Disentangling choice value and choice conflict in sequential decisions under risk

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.

Cognitive models of optimal sequential search with recall

Many everyday decisions require sequential search, according to which available choice options are observed one at a time, with each observation involving some cost to the decision maker. In these tasks, decision makers need to trade-off the chances of finding better options with the cost of search. Optimal strategies in such tasks involve threshold decision rules, which terminate the search as soon as an option exceeding a reward value is found. Threshold rules can be seen as special cases of well-known algorithmic decision processes, such as the satisficing heuristic. Prior work has found that decision makers do use threshold rules, however the stopping thresholds observed in data are typically smaller than the (expected value maximizing) optimal threshold. We put forward an array of cognitive models and use parametric model fits on participant-level search data to examine why decision makers adopt seemingly suboptimal thresholds. We find that people's behavior is consistent with optimal search if we allow participants to display risk aversion, psychological effort cost, and decision error. Thus, decision makers appear to be able to search in a resource-rational manner that maximizes stochastic risk averse utility. Our findings shed light on the psychological factors that guide sequential decision making, and show how threshold models can be used to describe both computational and algorithmic aspects of search behavior.

Comparison between best-response dynamics and replicator dynamics in a social-ecological model of lake eutrophication

Social-ecological models are often used to investigate the mutual interactions between an ecological system and human behaviour at a collective level. The social system is widely represented either by the replicator dynamics or by the best-response dynamics. We investigate the consequences of choosing one or the other with the example of a social-ecological model for eutrophication in shallow lakes, where the anthropogenic discharge of pollutants into the water is determined by a behavioural model using the replicator or a best-response dynamics. We discuss a fundamental difference between the replicator dynamics and the logit formulation of the best-response dynamics. This fundamental difference results in a different number of equilibria. We show that the replicator equation is a limit case of the best-response model, when agents are assumed to behave with infinite rationality. If agents act less rationally in the model using the best-response dynamics, the correspondence with the model using the replicator dynamics decreases. Finally, we show that sustained oscillations observed in both cases may differ substantially. The replicator dynamics makes the amplitude of the limit cycle become larger and makes the system come closer to full cooperation or full defection. Thus, the dynamics along the limit cycle imply a different risk for the system to be pushed by a perturbation into a desirable or an undesirable outcome depending on the socioeconomic dynamics assumed in the model. When analyzing social-ecological models, the choice of a socioeconomic dynamics is often little justified but our results show that it may have dramatic impacts on the coupled human-environment system.