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Recent years have witnessed a surge of interest in understanding the neural and cognitive dynamics that drive sequential decision making in general and foraging behavior in particular. Due to the intrinsic properties of most sequential decision-making paradigms, however, previous research in this area has suffered from the difficulty to disentangle properties of the decision related to (a) the value of switching to a new patch versus, which increases monotonically, and (b) the conflict experienced between choosing to stay or leave, which first increases but then decreases after reaching the point of indifference between staying and switching. Here, we show how the same problems arise in studies of sequential decision-making under risk, and how they can be overcome, taking as a specific example recent research on the 'pig' dice game. In each round of the 'pig' dice game, people roll a die and accumulate rewards until they either decide to proceed to the next round or lose all rewards. By combining simulation-based dissections of the task structure with two experiments, we show how an extension of the standard paradigm, together with cognitive modeling of decision-making processes, allows to disentangle properties related to either switch value or choice conflict. Our study elucidates the cognitive mechanisms of sequential decision making and underscores the importance of avoiding potential pitfalls of paradigms that are commonly used in this research area., Competing Interests: The authors have declared that no competing interests exist.

[This corrects the article DOI: 10.1371/journal.pcbi.1003309.].

Understanding the cognitive and neural processes that underlie human decision making requires the successful prediction of how, but also of when, people choose. Sequential sampling models (SSMs) have greatly advanced the decision sciences by assuming decisions to emerge from a bounded evidence accumulation process so that response times (RTs) become predictable. Here, we demonstrate a difficulty of SSMs that occurs when people are not forced to respond at once but are allowed to sample information sequentially: The decision maker might decide to delay the choice and terminate the accumulation process temporarily, a scenario not accounted for by the standard SSM approach. We developed several SSMs for predicting RTs from two independent samples of an electroencephalography (EEG) and a functional magnetic resonance imaging (fMRI) study. In these studies, participants bought or rejected fictitious stocks based on sequentially presented cues and were free to respond at any time. Standard SSM implementations did not describe RT distributions adequately. However, by adding a mechanism for postponing decisions to the model we obtained an accurate fit to the data. Time-frequency analysis of EEG data revealed alternating states of de- and increasing oscillatory power in beta-band frequencies (14-30 Hz), indicating that responses were repeatedly prepared and inhibited and thus lending further support for the existence of a decision not to decide. Finally, the extended model accounted for the results of an adapted version of our paradigm in which participants had to press a button for sampling more information. Our results show how computational modeling of decisions and RTs support a deeper understanding of the hidden dynamics in cognition.