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A Behavioural Model of Bargaining

Published online by Cambridge University Press:  27 January 2009

Hugh Ward
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Extract

In this paper I shall present a very simple version of a bargaining model based on assumptions of limited information and limited capacity to make rational decisions. The justification for my work lies in the inadequacies both of the formal models in the microeconomic literature and of accounts of bargaining and other conflicts where power or closely related concepts lie at the basis of the discussion.

Type
Research Article
Information
British Journal of Political Science , Volume 9 , Issue 2 , April 1979 , pp. 201 - 218
Copyright
Copyright © Cambridge University Press 1979

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References

1 A complete bibliography is extensive but the most signficant contributions are: Edgeworth, F. Y., Mathematical Physics (London: Kegan Paul, 1881), pp. 20–30Google Scholar; Zeuthen, F., Problems of Monopoly and Economic Warfare (London: Routledge and Sons, 1930), pp. 104–50Google Scholar; Bishop, R. L., ‘A Zeuthen-Hicks Model of Bargaining’, Econometrica, XVIII (1950), 559–602Google Scholar; Feldes, L., ‘A Determinate Model of Bilateral Monopoly’, Economica, CXXII (1964), 117–31CrossRefGoogle Scholar; Nash, J. F., ‘The Bargaining Problem’, Econometrica, XVIII (1950), 128–40Google Scholar; and Cross, J. G., The Economics of Bargaining (New York: Basic Books, 1969), 42–90.Google Scholar

2 Although Nash, , ‘The Bargaining Problem’Google Scholar, and Cross, , The Economics of BargainingGoogle Scholar, deal with threats, they do no more than provide a framework within which to analyse the problem. They do not attempt to relate the threat strategies available to bargainers with any other variables and fail to discuss interdependencies between the costs of carrying out a threat and the costs imposed if it is carried out.

3 See for instance, March, J. G., ‘The Power of Power’, in Easton, D., ed., Varieties of Political Theory (Englewood Cliffs, N.J.: Prentice-Hall, 1966), pp. 49–68Google Scholar. For a typical empirical study employing the model see Salanik, G. R. and Pfeffer, J., ‘The Bases and Uses of Power in Organisational Decision Making,’ Administrative Science Quarterly, XIX (1974), 453–73.CrossRefGoogle Scholar

4 Community power studies, for example, have completely ignored the costs of decision making. In large-scale decision making such as the Windscale Enquiry these may be vast.

5 March, , ‘The Power of Power’Google Scholar, discusses a model in which resource levels change but does not attempt to explain why they might do so.

6 Friedman, M., ‘The Methodology of Positive Economies’ in Part Three of his Essays in Positive Economics (Chicago: University of Chicago Press, 1953)Google Scholar. Although there are notable dissenters this view has become the orthodoxy among neoclassical economists in the last decade.

7 The best available summary of the motivational literature is still Cofer, C. and Appley, M., Motivation: Theory and Research (New York: Wiley, 1964), especially pp. 56–106, 302–67 and 367–412.Google Scholar

8 Of particular interest in relation to wage bargaining is Patchen, M., ‘A Conceptual Framework and Some Empirical Findings Regarding Comparison of Social Reward’, Sociometry, XXIV (1961), 128–40.Google Scholar

9 See the discussion of coercive comparisons and the limited nature of management bargaining goals in Chamberlain, N. and Kuhn, J., Collective Bargaining (New York: McGraw-Hill, 1965), p. 216.Google Scholar

10 Walton, R. and McKersie, R., A Behavioral Theory of Wage Negotiation (New York: McGraw-Hill, 1965), p. 101.Google Scholar

11 Stevens, C. M., Strategy and Collective Bargaining (New York: McGraw-Hill, 1963), p. 53.Google Scholar

12 Baillie, W. M., Hammond, K. and Meyer, G. D., ‘An Alternative Approach to Labour Management Relations’, Administrative Science Quarterly, XIX (1974), 311–27.Google Scholar

13 See for example, Simon, H. A., ‘A Behavioral Model of Rational Choice’, Quarterly Journal of Economics, LXIX (1955), 99–118.CrossRefGoogle Scholar

14 The restrictions placed on the solution by Nash (Nash, ‘The Bargaining Problem’) cannot all be deduced from the assumption of rational ‘self-interested’ maximizing players. Within the game-theoretic framework proper only very weak predictions can be made in this case: the core of the game is often almost co-extensive with the set of possible outcomes to the game.

