Half empty, half full and why we can agree to disagree forever

Aumann [Aumann R., 1976. Agreeing to disagree. Annals of Statisitics 4, 1236–1239] derives his famous we cannot agree to disagree result under the assumption that people are expected utility (=EU) decision makers. Motivated by empirical evidence against EU theory, we study the possibility of agreeing to disagree within the framework of Choquet expected utility (=CEU) theory which generalizes EU theory by allowing for ambiguous beliefs. As our first main contribution, we show that people may well agree to disagree if their Bayesian updating of ambiguous beliefs is psychologically biased in our sense. Remarkably, this finding holds regardless of whether people with identical priors apply the same psychologically biased Bayesian update rule or not. As our second main contribution, we develop a formal model of Bayesian learning under ambiguity. As a key feature of our approach the posterior subjective beliefs do, in general, not converge to “true” probabilities which is in line with psychological evidence against converging learning behavior. This finding thus formally establishes that CEU decision makers may even agree to disagree in the long-run despite the fact that they always received the same information.     

Knightian uncertainty and poverty trap in a model of economic growth

This paper explores how Knightian uncertainty affects dynamic properties in an economic growth model. The decision-making theory employed in the analysis is the theory of expected utility under a non-additive probability measure, i.e., the Choquet expected utility model of preference. We apply this decision-making theory to an overlapping generations model where producers face “uncertainty” in their technologies. When the producer is averse to uncertainty, the firm's profit function may not be differentiable. Therefore, the firm's decision to invest and hire labor becomes rigid for a certain measurable range of real interest rates. In dynamic equilibrium, the existence of firm-level rigidity causes discontinuity in the wage function; this makes multiple equilibria the more likely outcomes under the log utility and Cobb–Douglas production functions. In this paper, we show that even if aversion to uncertainty is small, the “poverty trap” can arise for a wide range of parameter values.     

Attitude toward imprecise information

This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probability–possibility set, that is, a set P of probability measures on the state space. The decision maker is told that the true probability law lies in P and is assumed to rank pairs of the form (P,f) where f is an act mapping states into outcomes. The key representation result delivers maxmin expected utility (MEU) where the min operator ranges over a set of probability priors—just as in the MEU representation result of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141–153]. However, unlike the MEU representation, the representation here also delivers a mapping, , which links the probability–possibility set, describing the available information, to the set of revealed priors. The mapping is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probability–possibility set. This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probability–possibility set, i.e., is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealed probability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the “mean value” of the probability–possibility set, and (ii) shrinking the probability–possibility set toward the mean value to a degree determined by preferences.     

Preference for safety under the Choquet model: in search of a characterization

Victor prefers safety more than Ursula if whenever Ursula prefers a constant to an uncertain act, so does Victor. This paradigm, whose expected utility (EU) version is Arrow and Pratt’s more risk aversion concept, will be studied in the Choquet expected utility (CEU) model. Necessary condition Pointwise inequality between a function of the utility functions and another of the capacities is necessary and sufficient for the preference by Victor of safety over a dichotomous act whenever such is the preference of Ursula. However, increased preference for safety versus dichotomous acts does not imply preference by Victor of safety over a general act whenever such is the preference of Ursula. A counterexample will be provided, via the casino theory of Dubins and Savage. Sufficient condition Separation of the two functions by some convex function is sufficient for Victor to prefer safety more than Ursula, over general acts. Furthermore, a condition on the capacities will be presented for simplicity seeking, the preference by Victor over any act for some dichotomous act that leaves Ursula indifferent. This condition is met in particular if Victor’s capacity is a convex function of Ursula’s capacity. For these cases, the pointwise inequality (necessary) condition is a characterization of greater preference for safety, extending the Arrow–Pratt notion from EU to CEU and rank-dependent utility (RDU). These inequalities preserve the flavor of the “more pessimism than greediness” characterization of monotone risk aversion by Chateauneuf, Cohen and Meilijson in the RDU model and its extension by Grant and Quiggin to CEU. Preferences between safety and dichotomous acts are at the core of the biseparable preferences model of Ghirardato and Marinacci.     

