Techniques drawn from game theory have been applied to the analysis of a variety of economic questions, including policy cooperation between governments, the credibility of macroeconomic policy and the effectiveness of trade and industrial policies in oligopolistic markets. In Discussion Paper No. 328, Research Fellow John Treble investigates whether game-theoretic models can predict the behaviour of unions and employers bargaining over wages. He focuses on the experience of the conciliation boards established to govern industrial relations in the UK coal industry between 1893 and 1914, and in particular the role of `pendulum arbitration' in resolving impasses in negotiations.
Treble focuses on explaining the wide variation across coalfields in the proportion of appeals to the arbitrator. He finds no evidence for a wage round explanation, according to which the first coalfields to negotiate in any given year would be expected to experience a higher rate of appeal and longer negotiations, which then set a standard that would allow later negotiations to conclude more quickly. He also rejects the suggestion that coalfields varied simply because of the differing personalities of negotiators in each region, since the delay involved in appeal to an arbitrator would have sufficient impact on wages to deter negotiators from a gratuitous indulgence of their personalities.
In the paper, Treble outlines a simple, perfect equilibrium model of the frequency of appeal to the arbitrator in a cooperative game between owners and union, based on the constitutions of the conciliation boards. The strategies available to the players are offers and counter-offers regarding the quarterly, percentage addition to the basic wage rate. The speed with which negotiations were typically conducted and concluded provides substantial support for the hypothesis that negotiators behaved `rationally', Treble argues. Negotiations typically consisted only of an offer and then a counter-offer which was then either accepted or rejected. This is remarkably close to the two rounds suggested by theoretical analyses of rational games, contradicting popular perceptions of bargaining as an almost continuous sequence of small concessions leading to agreement.

The basis of his analysis is the differences in boards' constitutions concerning the course of events between an initial disagreement and an appeal to the arbitrator, causing delays which affected the strategic implications of various decisions by the parties. Since wage rates were determined largely by the price of coal, this meant that a delay in the date of settlement was advantageous to the union when the coal price was falling, and advantageous to the owners when it was rising. The constitutions of the boards were set up so that in three regions a delay could be obtained by appealing to the arbitrator, while in South Wales and Northumberland such delays were impossible.
If opportunities for delay are not present in a constitution, the theory predicts that the rate of appeal to the arbitrator will be unaffected by the rate of change of the coal price. In a regime where delay is feasible, however, the frequency of appeal to the arbitrator will be lower, the higher the absolute rate of change in the coal price. Treble conducts a logit analysis of the frequency of appeal to the arbitrator. The results show clear differences between the two sets of regions, lending support to the validity of his game-theoretic model. The absolute rate of change of coal prices appears to have been a significant determinant of the rate of appeal to the arbitrator in regions where arbitral delay is feasible, but not where such delay was not feasible

The Pit and the Pendulum: Arbitration in the British Coal Industry, 1893-1914
John G Treble

Discussion Paper No. 328, August 1989 (HR)