Experimental investigation of ODR systems

Treatments between subjects vary the way barganing is implemented.
One issue Two issues
Free bargaining (Barg). Barg1 Barg2
ODR direct one shot (DirODR) DirODR1 DirODR2
ODR sequential two steps (SeqODR) SeqODR1 SeqODR2

2023-06-25

2023-07-22

Settlement rates for markets where it is feasible, Settlement rates for hard markets (with sum of valuations above 75 but below 100)

Efficiency of markets where it is feasible

Efficiency of markets where it is feasible

Settlement rates for hard markets (with sum of valuations above 75 but below 100)

Equity of outcomes, measured as proportions of available bargaining surplus assigned to each player

There are 30 participants in the experiment in each session, split into two groups of 15 for the whole experiment.

The experiment consists of 20 rounds. Only one round is payoff relevant. At the beginning of each round, all participants of each group are randomly matched in pairs. Participants know they are matched with a new random participant from the group of 15 every round.

In each round, there are 100 items of type A and 100 items of type B to split.
For type A, participants have outside options, i.e., the number of items of type A they will receive in the case of bargaining failure. Subjects know that the outside options vi could be any number between 0 and 100 with equal probability and are drawn independently for each subject.

The outside options for the type B object are equal to 0 for both subjects, and they know it. However, each subject has a different multiplier for the points of type B. Multiplier is drawn independently for each subject from the uniform distribution between [0.7,1.3]. Subjects know their multiplier for the round and the distribution.

Finally, the market could either with or without deal-breaking for type A items. In markets with deal-breaking, subjects receive zero points if they end up with fewer A type items than their outside option. Subjects know that the presence of a deal-breaking property is the same for all subjects in the round. The utility function for each round is presented. To simplify the setup, subjects will play the first ten rounds under no deal-breaking, followed by 10 rounds of deal-breaking, or in the reversed order. We will balance the order. We will remind subjects of the switch in the utility function after round 10.

This corresponds to no information treatment of Bochet et al. 2023.

Under this parametrization, in expectation, 28% of markets have a surplus large enough to reach efficiency even in one-dimensional bargaining (the sum of outside options is less than 75). 22% of the markets have a small surplus and cannot reach an agreement despite a positive surplus from bargaining (the sum of outside options is between 75 and 100). 50% of the markets have no surplus, as the sum of outside values is higher than 100. This implies that, in expectation, we will have 22 hard markets


The deal-breaking property affects the utility function of subjects. Under no deal-breaking, a subject’s payoff for the round is

U_i=A_i+w_i*B_i
where A_i is agreed amount of type A items or v_i if agreement is not reached. B_i is agreed amount of the type B item or 0 is agreement is not reached.



Under deal-breaking a subject’s payoff for the round is
U_i=A_i+w_i*B_i if A_i≥v_i, or 0 if A_i<v_i
where A_i is agreed amount of type A items or v_i if agreement is not reached. B_i is agreed amount of the type B item or 0 if agreement is not reached. Thus, accepting an offer of type A item below outside option leads to zero payoff from type A items.

The points collected in U are transformed in euros with exchange rate of 10 cents per 1 point.



Treatments.
We have 3x2 between-subject design.

One issue Two issues
Free bargaining (Barg). Barg1 Barg2
ODR direct one shot (DirODR) DirODR1 DirODR2
ODR sequential two steps (SeqODR) SeqODR1 SeqODR2

in otree

subjects

Yes

matching groups or 10, 12 groups per treatment

120 per treatment, 720 in total

120 subjects, 12 matching groups