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Schultz, W.

Publications and source records attributed to Schultz, W..

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Compliance with the continuity axiom of Expected Utility Theory supports utility maximization in monkeys

Expected Utility Theory (EUT), the first axiomatic theory of risky choice, describes choices as a utility maximization process: decision makers assign a subjective value (utility) to each choice option and choose the one with the highest utility. The continuity axiom, central to EUT and its modifications, is a necessary and sufficient condition for the definition of numerical utilities. The axiom requires decision makers to be indifferent between a gamble and a specific probabilistic combination of a more preferred and a less preferred gamble. While previous studies demonstrated that monkeys choose according to combinations of objective reward magnitude and probability, a concept-driven experimental approach for assessing the axiomatically defined conditions for maximizing subjective utility by animals is missing. We experimentally tested the continuity axiom for a broad class of gamble types in four male rhesus macaque monkeys, showing that their choice behavior complied with the existence of a numerical utility measure as defined by the economic theory. We used the numerical quantity specified in the continuity axiom to characterize subjective preferences in a magnitude-probability space. This mapping highlighted a trade-off relation between reward magnitudes and probabilities, compatible with the existence of a utility function underlying subjective value computation. These results support the existence of a numerical utility function able to describe choices, allowing for the investigation of the neuronal substrates responsible for coding such rigorously defined quantity. SIGNIFICANCE STATEMENTA common assumption of several economic choice theories is that decisions result from the comparison of subjectively assigned values (utilities). This study demonstrated the compliance of monkey behavior with the continuity axiom of Expected Utility Theory, implying a subjective magnitude-probability trade-off relation which supports the existence of numerical subjective utility directly linked to the theoretical economic framework. We determined a numerical utility measure able to describe choices, which can serve as a correlate for the neuronal activity in the quest for brain structures and mechanisms guiding decisions.

animal behavior and cognition

Let a monkey do your bidding: Reward valuation in an auction-like mechanism

Economic choice is thought to involve the elicitation of the subjective values of the choice options. Thus far, value estimation in animals has relied upon stochastic choices between multiple options presented in repeated trials and expressed from averages of dozens of trials. However, subjective reward valuations are made moment-to-moment and do not always require alternative options; their consequences are usually felt immediately. Here we describe a Becker-DeGroot-Marschak (BDM) auction-like mechanism that provides more direct and simple valuations with immediate consequences. The BDM encourages agents to truthfully reveal their true subjective value in individual choices (incentive compatibility). Monkeys reliably placed well-ranked BDM bids for up to five juice volumes while paying from a water budget. The bids closely approximated the average subjective values estimated with conventional binary choices, thus demonstrating procedural invariance and aligning with the wealth of knowledge acquired with these less direct estimation methods. The feasibility of BDM bidding in monkeys paves the way for an analysis of subjective neuronal value signals in single trials rather than from averages; the feasibility also bridges the gap to the increasingly used BDM method in human neuroeconomics. SignificanceThe subjective economic value of rewards cannot be measured directly but must be inferred from observable behavior. Until now, the estimation method in animals was rather complex and required comparison between several choice options during repeated choices; thus, such methods did not respect the imminence of the outcome from individual choices. However, human economic research has developed a simple auction-like procedure that can reveal in a direct and immediate manner the true subjective value in individual choices (Becker-DeGroot-Marschak, BDM, mechanism). The current study implemented this mechanism in rhesus monkeys and demonstrates its usefulness for eliciting meaningful value estimates of liquid rewards. The mechanism allows future neurophysiological assessment of subjective reward value signals in single trials of controlled animal tasks.

animal behavior and cognition

How we choose multi-component rewards

Realistic, everyday rewards contain multiple components. An apple has taste and size. However, we choose in single dimensions, simply preferring some apples to others. How can such single-dimensional preference relationships refer to multi-component choice options? Here, we measured how stochastic choices revealed preferences for two-component milkshakes. The preferences were intuitively graphed as indifference curves that represented the orderly integration of the two components as trade-off: parts of one component were given up for obtaining one additional unit of the other component without a change in preference. The well-ordered, non-overlapping curves satisfied leave-one-out tests, followed predictions by machine learning decoders and correlated with single-dimensional Becker-DeGroot-Marschak (BDM) auction-like bids for the two-component rewards. This accuracy suggests a decision process that integrates multiple reward components into single-dimensional estimates in a systematic fashion. In inter-species comparisons, human performance matched that of highly experienced laboratory monkeys, as measured by accuracy of the critical trade-off between bundle components. These data describe the nature of choices of multi-component choice options and attest to the validity of the rigorous economic concepts and their convenient graphic schemes for explaining choices of human and non-human primates. The results encourage formal behavioral and neural investigations of normal, irrational and pathological economic choices.

neuroscience