Probability Weighting as Evolutionary Second-best

The economic concept of the second-best involves the idea that multiple simultaneous deviations from a hypothetical first-best optimum may be optimal once the first-best itself can no longer be achieved, since one distortion may partially compensate for another. Within an evolutionary framework, we translate this concept to behavior under uncertainty. We argue that the two main components of prospect theory, the value function and the probability weighting function, are complements in the second-best sense. Previous work has shown that an adaptive S-shaped value function may be evolutionary optimal if decision-making is subject to cognitive or perceptive constraints. We show that distortions in the way probabilities are perceived can further enhance fitness. The second-best optimum involves overweighting of small and underweighting of large probabilities. Behavior as described by prospect theory might therefore be evolution's second-best solution to the fitness maximization problem. We discuss under which circumstance our model makes empirically testable predictions about the relation between individuals' value and probability weighting functions.Probability Weighting, Prospect Theory, Evolution of Preferences

Competitive Screening in Insurance Markets with Endogenous Labor Supply

We examine equilibria in competitive insurance markets when individuals take unobservable labor supply decisions. Precautionary labor motives intro-duce countervailing incentives in the insurance market, and equilibria with positive profits can occur even in the standard case in which individuals exogenously differ in risk only. We then extend the model to allow for both privately known risks and labor productivities. This endogenously introduces two-dimensional heterogeneity in the insurance market since precautionary labor effects lead to differences in income and hence risk aversion. Under these circumstances, separating and pooling equilibria exist, which generally differ from those with exogenous two-dimensional heterogeneity considered by the existing literature. Notably, in contrast to standard screening models, profits may be increasing with insurance coverage, and the correlation between risk and coverage can be zero or negative in equilibrium, a phenomenon frequently observed in empirical studies.Insurance markets, adverse selection, precautionary labor

Competitive Screening in Insurance Markets with Endogenous Wealth Heterogeneity

We examine equilibria in competitive insurance markets with adverse selection when wealth differences arise endogenously from unobservable savings or labor supply decisions. The endogeneity of wealth implies that high risk individuals may ceteris paribus exhibit the lower marginal willingness to pay for insurance than low risks, a phenomenon that we refer to as irregular-crossing preferences. In our model, both risk and patience (or productivity) are privately observable. In contrast to the models in the existing literature, where wealth heterogeneity is exogenously assumed, equilibria in our model no longer exhibit a monotone relation between risk and coverage. Individuals who purchase larger coverage are no longer higher risks, a phenomenon frequently observed in empirical studies.Insurance Markets, Adverse Selection, Multidimensional Screening

Competitive Markets without Commitment

In the presence of a time-inconsistency problem with optimal agency contracts, we show that competitive markets implement allocations that Pareto dominate those achieved by a benevolent planner, they induce strictly more effort, and they sometimes make the commitment problem disappear entirely. In particular, we analyze a model with moral hazard and two-sided lack of commitment. After agents have chosen a hidden effort and the need to provide incentives has vanished, firms can modify their contracts and agents can switch firms. As long as the ex-post market outcome satisfies a weak notion of competitiveness and sufficiently separates individuals who choose different effort levels, the market allocation is Pareto superior to a social planner’s allocation. We construct a specific market game that naturally generates robust equilibria with these properties. In addition, we show that equilibrium contracts without commitment are identical to those with full commitment if the latter involve no cross-subsidization between individuals who choose different effort levels.Time-Inconsistency, Moral Hazard, Competitive Markets, Adverse Selection

Taxation, Insurance and Precautionary Labor

We examine optimal taxation and social insurance if insurance markets are imperfect. This requires the development of a theory of labor supply under uncertainty. We show that the case for social insurance is not generally reinforced by adverse selection in insurance markets as social insurance will have welfare-decreasing effects on the labor market. Furthermore, positive and normative implications are highly sensitive to the insurance market equilibrium concept. While for the Rothschild-Stiglitz case social insurance at least alleviates the inefficiency of underinsurance, with a Wilson pooling equilibrium this inefficiency might even be worsened by social insurance. This sheds new light on the question whether social insurance is an appropriate means of redistribution in the presence of an optimally chosen tax schedule

Probability weighting as evolutionary second-best

The economic concept of the second-best involves the idea that multiple simultaneous deviations from a hypothetical first-best optimum may be optimal once the first-best itself can no longer be achieved, since one distortion may partially compensate for another. Within an evolutionary framework, we translate this concept to behavior under uncertainty. We argue that the two main components of prospect theory, the value function and the probability weighting function, are complements in the second-best sense. Previous work has shown that an adaptive S-shaped value function may be evolutionary optimal if decision-making is subject to cognitive or perceptive constraints. We show that distortions in the way probabilities are perceived can further enhance fitness. The second-best optimum involves overweighting of small and underweighting of large probabilities. Behavior as described by prospect theory might therefore be evolution's second-best solution to the fitness maximization problem. Our model makes empirically testable predictions about the relation between individuals' value and probability weighting functions

