Fig 1.
Shaded grey areas represent decision settings after the IP (i.e., the point at which leaving the patch has the same expected utility as staying in the patch). Decisions made after the IP have lower choice conflict (black) than those made at the IP, and are thus crucial to discriminate conflict from the monotonically increasing switch value (blue). In Patch 1, for example, switch value and conflict are perfectly correlated. The decisions shown here were taken from 3 trials in our task of a participant in Experiment 1, but help illustrating a general pattern in foraging and sequential decision-making tasks.
Fig 2.
A: Example of two rounds of the ‘pig’ dice game, the top one ending with a decision to stop and a reward of 130, the bottom one ending because of a rolled 1 and with no reward. B: Probability of stopping (shaded areas) as a function of the cumulative sum within a round for a simulated risk-neutral player. The IPs (dashed lines) for the 1/6, 2/6, and 3/6 conditions are, respectively: 40, 85, and 200. C: Percentage of decisions before and after the IP for a simulated group of players with different risk preferences (risk neutral on average). The number of decisions made after reaching the IP increases with the probability of losing, making the task more balanced. D: Percentage of decisions made after the IP as a function of the IP itself, for the same group of simulated participants as in C. Participants with higher IPs (more risk seeking) experience a more imbalanced task in the 2/6 and 1/6 conditions.
Fig 3.
Regression analyses Experiment 1.
The left column shows the results of the logistic model fit on choice data, while the right column shows the results of the linear model fit on RTs. A Posterior distribution of the cumulative sum of rewards coefficient at the group level (the shaded area is the 95% HDI), when we predict the probability of stopping within a round. B Estimated logistic curve (colored shaded area) and the IP (grey shaded area) at the group level. C Distribution of trials before and after the estimated IP. D Posterior distributions of the round number, draw number within a round, and cumulative sum of rewards coefficients at the group level (the shaded area is the 95% HDI), when we predict RTs. E Posterior predictives of mean RT data as the probability of stopping increases within a round, against the mean RT data. F Comparison of the same posterior predictives, selectively at the points of maximum conflict and at the points of maximum probability of stopping. Here the vertical lines represent the data while the shaded bars are the predictions.
Fig 4.
Regression analyses Experiment 2.
The left column shows the results of the logistic model fit on choices, while the right column shows the results of the linear model fit on RTs. A: Posterior distribution of the cumulative sum of rewards coefficients (separate per condition) at the group level (the shaded area is the 95% HDI), when we predict the probability of stopping within a round. B: Estimated logistic curves (colored shaded area) and the IP (grey shaded area) at the group level. C: Distribution of trials before and after the estimated IP, separately by condition. D: Posterior distributions of the round number, draw number within a round, and cumulative sum of rewards coefficients at the group level (the shaded area is the 95% HDI), when we predict RTs.E: Posterior predictives of mean RT as the probability of stopping increases within a round. F: Comparison of the posterior predictives, selectively at the points of maximum conflict and at the points of maximum probability of stopping. Here the vertical lines represent the data while the shaded bars are the predictions.
Fig 5.
Model comparison of diffusion decision models (DDMs) based on WAIC (data: Experiment 2).
All the models included here have their drift-rate modulated by the cumulative sum of rewards, while their thresholds and starting-point could be either fixed (not modulated), or modulated by either the decision number or the cumulative sum of rewards. Lower WAICs indicate better fits to data after accounting for model complexity. The bars represent the estimated WAICse. **Best model. *These models do not fit credibly worse than the best model.
Fig 6.
A: Posterior distribution of the cumulative sum of rewards coefficients (separate per condition) at the group level (the shaded area is the 95% HDI) for three of the DDM parameters. B: Posterior predictives of mean RT data as the probability of stopping increases within a round. C: Distribution of trials after the estimated IP, separately by condition.D: Comparison of the posterior predictives, selectively at the points of maximum conflict and at the points of maximum probability of stopping. Here, the vertical lines represent the data while the shaded bars are the predictions.