We use a laboratory experiment to study bargaining in the presence of random implementation. Two players make simultaneous demands; if compatible, each receives the amount demanded as in the standard Nash demand game. If bargainers' demands are incompatible, then rather than bargainers receiving their disagreement payoffs with certainty, they receive them only with exogenous probability 1-q. With the remaining probability q, there is random implementation: either bargainer is equally likely to be chosen to receive his/her demand, with the remainder going to the other bargainer. The bargaining set is asymmetric, with one bargainer favoured over the other. We set disagreement payoffs to zero, and vary q over several values ranging from zero to one.
Our experimental results mostly support the directional predictions of standard game theory (though the success of its point predictions is mixed). There is a flavour of conventional arbitration, in that we observe a strong chilling effect on bargaining for values of q near one, with extreme demands and low agreement rates (but high efficiency) in these treatments. Raising q reinforces the built-in asymmetry of the game, giving the favoured player an increasingly large share of the payoffs. However, efficiency also rises with q, so that in general, the unfavoured player loses less than the favoured player gains, and in some cases increasing q leads to Pareto improvements. The effects we find are non-uniform in q: over some fairly large ranges, increases in q have minimal effect on bargaining outcomes, but for other values of q, a small additional increase in q leads to sharp changes in results.Paper (PDF)
Anbarci, Nejat and Nick Feltovich (2012), "Bargaining with random implementation: an experimental study", Games and Economic Behavior 76 (2), pp. 495-514. DOI: 10.1016/j.geb.2012.07.007.