Experimental Design
I. Study design
1. Design
1.1 Resource extraction (CPR)
In this game, two players manage a shared resource over two periods. The resource starts with an initial stock (S1). Each player (A and B) can extract a portion (x_A and x_B), up to a maximum of half the current stock (max x_A and max x_B = S/2).
Any remaining stock at the end of the period (R1 = S1 - x_A1 - x_B1) grows by a factor of 1 + alpha. The resource stock for the second period is then calculated as:
S2 = R1 * (1 + alpha) = (S1 - x_A1 - x_B1) * (1 + alpha)
In the second period, players can extract again (x_A2 and x_B2), following the same rule that their maximum extraction is half of the available stock (max x_A2 and max x_B2 = S2/2).
1.2 Depletion risk
Some treatments carry a risk of total resource depletion. There is a lambda% chance that the entire resource will be destroyed (reduced to zero) between period 1 and period 2. Players are informed about this risk, including the exact probability.
1.3 Bargaining mechanism
In treatments with bargaining, players negotiate in real-time on how to extract for the current period. They propose an extraction vector, X = (S1 - x_A1 - x_B1, x_A1, x_B1), where the first element (R1=S1 - x_A1 - x_B1) represents the remaining stock after extraction, and the second and third elements represent the extraction amounts for Player A and Player B in period 1.
Players can take several actions during bargaining. They can make an offer, accept, reject, cancel their own offer, or end the bargaining stage early. If players quit early or do not reach an agreement within the allotted time, they move to the CPR game and make their own extraction decision. Players can simultaneously make offers to each other.
Depending on the treatment, the agreed allocation is either binding or non-binding. In the binding case, the agreed allocation enforces the extraction amounts for the current period. In the non-binding case, the agreed allocation serves as a suggestion, but players still make their own extraction decisions in the CPR game.
2. Treatments
Six treatments will be examined
IF - Extraction (CPR) + Risk Free: A standard CPR game with no disaster risk (no possibility of resource depletion in the second period)
IR - Extraction (CPR) + With Risk: A CPR game with non-binding bargaining and disaster risk (possibility of resource depletion in the second period)
NF - Non-binding bargaining + Risk Free: A CPR game with non-binding bargaining and disaster risk (no possibility of resource depletion in the second period)
NR - Non-binding bargaining + With Risk: A CPR game with non-binding bargaining and disaster risk (possibility of resource depletion in the second period)
BF - Binding bargaining + Risk Free: A CPR game with binding bargaining and disaster risk (no possibility of resource depletion in the second period)
BR - Binding bargaining + With Risk: A CPR game with binding bargaining and disaster risk (possibility of resource depletion in the second period)
3. Parameters
We set growth rate alpha = 0.6, depletion risk lambda = 0.3, initial stock S1 = 1000.
We determined the levels of risk and growth by aligning them with empirical estimates of participants' risk preferences derived from the Bomb Risk Elicitation Task (BRET). Using the CRRA utility framework, we identified that the median risk aversion parameter in existing BRET data is approximately r = 0.67. We then selected a combination of growth (g = 1.6) and depletion risk (p = 0.3) that allows us to discriminate the behaviors of risk averse players with the behaviors of risk neutral and seeking. This threshold effectively divides the sample into two distinct behavioral groups, those with r < 0.67 (mild or strong risk-aversion) and those with r > 0.67 (slightly risk averse to risk seeking), maximizing our ability to discriminate between individual risk preferences.
4. Side tasks
- Bomb Risk Elicitation Task (BRET) to measure risk aversion
- Modified dictator game, modified ultimatum game: Bayle (2025) to elicit the inequality aversion and the behavioral symmetry (in a Kantian morality perspective)
- NLE task to measure cognitive ability without relying on the standard CRT
- Socio demographic questionnaire: age, gender, degree, academic major
II. Sampling Plan
1. Data collection procedures
Data collection will take place at Waseda University’s laboratory in Japan, targeting student participants. The collection period is scheduled from July to December 2025. Participants will be invited in a way that ensures socio-demographic balance across experimental treatments, helping control for potential confounding variables.
Each session will include a minimum of 12 participants required to run a session. This minimum ensures perfect stranger matching and sufficient anonymity, preventing participants from identifying their partners.
We plan to recruit 36 participants per treatment group. With this sample size and a significance level of 0.05 (alpha), the power analysis yields a value of 0.81.
2. Sample size
We plan to recruit at least 216 subjects, 36 per treatment from Waseda University, Japan in order to achieve a power of 0.8 for an alpha of 0.05.
III. Variables
1. Manipulated variables
1.1. Risk of Depletion (2 levels):
No Risk: The resource grows predictably between periods (deterministic growth).
Risk: There is a 30% probability that the resource is destroyed before the next period.
1.2. Institutional Setting (3 levels):
No Bargaining (Baseline): Participants extract independently without any negotiation.
Non-Binding Bargaining: Participants negotiate extraction amounts, but agreements are not enforceable, they may still extract freely afterward.
Binding Bargaining: Participants negotiate extraction amounts, and agreements are binding, the agreed terms must be followed.
2. Measured variables
Measured variables include participants’ extraction amounts, agreed allocations during bargaining, individual risk aversion, and prosocial parameters and categories. We also collect all chat discussions and bargaining offers, including their content, timing, and status. In addition, data from the side tasks: risk elicitation (BRET), prosocial games, and cognitive assessments are recorded for each participant.
3. Indices
Results from the UG and DG will be transformed using the Bayle (2025)'s method.
CRRA utility function' parameter will be estimated used the BRET.
Cognitive ability will be estimated using the NLE.