15 Simon, , ‘A Behavioral Model of Rational Choice’.Google Scholar

16 Nicholson, M., ‘Tariff Wars and a Model of Conflict’, Journal of Peace Research, IV (1967), 26–38.CrossRefGoogle Scholar

17 A union negotiator, for example, might be satisfied with any settlement where the wage was higher than £x, the working week between y and z hours, and his pension more than £w.

18 See Salanik, and Pfeffer, , ‘The Bases and Uses of Power’Google Scholar, and Korpi, W., ‘Conflict, Power and Relative Deprivation’, American Political Science Review, LXVIII (1974), 1569–78CrossRefGoogle Scholar. Korpi's model has some similarity to my own, actors' level of aspiration for consumer goods being assumed to increase with their subjective power. The main emphasis in this paper, however, is on relating relative deprivation to ‘observable’ societal conflict.

19 That many resources are self-blunting is implicitly recognized in much informal writing on decision making but what I here call resource costs have received little attention in the formal literature on power.

20 In a fuller account one would have to allow for the use of resources to change the perceived incentive structure of the other actor through the making of threats and promises as well as changes in expectations brought about by resource costs.

21 See for example Rae, D. and Taylor, M., ‘Decision Rules and Policy Outcomes’, British Journal of Political Science, 1 (1971), 71–90.CrossRefGoogle Scholar

22 If both bargainers use this rule, and their initial bids are fairly close to their optima, the locus of their bids through time will lie close to the Edgeworth Contract Curve (the locus of points of tangency of their indifference curves). The bid satisfactory to A which yields the highest payoff to B will be on the contract curve where it intersects the indifference curve corresponding to A's level of aspiration. So long as the indifference curves are relatively flat, A's offer will only be fractionally inside this indifference curve and so long as the gradient of B's utility surface is not too great, the utility to B of the offer made will be close to that assumed in this paper.

23 The correlation will increase as the locus of bids approaches the contract curve and as the utility of any alternative approaches a linear function of its distance from the actors' optima.

24 Cross, , The Economics of Bargaining.Google Scholar

25 For the asymmetric case

and

where Dt is the function defined above, ΔA + ΔB = Δ, , KA + KB and KA - KB = K″

26 Many examples could be cited. Among the most widely discussed has been the withdrawal by the Russians of concessions made earlier in the test ban conferences of 1961–62. See Ikle, F. C., How Nations Negotiate (New York: Harper and Row, 1964), p. 101.Google Scholar

27 Shubik, M., Strategy and Market Structure (New York: Wiley, 1959), 203–87.Google Scholar

28 Consider a staircase. The height above ground of the staircase is an increasing, but not a strictly increasing, function of the distance measured along the ground.

29 For a discussion of real interests and their place in conceptualizing power see Lukes, S., Power: A Radica View (London: Macmillan, 1974), p. 24CrossRefGoogle Scholar. The opportunity costs of an action are, of course, only one of the factors affecting whether the action is in the real interests of the actor concerned.

30 Several authors have discussed the costs of exercising power but this is inconsistent if, as for instance Dahl and Harsanyi do, one thinks of power as involving intervention in a way that brings about a more favourable decision. If one ascribes power to an individual within such a framework one should already have considered costs because unless an intervention is to the actor's net advantage power cannot be said to have been exercised in this vocabulary. This conceptual confusion may in part account for the fact that costs of decision making have been ignored in community power studies. There are ramifications from the recognition of this point which raise severe conceptual difficulties for what Lukes in Power has called the one-dimensional view of power.