Performance and payout were only related to how close subjects’ behavior matched the normative optimal solution (thereby incentivizing an accurate correlation representation) but was independent of the actual amount or variance of

the produced energy mix. Importantly, during the experiment subjects never received direct feedback on their performance at minimizing energy fluctuations (i.e., only saw trial-by-trial outcomes) and the bonus and optimal weights were only revealed after the experiment. We omitted feedback during the task to prevent subjects www.selleckchem.com/products/ch5424802.html from using a strategy that is based on optimizing the performance feedback instead of learning the correlation of the individual outcomes. Although the portfolio value is shown on every trial, and the deviance of this value from its mean gives some hints to performance, this is only a crude measure of whether the current weights are good because even with optimal weights the amount of portfolio fluctuation depends on the current correlation. Because the optimal mixing weights (portfolio weights) in our task depend on individual variance from solar and wind power plants and their correlation strength, the best strategy is to learn the variances and correlations by observation of individual outcomes and then translate these estimates into an optimal ABT-888 molecular weight resource allocation (i.e., weightings). Although subjects

could learn the statistical properties underlying outcome generation by observation, the outcomes of individual trials were unpredictable. Their task was then to continuously mix the two resources into an energy portfolio and thereby minimize the fluctuation of the portfolio value from trial to trial. Both resources fluctuated around a common mean, with outcomes drawn from a rectangular distribution with a specific variance. In our task the standard deviation of one resource was always twice that of the other because this maximized the influence of the correlation on the portfolio weights (see Figure S1 for details). The sequence of correlated random numbers for the two resources

were generated by the Cholesky decomposition method (Gentle, 1998). This was realized by first drawing random numbers xA and xB for resources A, B from a rectangular distribution. Temozolomide The outcome of the second resource xB was then modified as xB = xA∗ r + xB∗ sqrt(1 − r2), whereby r is the generative correlation coefficient. Finally, xA and xB were normalized to their desired standard deviations (in the three blocks: 20/10, 15/30, 10/20) and common means (30, 50, 40). We chose a rectangular distribution to increase the sensitivity of our fMRI experiment in finding neural correlates of covariance and covariance prediction errors as the linear regression against BOLD activity is most sensitive if the values of the parametric modulators are distributed along their entire range. This is not true for normal distributed outcomes, which have proportionally the largest amounts of data close to the mean.