Cournot–Nash equilibria in limit exchange economies with complete markets and consistent prices

Codognato, Giulio; Ghosal, Sayantan

doi:10.1016/s0304-4068(99)00043-9

Cited by 23 publications

(33 citation statements)

References 5 publications

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“…Here, we show, for the Cournot-Walras equilibrium, a result similar to those obtained, in limit exchange economies, by Codognato and Gabszewicz (1993) for the homogeneous oligopoly equilibrium, and by Codognato and Ghosal (2000) for the Cournot-Nash equilibrium. More precisely, we assume that the space of traders is denoted by the complete measure space (T, T , µ), where the set of traders is denoted by T = T 0 ∪ T 1 , with T 0 = [0, 1] and T 1 = [2,3], T is the σ-algebra of all measurable subsets of T , and µ is the Lebesgue measure on T .…”

Section: Definition 6 a Pair (ẽX) Consisting Of A Strategy Selectisupporting

confidence: 85%

“…Now, given a strategy selection b ∈ L 1 (µ, B(·)), by Proposition 6, there exists an integrable function x p (b) : T 0 → R l + such that, for each t ∈ T 0 , x p (b) (t) ∈ X p (b) (t). By Lemma 5 in Codognato and Ghosal (2000), for each t ∈ T 0 , there exist λ W × t∈T 1 B…”

Section: Appendix 1 Proofs Of the Propositions And The Corollarymentioning

confidence: 99%

“…This reformulation of the Shapley's model allows us to define the following concept of Cournot-Nash equilibrium for exchange economies with a continuum of traders (see Codognato and Ghosal (2000)). t, b(t), p(b \ b(t)))), for all t ∈ T and for all b(t) ∈ B(t).…”

Section: Cournot-nash Equilibriummentioning

confidence: 99%

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Noncooperative oligopoly in markets with a continuum of traders

Busetto

Codognato

Ghosal

2011

Games and Economic Behavior

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In this paper, we study three prototypical models of noncooperative oligopoly in markets with a continuum of traders: the model of Cournot-Walras equilibrium of Codognato and Gabszewicz (1991), the model of Cournot-Nash equilibrium of Lloyd S. Shapley, and the model of Cournot-Walras equilibrium of Busetto et al. (2008). We argue that these models are all distinct and only the Shapley's model with a continuum of traders and atoms gives an endogenous explanation of the perfectly and imperfectly competitive behavior of agents in a one-stage setting. For this model, we prove a theorem of existence of a Cournot-Nash equilibrium.

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Section: Definition 6 a Pair (ẽX) Consisting Of A Strategy Selectisupporting

confidence: 85%

Section: Appendix 1 Proofs Of the Propositions And The Corollarymentioning

confidence: 99%

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Noncooperative oligopoly in markets with a continuum of traders

Busetto

Codognato

Ghosal

2011

Games and Economic Behavior

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“…Theorem 4 states that the condition which characterizes the nonempty intersection of the sets of Walras and Cournot-Nash allocations requires that each atom demands a null amount of one commodity. Moreover, Examples 6,7,8,and 9 show that this characterization condition is non-vacuous. Proposition 2 provides a rationale for these examples by exhibiting a necessary condition, expressed in terms of bounds on atoms' marginal rates of substitution, for Theorem 4 to hold when atoms' preferences are represented by additively separable utility functions, the same class considered in the examples.…”

Section: Resultsmentioning

confidence: 91%

“…The following theorem reminds us that, when the space of traders is atomless, the core coincides with the set of Walras allocations as proved by Aumann (1964) which, in turn, coincides with the set Cournot-Nash allocations of the Shapley window model as shown by Codognato and Ghosal (2000). Gabszewicz and Mertens (1971) and Shitovitz (1973) showed that an equivalence between the core and the set of Walras allocations may hold even when the space of traders contains atoms.…”

Section: The Equivalence Theoremsmentioning

confidence: 77%

Atomic Cournotian traders may be Walrasian

Codognato

Ghosal

Tonin

2015

Journal of Economic Theory

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In a bilateral oligopoly, with large traders, represented as atoms, and small traders, represented by an atomless part, when is there a non-empty intersection between the sets of Walras and Cournot-Nash allocations? Using a two-commodity version of the Shapley window model, we show that a necessary and sufficient condition for a Cournot-Nash allocation to be a Walras allocation is that all atoms demand a null amount of one of the two commodities. We provide four examples which show that this characterization holds non-vacuously. When our condition fails to hold, we also confirm, through some examples, the result obtained by Okuno et al. (1980): small traders always have a negligible influence on prices, while the large traders keep their strategic power even when their behavior turns out to be Walrasian in the cooperative framework considered by Gabszewicz and Mertens (1971) and Shitovitz (1973).

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Cournot–Walras equilibrium as a subgame perfect equilibrium

2008

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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.

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Cournot–Nash equilibria in limit exchange economies with complete markets and consistent prices

Cited by 23 publications

References 5 publications

Noncooperative oligopoly in markets with a continuum of traders

Noncooperative oligopoly in markets with a continuum of traders

Atomic Cournotian traders may be Walrasian

Cournot–Walras equilibrium as a subgame perfect equilibrium

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