Second-best probability weighting

Non-linear probability weighting is an integral part of descriptive theories of choice under risk such as prospect theory. But why do these objective errors in information processing exist? Should we try to help individuals overcome their mistake of overweighting small and underweighting large probabilities? In this paper, we argue that probability weighting can be seen as a compensation for preexisting biases in evaluating payoffs. In particular, inverse S-shaped probability weighting is a flipside of S-shaped payoff valuation. Probability distortions may thus have survived as a second-best solution to a fitness maximization problem, and it can be counter-productive to correct them while keeping the value function unchanged

Competitive Markets without Commitment

In the presence of a time-inconsistency problem with optimal agency contracts, we show that competitive markets implement allocations that Pareto dominate those achieved by a benevolent planner, they induce strictly more effort, and they sometimes make the commitment problem disappear entirely. In particular, we analyze a model with moral hazard and two-sided lack of commitment. After agents have chosen a hidden effort and the need to provide incentives has vanished, firms can modify their contracts and agents can switch firms. As long as the ex-post market outcome satisfies a weak notion of competitiveness and sufficiently separates individuals who choose different effort levels, the market allocation is Pareto superior to a social planner's allocation. We construct a specific market game that naturally generates robust equilibria with these properties. In addition, we show that equilibrium contracts without commitment are identical to those with full commitment if the latter involve no cross-subsidization between individuals who choose different effort levels

ATP as Phosphorus and Nitrogen Source for Nutrient Uptake by Fagus sylvatica and Populus x canescens Roots

The present study elucidated whether roots of temperate forest trees can take up organic phosphorus in the form of ATP. Detached non-mycorrhizal roots of beech (Fagus sylvatica) and gray poplar (Populus x canescens) were exposed under controlled conditions to 33P-ATP and/or 13C/15N labeled ATP in the presence and absence of the acid phosphatase inhibitor MoO42-. Accumulation of the respective label in the roots was used to calculate 33P, 13C and 15N uptake rates in ATP equivalents for comparison reason. The present data shown that a significant part of ATP was cleaved outside the roots before phosphate (Pi) was taken up. Furthermore, nucleotide uptake seems more reasonable after cleavage of at least one Pi unit as ADP, AMP and/or as the nucleoside adenosine. Similar results were obtained when still attached mycorrhizal roots of adult beech trees and their natural regeneration of two forest stands were exposed to ATP in the presence or absence of MoO42-. Cleavage of Pi from ATP by enzymes commonly present in the rhizosphere, such as extracellular acid phosphatases, ecto-apyrase and/or nucleotidases, prior ADP/AMP/adenosine uptake is highly probable but depended on the soil type and the pH of the soil solution. Although uptake of ATP/ADP/AMP cannot be excluded, uptake of the nucleoside adenosine without breakdown into its constituents ribose and adenine is highly evident. Based on the 33P, 13C, and 15N uptake rates calculated as equivalents of ATP the ‘pro and contra’ for the uptake of nucleotides and nucleosides is discussed.Short SummaryRoots take up phosphorus from ATP as Pi after cleavage but might also take up ADP and/or AMP by yet unknown nucleotide transporter(s) because at least the nucleoside adenosine as N source is taken up without cleavage into its constituents ribose and adenine

Frontiers: Polarized America: From political polarization to preference polarization

In light of the widely discussed political divide and increasing societal polariza-tion, we investigate in this paper whether the polarization of political ideology extends to consumers’ preferences, intentions, and purchases. Using three different data sets—the publicly available social media data of over three million brand followerships of Twitter users, a YouGov brand-preference survey data set, and Nielsen scanner panel data—we assess the evolution of brand-preference polarization. We find that the apparent polarization in political ideologies after the election of Donald Trump in 2016 stretches further to the daily lives of consumers. We observe increased polarization in preferences, behavioral intentions, and actual purchase decisions for consumer brands. Consistent with compensa-tory consumption theory, we find that the increase in polarization following the election of Donald Trump was stronger for liberals relative to conservatives, and that this asymmetric polarization is driven by consumers’ demand for “Democratic brands” rather than the sup-ply of such brands. From a brand perspective, there is evidence that brands that took a political stance observed a shift in their customer base in terms of their customers’ political affiliation. We provide publicly available (http://www.social-listening.org) access to the unique Twitter-based brand political affiliation scores