’s approach in the GT was a multiple equilibrium one is correct. However, economists do not understand how Keynes carried out his modeling of multiple equilibria because they have not been able to follow Keynes’s mathematical exposition in Chapters 20 and 21 of the GT. Keynes’s ASC represents a locus of a set of multiple equilibria, where D=Z, in chapter 20. Out of this set, one actual Y value will be realized. This Y value is then combined with r,the rate of interest, to model his IS-LP(LM) model in chapter 21 of the GT. Keynes, as pointed out by Townshend and confirmed by Keynes in the Townshend–Keynes exchanges, made it crystal clear that his Liquidity Preference (LP) equation, specified on page 199 of the GT, in his IS-LP(LM) model, is directly based on his analysis in his A Treatise on Probability of non numerical (interval valued ) probabilities and weight of the evidence, w. This is not surprising at all since Keynes explicitly defined uncertainty(not radical uncertainty) as an inverse function of the weight of the evidence, w, on page 148 of chapter 12 of the GT and explicitly redirected Townshend to his footnote on p.148 (Keynes also asked Townshend to reread page 240 of the GT) explicitly linking uncertainty to the concept of weight. Hence, there is no need to develop from scratch mathematical models of complexity to understand Keynes’s mathematical modeling in the A Treatise on Probability and General Theory.

I investigate the decision problem of a player in a game of incomplete information who faces uncertainty about the other players' strategies. I propose a new decision criterion which works in two steps. First, I assume common knowledge of rationality and eliminate all strategies which are not rationalizable. Second, I apply the maximin expected utility criterion. Using this decision criterion, one can derive predictions about outcomes and recommendations for players facing strategic uncertainty. A bidder following this decision criterion in a first-price auction expects all other bidders to bid their highest rationalizable bid given their valuation. As a consequence, the bidder never expects to win against an equal or higher type and resorts to win against lower types with certainty.

In computation theory, the complexity class NP-complete is one of the most studied classes of decision problem. We can verify any given solution to such a problem, but the most important characteristic of NP-complete problems is that no fast solution to them is known. Time required to solve the problem using any currently known algorithm increases very quickly as the size of the problem grows. So, NP-complete problems like traveling salesman and graph partitioning have various heuristic algorithms to find the optimal solution of these problems in much lesser time. Out of all the algorithms none of them will provide the exact solution of the problem. In this paper, we have considered two of graph based NP-complete problem (Traveling Salesmen Problem (Single and Multiple Salesman) and Graph Partitioning Problem). In TSP, the aim is to minimize the total distance travelled covering all the cities exactly once. In graph partitioning, the aim to partition the graph into smaller subset with each subset has almost equal number of nodes with minimized number of edges whose vertices are in different sets. To achieve these goals, we have implemented various heuristic algorithms of both of the problems. In addition to these, comparison of various algorithms on basis of cost and time of each problem is performed on a range of data set.

This paper sets out an analytical framework for decision-making under risk that assumes only utility-representable preferences but is capable of replicating and extending important results obtained in the EU framework. Focusing on decision problems where attitudes towards risk and correlation play an essential role, we show that characterizing attitudes towards risk and correlation in terms of an ordinal utility function of decision parameters enables the extension of existing results obtained in the EU framework on optimal decisions in their relation to how the endogenous and non-financial background risks are correlated to a setting assuming only utility-representable preferences.

Risk and uncertainty in decisions play an important role in many fields including engineering, economics and social sciences. In order to represent the decision problem mathematically or to compare prospects, a scalar either as dispersion measure or risk measure is used. Adequately measuring dispersion or risk is one of the most challenging topics in decision theory. According to well-known definitions in the literature, a dispersion or risk measure should satisfy several good properties; non-negativity, monotonicity, and convexity. In this paper, we investigate properties of two dispersion measures of Geometric Dispersion Theory (GDT) which are based on arithmetic-geometric means and show that they are nonnegative and convex. Also, these new dispersion measures of GDT are less sensitive to noise in comparison to standard deviation and its generalizations. Furthermore, we show that these new measures can present riskiness of alternatives better than other measures; thus enabling GDT to explain several well-known decision-making paradoxes.

