In a 30-period laboratory newsvendor experiment with and without demand-distribution information, D'Urso, Di Mauro, Chiacchio and Compagno (2017) estimated, for each participant, an anchoring-and-adjustment decision rule in which the period order is the sum of an anchor term (a fixed anchor plus a weight aa on the running sample mean of demand) and an adjustment term (an exponentially smoothed deviation from that mean, smoothed by bb and amplified by kk). They found that anchor composition differs systematically with information: without distribution information most participants anchor on the progressive sample mean, whereas with it most use a fixed anchor, and information brings no profit advantage. The paper left open four linked questions that define the cognitive micro-foundations and the practical value of this parametrization: which measurable individual traits determine the parameter vector (a,C,b,k)(a, C, b, k); whether the information-dependent anchoring patterns found in the high-profit regime (critical ratio 0.75) generalize to the low-profit regime (critical ratio below 0.5); how anchors form from small-sample experience and how anchor versus adjustment weights evolve over longer horizons; and whether individual-level parameter estimates can inform effective debiasing, training, or contract interventions. Later experiments relate traits and personality to bias and profit outcomes rather than to the anchor and adjustment parameters, learning models do not decompose dynamics into anchor versus adjustment weights, and existing debiasing and contract studies are not parameter-informed. All four components remain open.

Background

The newsvendor problem is the canonical single-period inventory decision: a buyer must order a quantity QQ before stochastic demand DD is realized, earning unit price pp per unit sold, paying unit cost cc per unit ordered, and salvaging unsold units at ss per unit. A risk-neutral decision maker who knows the demand distribution FF orders the quantile Q∗=F−1[(p−c)/(p−s)]Q^{*}=F^{-1}[(p-c)/(p-s)], where the fraction (p−c)/(p−s)(p-c)/(p-s) is called the critical ratio. When this ratio exceeds one half (the high-profit condition) the optimal order lies above mean demand; when it is below one half (the low-profit condition) the optimal order lies below mean demand.

Laboratory experiments starting with Schweitzer and Cachon (2000) showed that human orders systematically deviate from Q∗Q^{*} toward the mean demand in both regimes — the so-called pull-to-center effect — and motivated two families of mechanistic explanations: anchoring-and-adjustment (decision makers anchor on a salient quantity such as the mean demand and adjust insufficiently toward the optimum) and demand chasing (orders track the previous period's realized demand). Benzion, Cohen, Peled and Shavit (2008) documented these deviations across profit levels and demand distributions. Individual differences matter as well: Moritz, Hill and Donohue (2013) showed that scores on the cognitive reflection test (CRT), a three-item instrument distinguishing intuitive from deliberative responders, predict who is less affected by pull-to-center in the high-margin condition, and Ren and Croson (2013) linked the bias to overconfidence about demand variability. Measurement itself is delicate: Lau and Bearden (2013) showed by simulation that several popular demand-chasing metrics produce false positives and recommended a simple order-demand correlation instead.

D'Urso, Di Mauro, Chiacchio and Compagno (2017) unified these threads in a single estimable decision rule. In each period tt the order is Qt=a Dmp,t−1+C+k AtQ_t = a\,D_{mp,t-1} + C + k\,A_t, where Dmp,t−1D_{mp,t-1} is the progressive mean of demand observed through period t−1t-1, At=b (Dt−1−Dmp,t−1)+(1−b) At−1A_t = b\,(D_{t-1}-D_{mp,t-1}) + (1-b)\,A_{t-1} is an exponentially smoothed deviation of the last demand from that mean, aa is the weight on the progressive-mean anchor (aa near 1 means a self-updating sample-mean anchor, aa near 0 means a fixed anchor absorbed into the constant CC), bb is the smoothing weight on the most recent demand signal, and kk amplifies or damps the accumulated adjustment. Boundary values of the parameters nest the classical heuristics (mean anchoring, demand chasing, the optimum). Estimating the rule by ordinary least squares per participant in a 30-period high-profit treatment (critical ratio 0.75, demand mean 100, standard deviation 30, optimum 120) under two information conditions — INFO, in which the demand distribution's parameters are announced, and NO INFO, in which they are not — they found strong heterogeneity: 47% of NO INFO participants had a=1a=1 against 26% in INFO, while 57% of INFO participants had a<0.2a<0.2, with anchor parameters differing significantly between treatments only in the final periods (21-30), and no profit advantage from information.

Related learning research had already established that experience alone improves performance only slowly: Bolton and Katok (2008) showed that how experience and feedback are organized matters more than repetition, Bostian, Holt and Smith (2008) fitted an adaptive learning model with memory and reinforcement to individual pull-to-center paths, Lurie and Swaminathan (2009) found that less frequent feedback can improve decisions, and Gavirneni and Xia (2009) observed that subjects do not anchor on one fixed value but select anchors closer to the optimum. None of these, however, characterizes how the anchor and adjustment components of a decomposed rule like the D'Urso et al. model emerge from small samples and reweight with experience — the dynamics question at the heart of the present problem.

Problem Statement

For the individual-level anchoring-and-adjustment model of newsvendor ordering Qt=a Dmp,t−1+C+k AtQ_t = a\,D_{mp,t-1} + C + k\,A_t with At=b (Dt−1−Dmp,t−1)+(1−b) At−1A_t = b\,(D_{t-1}-D_{mp,t-1}) + (1-b)\,A_{t-1}, where Dmp,t−1D_{mp,t-1} is the progressive sample mean of demand and the boundary values of (a,C,b,k)(a, C, b, k) nest mean anchoring, progressive-mean anchoring, demand chasing, and the optimal order: (1) identify, with adequate statistical power and appropriate handling of the near-collinearity between aa and CC, which measurable individual traits (such as cognitive reflection, overconfidence or overprecision (excessively narrow subjective confidence intervals), belief in the law of small numbers (the erroneous expectation that small samples faithfully reflect the population), decision style, and personality inventories) determine the estimated parameter values and thereby predict whether a person adopts a fixed-anchor versus progressive-mean anchor and how strongly they adjust, in the information and no-information conditions of the repeated newsvendor task; (2) determine experimentally whether the documented information-dependent anchoring patterns of the high-profit regime (critical ratio 0.75) — more fixed anchors under announced demand-distribution information, more progressive-mean anchors without it — generalize to the low-profit regime (critical ratio below 0.5), using the same individual-level estimation; (3) characterize the causal pathway by which anchors form from small-sample experience, and how the anchor weight aa and the adjustment weights bb and kk evolve as the decision horizon extends beyond the 30 periods studied; and (4) evaluate whether interventions — debiasing, training, or supply-chain contract design — that are informed by the individual parameter estimates measurably improve ordering performance relative to uninformed baselines. The four components are linked by one scientific objective: to establish and exploit the cognitive micro-foundations of the anchoring-and-adjustment parametrization of newsvendor behavior; the four components are jointly necessary to that objective, so a solution that addresses only some of them leaves the remaining components open.

References

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