Aggregation of multiple prior opinions

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker?s utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker?s set of priors is precisely all the weighted-averages of priors, where an expert?s prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker?s valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts? valuations.     

Nest-monotonic two-stage acts and exponential probability capacities

This paper examines conditions for Choquet expected utility (CEU) to satisfy both the reduction of two-stage acts and the recursion axioms, which are taken for granted in economics. A key idea of this paper is to consider nest-monotonic two-stage acts, which share their rankings of states with those of their reduced one-stage acts. Our main theorem shows that the axioms, one of which is restricted to nest-monotonic two-stage acts, and consequentialism are satisfied if and only if the preference is exponential CEU, which is such that the probability capacity is an exponential transformation of a probability measure. This result indicates that within a specified range of decision problems, exponential CEU is the only form of CEU that derives indifference to the timing of information resolution. Furthermore, the relation between first- and second-stage exponential CEU is characterized both by the f*-Bayesian updating rule and by comonotonic dynamic consistency. Conditions to establish the law of iterated expectation for CEU are also discussed.     

Unambiguous events and dynamic Choquet preferences

This paper explores the relationship between dynamic consistency and existing notions of unambiguous events for Choquet expected utility preferences. A decision maker is faced with an information structure represented by a filtration. We show that the decision maker’s preferences respect dynamic consistency on a fixed filtration if and only if the last stage of the filtration is composed of unambiguous events in the sense of Nehring (Math Social Sci 38:197–213, 1999). Adopting two axioms, conditional certainty equivalence consistency and constrained dynamic consistency to filtration measurable acts, it is shown that the decision maker respects these two axioms on a fixed filtration if and only if the last stage of the filtration is made up of unambiguous events in the sense of Zhang (Econ Theory 20:159–181, 2002).     

RECURSIVE AMBIGUITY AND MACHINA'S EXAMPLES

Machina (American Economic Review 99 (2009), 385–392; American Economic Review 104 (2014), 3814–40) lists a number of situations where Choquet expected utility, as well as other known models of ambiguity aversion, cannot capture plausible features of ambiguity attitudes. Most of these problems arise in choice over prospects involving three or more outcomes. We show that the recursive nonexpected utility model of Segal (International Economic Review 28 (1987), 175–202) is rich enough to accommodate all these situations and, moreover, that this can be done using the same functional form for all situations.     

An introduction to nanotechnology policy: Opportunities and constraints for emerging and established economies

Nanotechnology has captured wide attention all over the world and excited the imagination of young and old alike. Interest in the subject has increased remarkably during the last few years because of potential technological applications, and commercial interest has skyrocketed. The promise of nanotechnology as an economic engine that can redefine the wellbeing of regions and nations is pervasive; yet the imprecise language, and overuse of the term nanotechnology, has made that term fuzzier, broader, and trendier than many imagined possible. This is especially evident in nanotechnology market projections, which rose dramatically over the past five years as more traditional “product families” were engulfed by the expanding use of the term. Government policy regarding nanotechnology has often resembled an embrace of imagination rather than a systematic use of what Sun Tzu and others have taught about strategic decision making. Further, if nanotechnology is truly the next wave of technology product paradigms, how will we provide an educated workforce to support it? Moreover, in company with these societal benefits come increased societal risks. This paper is intended to provide policy makers and strategists with observations that might limit actions such as those that led to the “over-hype” of nanotechnology and to the fear (or discounting) of societal risks. In the latter case we might learn from the experiences of policy makers connected with other emerging enabling-technology bases, such as nuclear energy and, to a lesser extent, the “dot-com” boom.     

Decision-foundations for properties of nonadditive measures: general state spaces or general outcome spaces

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.     

