Cournot–Walras equilibrium as a subgame perfect equilibrium

Abstract

In this paper, we investigate the problem of the strategic foundation of the Cournot-Walras equilibrium approach. To this end, we respecifyà la Cournot-Walras the mixed version of a model of simultaneous, noncooperative exchange, originally proposed by Lloyd S. Shapley. We show, through an example, that the set of the Cournot-Walras equilibrium allocations of this respecification does not coincide with the set of the Cournot-Nash equilibrium allocations of the mixed version of the original Shapley's model. As the nonequivalence, in a one-stage setting, can be explained by 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 the set of the Cournot-Walras equilibrium allocations coincides with a specific set of subgame perfect equilibrium allocations of this two-stage game, which we call the set of the Pseudo-Markov perfect equilibrium allocations. Journal of Economic Literature Classification Numbers: C72, D51. * We would like to thank Pierpaolo Battigalli, Marcellino Gaudenzi, and an anonymous referee for their comments and suggestions.

On Cobb-Douglas Preferences in Bilateral Oligopoly

“…These deductions are consistent with the findings of Codognato (1995) who found that in a mixed exchange economy with some atoms and an atomless sector the set of 'Cournot-Walras' equilibria (in which the atomless sector are assumed to behave as price-takers) may be disjoint from the set of 'Cournot-Nash' equilibria (in which all traders engage in trade via the strategic market game mechanism without price-taking assumptions being imposed), but that they intersect when traders have Cobb-Douglas preferences (see also Busetto et. al.…”

“…The Cobb-Douglas assumption has been used to good effect in the investigation of certain issues. For example, under the assumption of Cobb-Douglas preferences for one set of traders Codognato and Julien (2013) are able to extend the existence theorem of Busetto et. al.…”

Unemployment equilibrium and economic policy in mixed markets

“…Additionally, 2 (0; 1) is the constant elasticity of utility with respect to consumption, which also measures the strength of the demand linkage across both sectors. Additionally, " represents the Frisch elasticity of labor supply (constant marginal utility of wealth) 7 . 4 Some models assume agents do not consume the good they produce in order to circumvent "Ford e¤ects" (Diamond (1982), Heller (1986), Roberts (1987) and Weitzman (1982)).…”

“…6 We can notice that for = 0 the economy is autarkic; and for = 1 commodity 2 is a pure input and agents only consume good 1. 7 Moreover, " 1 is the elasticity of marginal disutility with respect to work.…”

Bilateral oligopoly and quantity competition

“…There are few recent exceptions to this: Codognato [2] provides two examples demonstrating convergence in one case, and non-convergence in the other, of outcomes in bilateral oligopoly to Cournot outcomes as the number of buyers increases by replication. Busetto, Codognato and Ghosal [1] also highlight this non-equivalence in a model with a continuum of agents with some atoms (the oligopolists), and proceed by considering the relationship between a two-stage respeci…cation of the strategic market game and Cournot's model. We contribute to this literature by identifying a game that is the many-buyer limit of bilateral oligopoly and develop necessary and su¢ cient conditions under which outcomes in this model of quantity competition will be equal to those in Cournot oligopoly.…”