Experimental Design
Experimental Design Details
Our proposed experiment will run on the online platform Prolific using their subject pool, recruiting subjects from the UK.
After reading the instructions and completing control questions, each subject is assigned a color, either Red or Blue. Subjects know their color when the next steps happen.
Each subject is then either randomly assigned (treatment Control) or chooses (treatment Mutual) one of two options: (1) Play an individual lottery giving 3 pounds with probability 1/4 and 0 pounds else, or (2) playing a paired lottery with another participant of the opposite color. In the paired lottery, there is a 3/4 chance that the blue player earns 10 pounds and the red player zero, and a 1/4 chance that the red player earns 10 pounds and the blue player zero. In treatment Mutual, subjects who choose the paired lottery are subsequently matched to another subject who also chose this and is of the opposite color.
After the outcome of the paired lottery is determined, each subject in the pair can choose to accept or reject the outcome. If both accept, the payoffs from the lottery are paid. If either subject in a pair rejects, both are paid 1 pound instead.
UPDATED Preregistration:
After running treatments Control and Mutual we found no significant differences for the measures described in the preregistration from April 30, 2025.
Therefore, we decided to run a modified version of treatment Mutual, Agreement, which is identical in sample size and game form. The only difference is that subjects have to agree more explicitely that they want to play Spin the Wheel Version 2, e.g. by a pop-up windows that says: “I agree to play Version 2”.
2nd update:
After running treatment Agreement as preregistered on July 17, 2025, we again found no significant differences for the measures described in the preregistration.
We therefore decided to run another two treatments, Control0 and Agreement0, which differ from Control and Agreement, respectively, by what happens after the paired lottery is determined and at least one player rejects the outcome: rather than both receiving 1 pound, they receive 0 pound in the new treatments. This eliminates selfish reasons for rejecting an outcome and should make the power of the agreement stronger.
3rd update:
After running treatment Agreement as preregistered on July 30, 2025, we again found no significant differences for the measures described in the preregistration.
We therefore decided to run another two treatments, AGR_Observe_R1 and IMP_Observe_R1, which differ from Control (IMP_R1) and Agreement (AGR_R1), respectively, by what happens after the paired lottery is determined. In the new treatments, the subjects cannot reject the outcome of the biased wheel (Mutual). Rather, there is a third party, a subject who observes the outcome and who has the option of rejecting the outcome. In this case, both subjects in the pair receive 1 pound.
Observers get a fixed payment of 2 pounds.
Number of observations: in all other treatments so far we were aiming for 250 observations per treatment, assuming 80% would choose the biased wheel (Mutual) and 75% of those would get zero payoff. This yields 150 observations if interest.
Thus, we also aim for 150 observations of observers for the case that the red player gets a payoff of zero for both treatments AGR_Observe_R1 and IMP_Observe_R1.
We recruit 10 observers for the case that the blue player gets a payoff of zero for both treatments AGR_Observe_R1 and IMP_Observe_R1.
Since we are not interested in the behavior of the two players in the pair, we just recruit 10 pairs for each treatment that choose to play the the biased wheel (Mutual). We tell observers that their decision affect the prior participants’ payments only if it is randomly chosen.