In a dynamic choice environment, an agent's tastes may change over time, leading to a conflict between plans made today and choices made in the future. In response, a consistent planner restricts herself to plans that she will actually follow, by anticipating today how she will rank continuation plans in the future. Since the agent's expected future rankings often play an important role in policy analysis, they need to be elicited from observable choices. In this paper, we provide a method to elicit expected future rankings by considering the agent's preferences today over dynamic decision problems. Our identification strategy exploits that, in many applications of the consistent planning model, future rankings are monotone with respect to a partial order, which provides an unambiguous ranking of some alternatives. Our results are developed in a general framework, and can therefore be used to elicit expected future rankings in many applications of the consistent planning model. To illustrate our findings, we consider a dynamic consumption problem with quasi-hyperbolic discounting, and show how the agent's expectations about her present-bias in the future can be elicited from simple choice experiments today.

A decision-maker (DM) faces an intertemporal decision problem, where his payoff depends on actions taken across time as well as on an unknown Gaussian state. The DM can learn about the state from different (correlated) information sources, and allocates a budget of samples across these sources each period. A simple information acquisition strategy for the DM is to neglect dynamic considerations and allocate samples myopically. How inefficient is this strategy relative to the optimal information acquisition strategy? We show that if the budget of samples is sufficiently large then there is no inefficiency: myopic information acquisition is exactly optimal.

Many theoretical results rely on delayed review of imperfect information for sustaining cooperative outcomes. Using two laboratory experiments, this paper shows that delayed review can hinder cooperation in practice through a mechanism not captured by standard theory. The experiments make use of two different but closely related environments: a repeated prisoner's dilemma game with imperfect monitoring and pre-programmed grim triggers (but flexibility about what action to choose before the trigger is set off), and a decision problem played against a computer with a known strategy. At odds with the theoretical predictions, subjects cooperate less in both experiments when information is delayed. The results can be rationalized by a simple stochastic choice model with a bias toward survival.

In decision problems, frictions as well as constraints play an increasingly important role. Especially, optimal timing problems can be affected by potentially “non-rational” behavior of the decision maker which is not incorporated in the standard theory. A relevant problem of this kind is the real option to abandon a project. Limited cognitive resources and external restrictions to option exercise may result in a suboptimal outcome. The term inattention can summarize such frictions and constraints. In this paper, we address this issue by proposing a Markovian model to value American-style contracts of agents who are temporarily inattentive. Exercise decisions maximizing the contract’s payoff are not admissible continuously but at random intervention times arriving with possibly state and time dependent intensities. An optimal stopping problem provides the contract value. It is converted to optimal control which, given sufficient regularity, induces a characterisation in terms of a partial integro differential equation. We consider three numerical approaches, forward improvement iteration, least squares Monte-Carlo and finite differences, each corresponding to one particular characterization of the contract value. Our adapted least squares Monte-Carlo method can treat complex and possibly multi-dimensional settings.

We present a theory that rationalizes voters' preferences for decisive leaders. Greater decisiveness entails an inclination to reach decisions more quickly conditional on fixed information. Although speed can be good or bad, agency problems between voters and politicians create preferences among voters for leaders who perceive high costs of delay and have little uncertainty about how to weigh different aspects of the decision problem, and hence who make decisions more rapidly than typical voters. Officials who aspire to higher office therefore signal decisiveness by accelerating decisions. In elections, candidates with reputations for greater decisiveness prevail despite making smaller compromises, and therefore earn larger rents from office holding.

When a stochastic decision problem is time inconsistent, the decision maker would always be troubled by his conflicting decisions “optimally” derived from his time-varying preferences at different time instants. The long-run self (LR) of the decision maker pursues the long-term optimality and thus would like to take the pre-committed strategy. On the other hand, the short-run selves (SRs) of the decision maker at different time instants lack foresight, bow to short-term temptations and would like to take the so-called time consistent strategy. As these two extreme strategies have been criticized for their incomplete viewpoints in dealing with time inconsistency, the emerging literature of self-control game models recognizes an importance to strike a balance between the LR’s and SRs’ interests. While most risk measures in financial decisions are of a non-expectation nature, the existing results of self-control game models are confined to situations where the decision maker’s preferences involve only expectation operators. We take a step forward to develop in this study an operable unified two-tier dual-self game model with commitment by punishment in continuous time setting, which can cope with general time inconsistent stochastic financial decision problems with both expectation and non-expectation operators in the objective function. By attaching to both the preferences of LR and SRs certain punishment terms which quantitatively evaluate the internal conflict among different selves, our game model can align the interests of the LR and SRs to any desired degree. The equilibrium strategy, termed strategy of self-coordination in this paper, achieves some degree of internal harmony among various selves. We demonstrate in the paper successful applications of our dual-self game model to two long standing challenges in the literature, the continuous-time investment and consumption problem with quasi-hyperbolic discounting and the continuous-time mean-variance portfolio selection problem.

