Essays in Honour of Karl-Göran Mäler
Edited by Bengt Kriström, Partha Dasgupta and Karl-Gustaf Löfgren
Chapter 18: The Core of the Cooperative Game Associated with Oligopoly Firms
18. The core of the cooperative game associated with oligopoly firms Hirofumo Uzawa 1 INTRODUCTION In Uzawa (1996, 1999), we developed an analytical framework in which the structure of the n-person cooperative games associated with the economies involving public goods in the Samuelsonian sense is examined in detail. Our approach was originally formulated with the specific purpose of examining the conditions under which the core of the n-person cooperative game for global warming is non-empty, as in detail described in Uzawa (1999). The analysis may be equally applicable to the general situation where both the schedules of marginal utilities and products depend upon the aggregate quantities of private or public goods (or public bads in the case of global warming) produced in the economy. In this chapter, we apply our approach to the analysis of the behavior of oligopoly firms engaged in the production of single or differentiated products, with a particular emphasis on the conditions under which the core of the nperson cooperative game arising out of the oligopoly market is non-empty. As regards the analysis of the behavior of oligopoly firms, there is an extensive list of literature, beginning with the classic contribution of Cournot (1838) to the recent game-theoretic approaches. The recent game-theoretic contributions are given a well-balanced overview by the excellent survey articles of Friedman (1982) and Shapiro (1989). This chapter is largely based upon the general framework of the oligopoly theory as provided by Friedman’s and Shapiro’s survey articles, but also Friedman (1977, 1983), Fudenberg...
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