Oligopoly equilibria in exchange economies: a limit theorem

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.