Problem definition: Inpatient beds are usually grouped into several wards, and each ward is assigned to serve patients from certain "primary" specialties. However, when a patient waits excessively long before a primary bed becomes available, hospital managers have the option to assign her to a non-primary bed though it is undesirable. Deciding when to use such "overflow" is difficult in real time and under uncertainty. Relevance: To aid the decision making, we model hospital inpatient flow as a multi-class, multi-pool parallel-server queueing system and formulate the overflow decision problem as a discrete-time, infinite-horizon average cost Markov decision process (MDP). The MDP incorporates many realistic and important features such as patient arrival and discharge patterns depending on time of day. Methodology: To overcome the curse-of-dimensionality of this formulated MDP, we resort to approximate dynamic programming (ADP). A critical part in designing an ADP algorithm is to choose appropriate basis functions to approximate the relative value function. Using a novel combination of fluid control and single-pool approximation, we develop analytical forms to approximate the relative value functions at midnight, which then guides the choice of the basis functions for all other times of day. Results: We demonstrate, via numerical experiments in realistic hospital settings, that our proposed ADP algorithm is remarkably effective in finding good overflow policies. These ADP policies can significantly improve system performance over some commonly used overflow strategies, e.g., in a baseline scenario, the ADP policy achieves a congestion level similar to that achieved by a complete bed sharing policy, while reduces the overflow proportion by 20%. Managerial Implications: We quantify the trade-off between the overflow proportion and congestion from implementing ADP policies under a variety of system conditions and generate useful insights. The plotted efficient frontiers allow managers to observe various performance measures in different parameter regimes, and the ADP policies provide managers with operational strategies to achieve the desired performance.

The Courchevel environment is hereby published to ease the development of streaming machine learning algorithms. In first solving this problem, a rapid reinforcement learning algorithm was invented. A simple transformation is added to the Bellman equation, a principal pillar of AI, particularly for solving Markov Decision Problems. By adding stochasticity to Bellman, sustained Reward-Per-Episode gains of an order of magnitude are validated, for environments where the reward function is structurally anticipated to be multi-modal. Courchevel as a decision problem, a first solution, and the Biased Bellman innovation are revealed -- with accompanying data. For ease of discussion, Courchevel's dynamics are described in military terms.

This paper studies lying in a novel context. Previous work has focused on situations in which people are either fully aware of the economic consequences of all available actions (e.g., die-under-cup paradigm), or they are uncertain, but this uncertainty cannot be cleared in any way (e.g., sender-receiver game). On the contrary, in reality, people oftentimes know that they will have a chance to lie, they are initially uncertain about the economic consequences of the available actions, but they can invest resources (e.g., time) to find them out. Here we capture the essence of this type of situations by means of a novel decision problem. Two experiments provide evidence of four empirical regularities regarding the distribution of choices, and suggest that participants vary along two dimensions: the moral cost of lying, and the cost of investing time to find out the payoffs associated to the available actions. Taking inspiration from these observations, we introduce a model that is consistent with the main empirical results.

In many revenue management applications risk aversion is crucial. In dynamic decision problems it is challenging to find the right balance between maximizing expected profits and minimizing their variance. In this paper, we present an efficient dynamic programming approach to leverage mean variance optimization in discounted Markov decision processes with finite time horizon. We show how to derive optimal risk-sensitive policies which allow for state-dependent mean variance balancing. We compare our approach to risk-neutral policies as well as risk-averse policies of the exponential utility model. Based on state-probabilities, we analytically evaluate the expected evolution of accumulated profits as well as profit variances. Our general concepts are demonstrated for dynamic pricing applications.

