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In this paper, a solution concept from cooperative game theory is applied to a special kind of oligopolistic markets. Traditionally, oligopoly theory uses non-cooperative game theory. The cooperative solution concept, the Price Core, has been specially developed for this paper. In contrast to the Core, in the Price Core, different consumers may pay different prices for the same commodity. An example shows that the set of competitive allocations may be a proper subset of the Core and that the Core may be a proper subset of the Price Core.

Solves von Stackelberg equilibria in a Bertrand‐Edgeworth duopoly game. Shows that, initially, the environment is characterized by efficient rationing and capacity constraints. Since interest lies in sustaining monopoly outcomes from non‐co‐operative behaviour, introduces the buyout option, where rivals can absorb one another’s output before any consumer. Reveals that the outcomes change drastically in that players together are able to reach the monopoly profits.

“Solving Games by Differential Equations”: was the title of a paper by Brown and von Neumann (1950). The idea of solving bargaining games by differential equations goes back to Raiffa (1953). The present paper starts with a solution ϕ of a bargaining game and constructs, by means of solving a set of differential equations, a new solution Cϕ, the continuation of ϕ. A property is called hereditary when it holds for Cϕ whenever it holds for ϕ. Hereditary properties and properties of Cϕ in relation to properties of ϕ are studied. The paper includes a number of open problems.

We show that both cooperative and non-cooperative game models can substantially increase our understanding of the functioning of actual markets. In the first part of the paper, we provide a brief historical sketch of the differences and complementary between the two types of models, by going back to the work of the founding fathers, Von Neumann, Morgenstern and Nash. In the second part, we illustrate our main point by means of examples of bargaining, oligopolistic interaction and auctions.