In this paper, we investigate the problem of the strategic foundation of the Cournot-Walras equilibrium approach. To this end, we\ud respecify à la Cournot-Walras the mixed version of a model of simultaneous, noncooperative exchange, originally proposed by Lloyd S.\ud Shapley. We show, through an example, that the set of the Cournot-\ud Walras equilibrium allocations of this respecifcation does not coincide\ud with the set of the Cournot-Nash equilibrium allocations of the mixed\ud version of the original Shapley's model. As the nonequivalence, in a\ud one-stage setting, can be explained by the intrinsic two-stage nature of\ud the Cournot-Walras equilibrium concept, we are led to consider a further reformulation of the Shapley's model as a two-stage game, where\ud the atoms move in the first stage and the atomless sector moves in\ud the second stage. Our main result shows that the set of the Cournot-Walras equilibrium allocations coincides with a specific set of subgame\ud perfect equilibrium allocations of this two-stage game, which we call\ud the set of the Pseudo-Markov perfect equilibrium allocations
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