In this part of the book so far, it has been assumed (along the lines of Roth, 1979 and Svejnar, 1986) that bargaining power may differ from one individual to another, but only individuals have bargaining power. But the history of human action points to a possibility excluded by that assumption: individuals may often enhance their bargaining power by banding together. The examples of strikes and slowdowns already discussed would seem to be instances of this. If so, it would seem that this possibility is particularly important in the modern business firm. With this possibility in mind, it will be appropriate to reconsider the role of collective action in determining bargaining power and the results of the study so far.

Suppose, then, that employees gain some bargaining power as a group by means of a threat of collective action such as a strike, work-to-rules slowdown, or other noncooperative effort withdrawal. A model along these lines is developed in McCain (2013, Chapter 6, Section 6.2) for a TU game. For the NTU game discussed in the appendix to Chapter 11 in connection with expressions (A11.1a)-(A11.7n), the gain for the workforce as a whole cannot be expressed except in terms of the distributive weights l. Accordingly, adapting the bargaining model of McCain (2013, Chapter 6, section 6.5) to this case, the objective function for the maximization program is as shown in the appendix to this chapter as (A14.1a). A new term for the aggregate gain of the employee group is added to the objective function of the decisions.

For non-employee members of the coalition, we see

where p? is the bargaining power of the employees as a group. That is, for non-employee members of the coalition, as before, the distributive weight l will be the proportion of the individual’s bargaining power to the total bargaining power in the game. This is equation (A14.1d) in the appendix. In this case the total bargaining power includes that of the employee group as a whole, p?. For employees the case is more complex, but the distributive weight l will be increased by a proportion of the collective bargaining power p?. This is equation (A14.1e). Thus, the threat of collective action reduces the relative bargaining power of those outside the group that threaten the collective action, as we might expect. Nevertheless, the firm’s allocative decisions will not be modified by this shift in bargaining power (equations A14.4a-c) and the maximized net value creation will be distributed among the members of the coalition in proportion to their distributive weights as modified by the threat of collective action. That is to say, briefly, the impact of a threat of collective action will be only on the distribution of the surplus, but will not affect the coalition’s decisions on the allocation of resources nor, consequently, on the surplus value itself. The value creation approach is applicable despite the exercise of collective bargaining power.

In this model (following Schmeidler, 1969 and McCain, 2013) the bargaining model is treated as a core assignment algorithm. That is, it distributes the entire surplus of the coalition, not the excess over some threat outcome. The role of threats is to determine bargaining power. Since the surplus is defined relative to the outside option, the outside option will enter into the determination of the wage, z.

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