Bargaining with random arbitration: an experimental study

We use a laboratory experiment to study bargaining in the presence of random arbitration. 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 probability q, there is random arbitration instead, with one bargainer randomly selected to receive his/her demand and the other bargainer receiving the remainder. 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 main experimental results support the directional predictions of standard game theory (though the success of its point predictions is mixed). In the spirit of typical results for conventional arbitration, we observe a strong chilling effect on bargaining for values of q near one, with extreme demands and low agreement rates in these treatments. For the most part, increases in q reinforce the built-in asymmetry of the game, further benefiting the favoured player at the expense of the unfavoured player. 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.