Contingent reasoning and quality of decision-making in different risk contexts

The main intervention is that subjects are either in a Correlated Risk treatment, a Risk treatment, or a Certain treatment. In the Correlated Risk treatment, the subjects face problems with correlated risk. In the Risk treatment, subjects face problems with independent risk. In the Certain treatment, subjects face problems without any uncertainty.

The secondary intervention is that in each treatment, subjects experience two types of decision-making environments: optimization problems, and payoff-equivalent lotteries choices. Therefore, we can also compare the behavior difference between these two choice environments.

Finally, a third intervention is that the optimization problems can be further divided to two types of problems. In the first type, the ratios of high and low values are greater than 2 (and smaller than 6). In this type of problems, choosing a low bid is optimal in the first two treatments unless the subjects are sufficiently risk seeking, and choosing a low bid is definitely optimal in the Certain treatment. In the second type, the ratios of high and low values are smaller than 1.5 (and greater than 1). In this type of problems, choosing a high bid stochastically dominates choosing a low bid, and is therefore optimal, in all treatments.

2025-04-01

2025-10-01

There are two main outcomes variables: 1. The rate of choosing the optimal bid for each type of optimization problems. 2. The rate of choosing the (dominant) choices for each type of lotteries.

Our experiment is to investigate the effect of risk contexts (correlated risk, risk, and certainty) on the quality of decision-making (both in optimization problems and in lottery choices). Thus, by varying the risk contexts, we aim to compare two major aspects of decision-making under uncertainty: whether people are able to perform well in optimization problems, and whether they can choose the (dominant) choices in lottery environment, across different risk contexts.

Consistency between the optimization-problem environment and lottery environment.

The consistency between optimization problems and lottery choices can reflect the effect of computational and understanding complexity between these two types of environments.

The experiment is about how the risk contexts of both optimization problems and lottery choices affect contingent thinking and decision-making. For the optimization problem, we consider the Acquiring-a-Firm problems, in which the firm has two possible values, high or low. People can choose a bid, either high or low, to acquire the firm. The optimal bid depends on the ratio between the high and low values. For the lottery choices, we reduce the optimization problems into simpler lottery choices, where each bid has two possible payoffs that is equivalent to the payoffs one could receive in the optimization problems. In all treatments, subjects first play 24 rounds of the optimization problems, followed by 12 rounds of lottery choices. The 12 rounds of lottery choices are payoff-equilvalent to the last 12 rounds of optimization problems. We have three between-subjects design, varying in how the underling risk is constructed.

In the Correlated Risk treatment, for the Acquiring-a-Firm problems, the firm’s value is either high or low with equal chance, and subjects can choose to a bid of high or low value. Subjects’ payoffs are determined by the firm’s realized value and their own bids. Therefore, they face a decision-making problem under risk, where the risk is correlated, depending on the state of the company. The following lottery problems are constructed similarly, with correlated risk.

In the Risk treatment, for the Acquiring-a-Firm problems, the firm’s value is either high or low, and subjects can choose a bid of high or low value. However, each bid corresponds to two possible outcomes with equal chance, which is the payoff if the firm is of high value, or the payoff if the firm is of low value. Subjects’ payoffs are the realization of one of the possible outcomes, given their bidding price. The following lottery problems are constructed similarly, with independent risk.

In the Certain treatment, there are two firms in the Acquiring-a-Firm problems, one of high value and one of low value. Subjects can choose to a bid of high or low value. Their payoff is the sum of the payoffs from the two firms, divided by two. The following lottery problems are constructed similarly, without any uncertainty.

In sum, there are 3 between-subject treatments. And within each treatment, subjects experience both “optimization problems” and “lottery choices” that are payoff-equivalent. Therefore, we can treat the “optimization problems” and “lottery choices” as within-subject design.

Once a subject signs up for our experiment on Prolific, he or she will be randomly assigned to one of the three treatments (using block randomization method, pre-drawn order in the computer).

Individual-level randomization

No

We are aiming to collect about 200-300 responses in each of the 3 treatment arms.

In total, about 600-900 individuals, recruited via Prolific.

About 200-300 subjects per treatment arm.