Oligopoly games with and without transferable technologies
by
Kim Hang Pham Do
Tilburg University
Coauthors: Henk Norde (Tilburg University), Stef Tijs (Tilburg University)

We consider a cooperative approach to oligopoly situations. Hereby we will distinguish between two different types of oligopoly, namely oligopoly with transferable technologies and oligopoly without transferable technologies. The first type is characterized by the fact that a group of cooperating firms is allowed to produce according to the cheapest technology present in this group, whereas this transferable of technologies is not possible for the second type of oligopoly. An illustrative example of the first type is a collection of potato farmers and an example of the second type is a group of fishery companies in competition for the market of some species of fish. Cooperative farmers are able to exchange their production techniques, i.e. their knowledge, which is a costless operation. However, cooperative fishery companies can not transferable their technologies, since such an operation would imply that some firms have to replace their fleet.

Usually, oligopoly situations are modelled by means of non-cooperative games. Aumann (1959) introduced two ways of converting a non-cooperative game into a cooperative one. In the first approach every coalition S computes the amount of money which they can guarantee themselves regardless what the players outside S do. The second approach computes for every coalition S the minimal amount of money which is such that the players outside S can prevent that the players in S get more. Zhao (1999) showed that for the case of duplicate technologies these two approaches lead to the same cooperative game. He provided a necessary and sufficient condition for convexity of special situations in these games.

In this paper we focus on the case of oligopoly without transferable technologies. In the spirit of Aumann (1959) two cooperative games are defined which, again, happen to coincide. We show that the resulting game is a convex game in general (for the specific case that all firms are symmetric this result was already obtained by Meinhardt (1999)). Moreover, using the same techniques, we can show that oligopoly games with duplicate strategies are totally balanced in general.

Date received: April 27, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caez-67.