Cournot-Walras equilibrium as a subgame perfect equilibrium

In this paper, we respecify à la Cournot-Walras the mixed version of a model of noncooperative exchange, originally proposed by Lloyd S. Shapley. We first show that this respecification has a Cournot-Walras equilibrium allocation, which does not correspond to any CournotNash equilibrium of the mixed version of the original Shapley’s model. As this is due to the intrinsic two-stage nature of the Cournot-Walras equilibrium concept, we are led to consider a further reformulation of the Shapley’s model as a two-stage game, where the atoms move in the first stage and the atomless sector moves in the second stage. Our main result shows that any Cournot-Walras equilibrium allocation corresponds to a subgame perfect equilibrium of this two-stage game, thereby providing a game theoretical foundation to the Cournot-Walras equilibrium approach. Journal of Economic Literature Classification Numbers: C72, D51. ∗We would like to thank Pierpaolo Battigalli, Marcellino Gaudenzi and Sayantan Ghosal for their comments and suggestions. †Dipartimento di Scienze Economiche, Università degli Studi di Udine, Via Tomadini 30, 33100 Udine, Italy. ‡Dipartimento di Scienze Economiche, Università degli Studi di Udine, Via Tomadini 30, 33100 Udine, Italy.