Bargaining power and majoritarian allocations

Bargaining models in the tradition of Zeuthen and Nash have been extended to cases of unequal bargaining power (Roth, Svejnar) and to “the bargaining problem” with n>2 bargainers. However “the bargaining problem” excludes by assumption any bargaining power attributable to any group other than a singleton or the grand coalition of the whole group. Thus, in particular, it is impossible to attribute any bargaining power to a majority group. By contrast, Schmeidler’s nucleolus can attribute bargaining power to any subset of the population, but only the least advantaged subset has positive bargaining power. Recently, McCain synthesized and extended Nash’ and Schmeidler’s models to a bargaining model that can attribute bargaining power to any subset of the population, and positive bargaining power to groups that may not be least advantaged.

            For a coalition of n members, define a majoritarian decision as one in which any subgroup of n/2+1 has bargaining power 1, and all other subsets have bargaining power zero. The bargaining power solution to this model is shown to be equivalent to the maximization of the (utility) payouts to the group. As an example, this result is applied to the economics of a worker cooperative.

McCain, Roger A.  (2013), Value Solutions in Cooperative Games (Singapore: World Scientific).

Nash, John (1950), “The Bargaining Problem,” Econometrica v. 18,  pp. 155-162.

Roth, Alvin (1979), Axiomatic Models of Bargaining (Berlin: Springer-Verlag).

Schmeidler, David (1969), “The Nucleolus of a Characteristic Function Game,” SIAM Journal on Applied Mathematics v. 17,  no. 6 (Nov.) pp. 1163-1170.

Svejnar, Jan (1986), “Bargaining Power, Fear of Disagreement, and Wage Settlements: Theory and Evidence From U. S. Industry,” Econometrica v. 54, no. 5 (Sep) pp. 1055-1078.

Zeuthen, Frederick (1930), Problems of Monopoly and Economic Warfare (London:  Routledge and Kegan Paul).