Bargaining, coalitions and competition

We study a decentralized matching model in a large exchange economy, in which trade takes place through non--cooperative bargaining in coalitions of finite size. Under essentially the same conditions of core equivalence, we show that the strategic equilibrium outcomes of our model coincide with the Walrasian allocations of the economy. Our method of proof exploits equivalence results between the core and Walrasian equilibria. Our model relaxes differentiability and convexity of preferences thereby covering the case of indivisible goods.