Optimizing the shares of native tree species in forest plantations with biased financial parameters

Addressing uncertainty is a key requirement to follow the principle of precaution in sustainable ecosystem management. The maximization of worst-case outcomes according to the “maximin” decision rule, based on the two parameters mean and variance of a financial indicator, is a prominent approach to integrate uncertainty in decision-making. In forestry, the problem of selecting the optimum tree species combination for a forest plantation investment can be seen as a problem of optimal portfolio selection, to be solved according to the “maximin” decision rule. Yet, it is well known that portfolios computed from expected means and variances are highly sensitive to changes in the estimated parameters. The financial results may be poor if we rely too much on the historical data. This paper tests an extended worst-case model that considers a lower bound for the expected mean net present value (NPV) of a tree species portfolio and an upper bound for its variance. Biased expected mean NPVs, variances and correlations for the tree species Picea abies [L.] Karst. (Spruce) and Fagus sylvatica L. (Beech) were used to test the variability of the resulting tree species portfolios (27 scenarios). A comprehensive simulated data set, which was adopted from an existing study and defined as the independent reference, served to evaluate the financial performance of the tree species portfolios obtained from optimization with the biased data. Compared with the results of classical worst-case optimization instances, it was feasible to reduce the variability of tree species shares effectively when the optimization was carried out with the extended worst-case approach. Furthermore, the financial performance of this approach was better when tested with the independent data. The worst-case forest NPVs achieved with the extended approach were on average 10% (statistical confidence 0.95) or 147% (statistical confidence 0.99) greater in comparison to the results of the classical approach. The influence of the uncertainty parameter selection was tested and the results were discussed against the controversial viewpoints on the usefulness of the “information-gap decision theory”. Finally, the significance of our results for sustainable ecosystem management is pointed out.     

Anonymous yes–no voting with abstention and multiple levels of approval

Symmetric (3,2) simple games serve as models for anonymous voting systems in which each voter may vote “yes,” abstain, or vote “no,” the outcome is “yes” or “no,” and all voters play interchangeable roles. The extension to symmetric (j,2) simple games, in which each voter chooses from among j ordered levels of approval, also models some natural decision rules, such as pass–fail grading systems. Each such game is determined by the set of (anonymous) minimal winning profiles. This makes it possible to count the possible systems, and the counts suggest some interesting patterns. In the (3,2) case, the approach yields a version of May's Theorem, classifying all possible anonymous voting rules with abstention in terms of quota functions. In contrast to the situation for ordinary simple games these results reveal that the class of simple games with 3 or more levels of approval remains large and varied, even after the imposition of symmetry.     

Player Types and Self-Impression Management in Dictatorship Games: Two Experiments

Recent experimental research on dictatorship games shows that many dictators share their outcomes with unknown, anonymous others. The data suggests that dictators can be “typed” as rational (taking the maximum), equal (splitting outcomes equally), or “other.” This paper experimentally tests the self-impression management model, which predicts that individuals act to show themselves in a positive light, even when they are the only observer of their own behavior. The model predicts that the “other” type of dictator will avoid being greedy by taking more only as their choices are increasingly restricted. Results from two experiments support the model's predictions. The conclusion advocates differentiating basic psychological motivations in modeling individual behavior. Journal of Economic Literature Classification Numbers: C78, C91, D63.     

The Choquet Bargaining Solutions

We axiomatically investigate the problem of rationalizing bargaining solutions by social welfare functions that are linear in every rank-ordered subset of Rⁿ₊ . Such functions, the so-called Choquet integrals, have been widely used in the theories of collective and individual choice. We refer to bargaining solutions that can be rationalized by Choquet integrals as Choquet bargaining solutions. Our main result is a complete characterization of Choquet bargaining solutions. As a corollary of our main result, we also obtain a characterization of the generalized Gini bargaining solutions introduced by Blackorby et al. (1994, Econometrica62, 1161–1178). Journal of Economic Literature Classification Numbers: D71, C78.     

Consistent representative democracy

We study axioms which define “representative democracy” in an environment in which agents vote over a finite set of alternatives. We focus on a property that states that whether votes are aggregated directly or indirectly makes no difference. We call this property representative consistency. Representative consistency formalizes the idea that a voting rule should be immune to gerrymandering. We characterize the class of rules satisfying unanimity, anonymity, and representative consistency. We call these rules “partial priority rules.” A partial priority rule can be interpreted as a rule in which each agent can “veto” certain alternatives. We investigate the implications of imposing other axioms to the list specified above. We also study the partial priority rules in the context of specific economic models.     