Research on problem solving drawing on the Carnegie School suggests that if a problem is of elevated complexity an appropriate representation is key to tackling it. However, when an appropriate representation is not in the decision maker’s knowledge base, it is unclear what determines whether the decision maker searches for novel representations. We theorize that novel representations can be explored only if the search is cognitively affordable. Yet, as problem complexity increases, the search becomes less cognitively affordable. High complexity obstructs the exploration of novel representations and prompts the exploitation of familiar search rules that requires less cognitive resources. Familiar search rules, however, are typically inappropriate for solving a novel problem when complexity is high. We designed and conducted an experiment to test our theory. Participants tackled a multi-period financial decision problem in an environment featuring rare but potentially payoff-devastating random shocks. Our findings corroborate that, as problem complexity increased, fewer participants explored novel representations and more participants exploited familiar search rules. The participants who explored novel representations performed better than those who used familiar search rules. The challenge of problem complexity therefore highlights the exploration of novel representations as an important direction for the research on search processes.

Choices made under risk appear to be different depending on decision problem either presented as an explicit description or experienced by subjects in a series of choices and outcomes. The difference, labeled the description-experience gap (DEG; Hertwig and Erev, 2009), has recently attracted a fair amount of attention and generated a substantial body of research. Alongside important insights gained, noticeably (and puzzlingly) absent from this literature are emotions – a feature more pertinent to actual experience than to mere description of events, thus potentially a source of difference in decisions observed in these two conditions. Even though emotions are considered a hallmark of experience, existing studies concerned with various aspects of DEG do not seem to address this facet of the question. This paper suggests the possibility that emotions comprise an important factor contributing to DEG. Theoretical considerations and relevant empirical evidence of decision-making guided by emotions are reviewed to support the proposed hypothesis. General perspective, directions for future research, and possible caveats are discussed.

We provide an axiomatic analysis of dynamic random utility, characterizing the stochastic choice behavior of agents who solve dynamic decision problems by maximizing some stochastic process ( U t ) of utilities. We show first that even when ( U t ) is arbitrary, dynamic random utility imposes new testable across‐period restrictions on behavior, over and above period‐by‐period analogs of the static random utility axioms. An important feature of dynamic random utility is that behavior may appear history‐dependent, because period‐ t choices reveal information about U t , which may be serially correlated; however, our key new axioms highlight that the model entails specific limits on the form of history dependence that can arise. Second, we show that imposing natural Bayesian rationality axioms restricts the form of randomness that ( U t ) can display. By contrast, a specification of utility shocks that is widely used in empirical work violates these restrictions, leading to behavior that may display a negative option value and can produce biased parameter estimates. Finally, dynamic stochastic choice data allow us to characterize important special cases of random utility—in particular, learning and taste persistence—that on static domains are indistinguishable from the general model.

This paper explores the link between bounded rationality, and complexity of decision problems in a newsvendor setting. We compare behaviors of newsvendors who manage one versus two stores, and find that individuals making two simultaneous newsvendor decisions, in both same-margin and mixed-margin scenarios, exhibit worse performances than making a single newsvendor decision, driven by lower levels of learning, and stronger demand chasing behavior. Furthermore, while in our setting, the two newsvendor decisions are independent to each other, order decisions are impacted by both exogenous demand signals and endogenous order decisions of the other store. We call it the “cross store influence.” We develop a behavioral model, based on linear adjustment dynamics, to explain the findings, and provide an theoretical analysis of the long term behavior of this model. These results highlight the importance of assigning the right amount of decision responsibilities to managers, and keeping them not distracted from unrelated information.

A data buyer faces a decision problem under uncertainty. He can augment his initial private information with supplemental data from a data seller. His willingness to pay for supplemental data is determined by the quality of his initial private information. The data seller optimally offers a menu of statistical experiments. We establish the properties that any revenue-maximizing menu of experiments must satisfy. Every experiment is a non-dispersed stochastic matrix, and every menu contains a fully informative experiment. In the cases of binary states and actions, or binary types, we provide an explicit construction of the optimal menu of experiments. (JEL D42, D81, D82, D83)

This paper considers a decision problem in the context of the worth of a wind mill project with profitability dependent on the average wind speed. This is partly known and the issue is whether to go on with the project now or, with an additional cost, put up a test mill and observe, say for a year, and then decide. The problem is studied within a Bayesian framework and given a general analytic solution for a specific loss function of linear type, with the normal case as illustration. Explicit formulas are then derived in the case when the wind speed distribution is Weibull with known shape parameter, and the sensitivity with respect to the specification of this parameter is explored. Based on Norwegian wind speed data we then give a justification of the Weibull model. This also provides some insight to parameter stability. Finally, a complete numerical scheme for the Bayesian two-parameter Weibull model is given, illustrated with an implementation of pre-posterior Weibull analysis in R.