Expectations of reward and efficacy guide cognitive control allocation

Figures

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  Fig. 1. The expected value of control (EVC) model predicts that control should increase with expected reward and efficacy. A EVC model. Control intensity is chosen to optimize the trade-off between effort costs and payoff, maximizing the expected value of the control. The payoff of a given control signal is determined by the expected reward and efficacy for a given control intensity. B The EVC model proposes that higher intensities of control (x axis) are associated with greater effort costs (red) but that these effort costs can be outweighed by the expected payoff for a given control intensity (blue). These payoffs typically increase as a function of task performance, and task performance typically improves as a function of control intensity. The EVC of each control intensity (purple) is calculated as the difference between its payoff and its cost. The optimal level of control to invest is the one that maximizes EVC (vertical black arrows). Left: When the expected reward for performing the task well is higher (from dashed to the solid line), higher control intensities achieve even higher payoffs. Right: When performance matters less for acquiring a given reward (low efficacy (dashed…

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  Fig. 2. Manipulation of expected reward and efficacy. On each trial, participants view an incentive cue followed by a Stroop stimulus (target) and then feedback indicating how much reward they received. Four different cues indicate whether a trial is high or low in reward and efficacy. The P3b and CNV event-related potentials are measured during the interval between cue and target, as indices of cue evaluation (P3b) and control allocation (CNV).

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  Fig. 3. Reward and efficacy improve performance. Across Studies 1–3, participants were fastest to give a correct response when both reward and efficacy were high, suggesting that these variables jointly determined control allocation. Panels A and B show average RTs for each of the four conditions when the reward ($0.10 or $1.00) and efficacy (0% or 100%) were varied dichotomously in Study 1, n = 21 participants (A) and Study 2, n = 44 participants (B) (see Fig. 2). Error bars represent the within-subject standard error of the mean. Panel C shows the estimated effect of parametrically varied levels of reward ($0.10, $0.20, $0.40, or $0.80) and efficacy (25%, 50%, 75%, or 100%) in Study 3, n = 35 participants, based on a linear mixed-effect model. For visual comparison with panels A and B, this is shown based on a fit to within-subject z-scored accurate RT (therefore omitting random intercepts), but the statistics reported in the text are based on the full model. Shaded error bars represent the standard error of the mean. Source data are provided as a Source Data file.

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  Fig. 4. P3b and contingent negative variation (CNV) amplitudes track increases in expected reward and efficacy. A ERP averages for each incentive condition, separately for the P3b (top) and CNV (bottom). Shaded areas indicate time windows used for quantification. Topographies show group-level (fixed-effect) contrasts for reward and efficacy, respectively. B Average ERP amplitudes within the relevant time windows show that the magnitude of the (positive-going) P3b and the (negative-going) CNV increase with greater reward and efficacy. The CNV but not the P3b tracked the interaction of reward and efficacy, mirroring the behavioral effects of these incentives (cf. Fig. 3). Error bars represent the within-subject standard error of the mean. C, D Fixed (group-level) effects of ERP amplitude on accuracy (C) and accurate RT (D) show that increased P3b and CNV predicted better performance when the target appeared. Shaded error bars represent the standard error of the mean. A–D n = 44 participants. Source data are provided as a Source Data file.