Government spending, capital accumulation and the optimal policy rule: The role of public service capital

In this paper, we modify the Djajić [Djajić, S., 1987. “Government Spending and the Optimal Rates of Consumption and Capital Accumulation,” Canadian Journal of Economics 20, 544–554.] model in such a way that government consumption expenditure provides utility to households via the total stock of government services rather than the government consumption flow alone. By using such a framework, we show that the optimality condition for the public service capital stock is the marginal rate of substitution between public service capital and consumption that equals the intertemporal marginal rate of transformation between the two goods. In addition, we show that the relationship between private consumption and public service capital in a household's utility plays an important role in determining the transitional behavior of relevant variables. We also examine the second-best government consumption expenditure policy. By contrast, in the standard flow specification, e.g., Turnovsky and Brock [Turnovsky, S.J. and Brock, W.A., 1980. “Time Consistency and Optimal Government Policies in Perfect Foresight Equilibrium,” Journal of Public Economics 13, 183–212.], Ihori [Ihori, T., 1990. “Government Spending and Private Consumption,” Canadian Journal of Economics 23, 60–69.], and Turnovsky and Fisher [Turnovsky, S.J. and Fisher, W.H., 1995. “The Composition of Government Expenditure and its Consequences for Macroeconomic Performance,” Journal of Economic Dynamics and Control 19, 747–786.], the second-best government consumption expenditure is decided on the basis that the marginal utility of consumption is equal to the discounted sum of the marginal utility of the government's flow spending.     

Subjective Expected Utility Theory with State-Dependent Preferences

This paper extends Savage′s subjective expected utility theory to include state-dependent preferences. The dependence of the decision maker′s preferences over consequences on the states of nature is represented by state-specific mappings of the set of consequences onto itself. Within this framework Savage′s postulates are reformulated and it is shown that there exist subjective expected utility representations of the preference relation over acts with unique, nonatomic, probability measure on the algebra of all events, and a state-dependent utility function over the set of consequences. Journal of Economic Literature Classification Number: D81.     

A theory of natural addiction

Economic theories of rational addiction aim to describe consumer behavior in the presence of habit-forming goods. We provide a biological foundation for this body of work by formally specifying conditions under which it is optimal to form a habit. We demonstrate the empirical validity of our thesis with an in-depth review and synthesis of the biomedical literature concerning the action of opiates in the mammalian brain and their effects on behavior. Our results lend credence to many of the unconventional behavioral assumptions employed by theories of rational addiction, including adjacent complementarity and the importance of cues, attention, and self-control in determining the behavior of addicts. We offer evidence for the special case of the opiates that “harmful” addiction is the manifestation of a mismatch between behavioral algorithms encoded in the human genome and the expanded menu of choices faced by consumers in the modern world.     

Simple sequencing problems with interdependent costs

In this paper we analyze simple sequencing problems under incomplete information and interdependent costs. We prove the necessity of concave cost function for implementability of such problems. Implementability means that one can achieve aggregate cost minimization in ex-post equilibrium. We also show that simple sequencing problems are implementable if and only if the mechanism is a ‘generalized VCG mechanism.’ We then consider first best implementability, that is implementability with budget balancing transfer. We prove that for implementable n agent simple sequencing problems, with polynomial cost function of order (n−2) or less, one can achieve first best implementability. Finally, for the class of implementable simple sequencing problems with “sufficiently well behaved” cost function, this is the only first best class.     

An equilibrium model of a second economy market in a centrally planned economy

We study a CPE in which an identical good is sold on the official market (OM) and a “second economy” market (SEM ). Planners set parameters. Managers divide inputs between markets to maximize expected utility of wealth. Consumers are expected utility maximizers who purchase the good on the OM or SEM. On the OM, excess demand exists at the non-Walrasian price; delivery date is stochastic. The SEM offers immediate availability. Our solution concept involves the rational expectations of managers, the consistency of consumers' decisions, and a market-clearing SEM. We solve for SEM price and supply and investigate various comparative statics.