Economic Theory 17, 665–674 (2001) Oligopoly equilibria in exchange economies: a limit theorem ⋆ Rim Lahmandi-Ayed Ecole Polytechnique de Tunisie, BP 743, 2078 La Marsa, TUNISIA (e-mail: rim.lahmandi@excite.com) Received: May 26, 1999; revised version: April 3, 2000 Summary. In a pure exchange economy, agents have the possibility of behaving strategically by putting only a part of their initial endowments on the market. An oligopoly equilibrium is defined to be a Nash equilibrium of the game in which agents choose simultaneously quantities to be put on the market. It is proved that under standard hypotheses, the oligopoly equilibrium leads to the competitive equilibrium when the economy is replicated an infinite number of times. Keywords and Phrases: Strategic behaviour, Oligopoly equilibrium, Replica- tion, Convergence, Competitive equilibrium. JEL Classification Numbers: C72, D51. 1 Introduction The intuition behind the competitive behaviour is that the agents are in very “large” number, then their influence on the price is “negligible” and they are price-takers. In real life, no competition is perfect, but “in economics, as in the physical sciences, the study of the ideal state has proved very fruitful, though in practice, it is at best, only approximately achieved.”, Aumann (1964). However, it must be proved that this ideal state is a “good” approximation of what really happens. Therefore, it must be checked that it does not pay to behave strategically when the number of agents increases unboundedly. Two questions have to be investigated: first, does strategic behaviour lead to the competitive outcome as the economy is enlarged? Second, does there exist a sequence of strategic equilibria that converges to the competitive outcome? ⋆ Greatful thanks are due to Jean-Marc Bonnisseau for his very helpful suggestions and discussions, and to an anonymous referee for very helpful comments.