Utility functions predict variance and skewness risk preferences in monkeys

Abstract

Utility is the fundamental variable thought to underlie economic choices. In particular, utility functions are believed to reflect preferences toward risk, a key decision variable in many real-life situations. To assess the validity of utility representations, it is therefore important to examine risk preferences. In turn, this approach requires formal definitions of risk. A standard approach is to focus on the variance of reward distributions (variance-risk). In this study, we also examined a form of risk related to the skewness of reward distributions (skewness-risk). Thus, we tested the extent to which empirically derived utility functions predicted preferences for variance-risk and skewness-risk in macaques. The expected utilities calculated for various symmetrical and skewed gambles served to define formally the direction of stochastic dominance between gambles. In direct choices, the animals' preferences followed both second-order (variance) and third-order (skewness) stochastic dominance. Specifically, for gambles with different variance but identical expected values (EVs), the monkeys preferred high-variance gambles at low EVs and low-variance gambles at high EVs; in gambles with different skewness but identical EVs and variances, the animals preferred positively over symmetrical and negatively skewed gambles in a strongly transitive fashion. Thus, the utility functions predicted the animals' preferences for variance-risk and skewness-risk. Using these well-defined forms of risk, this study shows that monkeys' choices conform to the internal reward valuations suggested by their utility functions. This result implies a representation of utility in monkeys that accounts for both variance-risk and skewness-risk preferences.experimental economics | stochastic dominance | choice | decision making | neuroeconomics F uture rewards can rarely be predicted with complete accuracy; often, they are inherently risky. A principled approach with well-defined forms of risk is therefore highly desirable for a thorough understanding of economic decisions. Good definitions of risk are available when considering rewards as probability distributions of different values. For instance, rewards can fluctuate symmetrically around a mean value, a form of risk captured by the statistical variance. This simple form of risk is commonly studied by economists, ethologists, and neurophysiologists (1-9). Reward distributions are often asymmetrical, however. This asymmetry can be described formally by considering the statistical "skewness" or "skewness-risk." For instance, a tree may usually be barren but occasionally be rich with fruit (positive skewness), or a bush may produce a handful of berries most of the time but occasionally yield nothing (negative skewness). Skewness is an important form of risk that is abundant in natural environments, and thus is also likely to be of fundamental importance for the animals' behavior. Despite their prevalence in real-life situations, preferences for these distinct forms of risk are not well char...

Monkeys choose as if maximizing utility compatible with basic principles of revealed preference theory

“…Thus, the behavioral data obtained with two-good choice options (bundles) compared well with data from single-good options tested in the same animals. Further similarities between of our bundle options and previously used singlegood options are seen with higher choice frequencies for larger, more frequent, or subjectively higher valued rewards (18)(19)(20)(21)(22)(23)(24) and with satisfaction of transitivity in noisy choices (9,24). Taken together, our use of choice options with two goods (bundles) did not seem to generate undue choice biases.…”

“…Thus, when presented with a set of several feasible options to which the animal revealed noisy preference or indifference, the choices from a smaller subset or larger set containing some previously chosen and unchosen elements should be similarly frequent. For several months before undergoing these tests, our monkeys had experienced a stable reward distribution, which is known to slow behavioral adaptations (36) and to render economic choices resistant to short-term adaptation (9). Such stable conditions would favor investigating the influence of option set size on preferences with little intervening adaptation to instantaneous change of option distributions.…”

“…skewed gambles follows third-order stochastic dominance and prediction from empirical utility functions (9), and their amygdala neurons code internally represented values across multistep reward-saving behavior (10). Important for trading, monkeys exchange tokens for food (11,12) and smartly trade stolen items (13).…”

A normative account of choice history effects in mice and humans

“…This effect is distinct from reward history effects, which are predominantly associated with the volatility of the reward probabilities. Choice history effects are also distinct from the reaction times, which (Behrens et al, 2007;Genest, Stauffer, & Schultz, 2016;Kheifets, Freestone, & Gallistel, 2017) reflects the overall reward rates averaged over the options.…”

“…Animal behavior must be tuned to environmental statistics to maintain its adaptive function (Genest et al, 2016;Kheifets et al, 2017;Behrens et al, 2007). Different dynamics can be discerned in natural habitats that are expected to shape foraging decisions.…”