ECONOMISTS AND STRIKES
| Date | 01 February 1979 |
| DOI | http://doi.org/10.1111/j.1468-0084.1979.mp41001001.x |
| Author | K. MAYHEW |
| Published date | 01 February 1979 |
OXFORD BULLETIN
of
ECONOMICS and STATISTICS
ECONOMISTS AND STRIKES
By K. MAYHEW
Given the long history of bargaining theory in economics, it is perhaps sur-
prising that economists have had so little to say about strikes.' Only recently have
economists in any number begun to build and to test models explicitly designed
to explain variations in strike activity. This paper surveys these recent develop-
ments, relates them to earlier bargaining theory, and goes on to suggest an alterna-
tive approach.
BARGAINING THEORY
There are two general categories of games in game theory:2 zero sum and non-
zero sum games. In the former one party must lose and the other must gain if
the game is played. In the latter both parties may gain. Non-zero sum games
may be either cooperative or non-cooperative. Nash described a two person non-
zero sum cooperative bargaining game.3 It is a 'fixed threat' game in that each
player has a unique status quo in the event of no cooperation. The game concerns
the share of a particular good, of which individual 1 gets A and individual 2 gets B.
Each player has a utility function [U,=U1(A); U2(B)], unique up to an
order-preserving linear transformation, and he knows the rules of the game, the
payoffs associated with every possible outcome and the utility function of his
opponent. Each game has an attainable set of outcomes depending on the
strategies adopted by the players. In a cooperative game the players can choose
their strategies together and extend the attainable set to their mutual gain. But
which point of the extended attainable set should the players choose? Following
the Pareto principle, they will not choose a particular payoff pair if there is another
attainable one which has more expected utility for one player and at least as
much for the other. Nor will one player accept a payoff pair in which he gets less
than he could get if there were no cooperation. The expected utility levels if a
player goes it alone are U,(A0) and U2(B0) respectively. Nash argues that an
1 For a long time the main exception to this was K. G. J. C. Knowles, StrikesA Study in
Industrial Conflict, Oxford, 1952.
2 For a recent discussion of game theory see M. Bacharach, Economics and the Theory of
Games, London, 1976.
J. F. Nash, 'Two person cooperative games', Econometrica, January 1953, pp. 128-140.
See also Nash, 'The bargaining problem', Econometrica, April 1950.
1
Volume 41 February 1979 No. 1
2BULLETIN
arbitrator between the bargainers would suggest a share-out of A* and ß* which
maximizes [U1(A *) - U1 (A - U2(B0)J, that is which maximizes the
product of the two players' utility increments measured from the status quo. This
is a unique solution if the utility frontier is quasi-concave. Nash shows that the
solution satisfies four conditions:
(j) it is on the efficiency frontier;
if the utility increments frontier between the two individuals is symmetrical
around a 45 degree line, the solution gives eclual utility gains to the two
parties;
it is not altered by a linear order-preserving transformation of the utility
function of either party;
it is independent of 'irrelevant alternatives'; if the solution for a given
utility frontier has been found, and if that utility frontier is altered any-
where except at the solution point, the solution is unchanged.
Two criticisms can be made of this. The first is that the arbitrator 'imposes'
a solution. The second is that the solution relies on the existence of a well-defined
status quo if no agreement is reached, whereas in fact each player may have at his
disposal many sanctions, thus implying no given status quo. In answer to the
first point, if players were rational they would behave as if there were an arbitrator.
To counter the second criticism, Nash developed a general multi-threat model
which on certain assumptions leads to a determinate solution.4 In Nash's model
threats are never realized and thus if the game were played between management
and unions, there would never be a strike. The players are perfectly rational and
they have complete information about feasible outcomes, about each other's
utility function, and hence about the payoff matrix. Thus, according to Nash's
theory of general cooperative games, strikes are the result of either irrationality or
mistakes.
An alternative approach is that represented by the work of Zeuthen and
Harsanyi.5 They emphasize the problem of risk in the maximization of expected
utility. During the bargaining process the parties are continually comparing the
options of immediately accepting the opponent's offer or of holding out at the risk
of stalemate. Zeuthen describes an 'atonement process' whereby the party with
the lowest propensity to fight always reduces his demand. To give an example,
suppose that Party 1 has been offered A2, but would like to achieve more favourable
terms A1, with utilities U1(A 2) and U1 (A ) respectively. Let P2 be the probability
that the second party will reject A1. Then Party 1 will accept A2 if U1(A2)>
(1 P2). U1(A1), or if [U1(A1) - U1(A2)]/U1(A1)
be written as LU1/U1. Party 2 has a utility quotient ¿U2/U2, which is similarly
derived. If ¿U1/U1 <¿U2/U2, Party 2 will be the more determined to insist on
See Bacharach, o. cii., pp. 111-17.
F. Zeuthen, Problems of Monopoly and Economic Welfare, London, 1930. J. C. Harsanyi,
'Approaches to the bargaining problem before and after the theory of games: a critical dis-
cussion of Zeuthen's, Hicks' and Nash's theories', Economeirica, April 1956, pp. 144-57. An
excellent discussion of these and other theories is given in G. de Menu, Bargaining: Monopoly
Power versus Union Power, Cambridge, Massachusetts, 1971. See especially Chapter 2.
To continue reading
Request your trial