This paper considers the measurement of monopoly power in light of recent advances in game theory, in particular those relating to the Shapley value [2, 3, 6]. Traditional measures of monopoly power (e.g., 17]) were all based on Cournot's model of monopoly , where the monopolist, knowing his demand curve and knowing that it is Independent of his action, maximizes his profits. Indeed, without the passivity of buyers, the hypothesis of profit maximization cannot operate, for then the situation is that of a game. The essential problem with this model, as pointed out by Aumann , is answering when buyers in a monopolized market become passive. Surely it takes more than one buyer, but will even a continuum of buyers be enough? Some examples in the literature [4, 9] suggest that with a very large number of buyers, monopoly will indeed be advantageous, in so far as a monopoly's imputation equals its Shapley value. Testing this hypothesis is the aim of the paper.
Gardner, Roy, "Shapley Value and Monopoly Power In A Two-Sector Model" (1976). Economic Staff Paper Series. 143.