Bargaining and the determination of wages

This part of the book has explored the view of the business firm as a cooperative coalition. Since the costs of coalition formation are sunk, and the same costs limit the formation of competitive firms, the successful coalitions we observe typically will realize surpluses. As a result bargaining power plays a key part in the models of Chapters 11 and 13. In these models the wage includes a share of the surplus and this is necessarily positive, since otherwise employees would not recover the sunk cost of their participation in labor markets. Thus, even in the absence of explicit collective bargaining, a labor share of the surplus must be determined, and the determinants of that share constitute (for the purposes of this book) bargaining, implicit if not explicit. Accordingly, this chapter reconsiders bargaining power and the determination of wages.


Bargaining power arises from threats. In a successful cooperative arrangement the threats are not carried out, so are not necessarily observable. Instead rational bargainers each assess the threats that others may make and moderate their demands so that a mutual agreement can occur. When we observe threats carried out, the attempt to form a cooperative coalition or to make a cooperative decision has failed. Most bargaining theory in the tradition of Zeuthen (1930) and Nash (1950b) explicitly consider only the threat to leave the coalition. For such a threat, the disagreement outcome - that is, the outcome if the threat is carried out - is the bargainer’s outside option. In Schmeidler’s (1969) nucleolus model, similarly, bargaining power depends on the difference between the payoff to a group or a singleton within the coalition and the value they can attain in another cooperative grouping, that is, the outside option. This identification of the disagreement outcome with the outside option is common in applications of bargaining theory, but not the only possibility. Nash (1953) relaxes this assumption somewhat, but Nash seems to assume that if there is no bargaining settlement there is no coalition.

In Nash’s variable threat model, the noncooperative choice of threat strategies determines the outcomes in case bargaining fails. Nash does not provide examples. The widely discussed efficiency wage model may provide a useful instance. It is not a bargaining model, as usually presented, but rather a Stackelberg leader-follower model with the employer as the leader. Nevertheless, we may identify a noncooperative solution and a cooperative solution that might be maintained with repeated play (MacLeod and Malcomson, 1989). At the noncooperative solution, effort and productivity are low, and pay is at the market-clearing rate. At the cooperative solution, effort and productivity are higher and so is the wage. The employees’ threat in this case is to withdraw effort to the noncooperative level. The employer’s threat is to cut pay. In case the threats are carried out (and the employees, as individuals, choose not to carry out the threat to quit) the coalition is not dissolved. Instead it continues with (noncooperative) reduced effort and low pay. For the employer, at least, this disagreement outcome is not dependent on the outside option.

Indeed, actual bargaining clearly sometimes takes place on the basis of threats that do not dissolve the coalition. Strikes and lockouts provide well- known examples. When employees go on strike, or when hockey players are locked out and part of their play schedule is cancelled, neither side means to leave the coalition or the league permanently. Another illustration of this sort of threat is the work-to-rules slowdown. If a work-to- rules slowdown is carried out, the coalition is not dissolved, and indeed production continues, but the rate of production is reduced and the size of the surplus produced by the coalition is diminished. The disagreement outcome depends on how the reduction in the surplus is allocated among the members of the coalition, presumably a noncooperative solution of some kind. In case one member receives the residual, while others are paid according to a pre-existing contract, the threat of the slowdown may enhance the bargaining power of those seeking a new contract.

This suggests one possible explanation of the failure of the bargaining model to fit the data on the (lack of) fluctuation of wages with unemployment: the bargainers might choose threats with disagreement outcomes that are independent of the outside options of the bargainers. In effect this is the strategy of Hall and Milgrom (2008). They adopt a different bargaining theory along the lines of Rubinstein (1982) in which offers are exchanged in a subgame perfect sequence. In that case, the disagreement outcomes are delays that are costly to both bargainers (note also Cross, 1965). However, this approach seems applicable only to new hires, and would be applicable to the wages of insiders only to the extent that insiders’ wages are determined for all time by the wage at the initial hire.

A shortcoming of Nash’s variable-threat model is that a bargainer, having chosen one threat, must renounce all others, so that only one threat influences the bargaining process. (He does assume, however, that the first- stage equilibrium will be a mixed strategy equilibrium, so that the ultimate outcome of the process may be influenced probabilistically by two or more threats.) But why would a bargainer choose just one among a number of threats, rather than use any and all threats that might extract a concession from the other side, at any stage in the bargaining process?

Threats may be classified by noncooperative credibility: those that, in Nash’s (1953) words, “will not be something [the threatener] would want to do, just for itself” (that is, that are not subgame perfect; Chapter 6 above) and those that are. In a cooperative game in which the existing allocation is dominated, the threat to leave the coalition is credible; otherwise not. In this way the core of a cooperative game may be thought of as a bargaining theory, although one that does not always give rise to a unique value solution. On the other hand, if the allocation is not dominated, the threat to leave the coalition will never be subgame perfect. Thus Nash says that “we must assume there is an adequate mechanism for forcing the players to stick to their threats and demands once made” (p. 130). But Nash goes too far, here. Strikes and lockouts are surely almost never subgame perfect, but they do occur in the actual world. It seems clear that real human beings have some capacity to carry out threats of retaliation, some capacity for spiteful (New York Times, 2014) behavior. That is, bargainers’ behavior may be more closely approximate ideal than perfect rationality.

Multiple threats, including some that are not credible in a world of “perfect” rationality and subgame perfect equilibrium, may explain differences in bargaining power that are independent of the outside options of the bargainers. Differences in bargaining power along these lines are allowed for by generalizations on Nash’s bargaining theory due to Roth (1979) and Svejnar (1986). These generalizations also allow for bargaining among more than two bargainers, but assumes that only individuals have bargaining power.

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