A New Proof of the Existence and Uniqueness of the Cournot Equilibrium

Szidarovszky, Ferenc; Yakowitz, S.

doi:10.2307/2525963

Cited by 139 publications

(62 citation statements)

References 6 publications

(1 reference statement)

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“…Theorems 1A and 1B are natural counterparts of results on existence of Cournot equilibrium that have been obtained in the literature in the complete information case (see, e.g., Novshek (1985) and Szidarovszky and Yakowitz (1977)). It is the nice behavior of the expected payo¤ functions that stands behind equilibrium existence in our theorems.…”

Section: Cournot Competition With Incomplete Informationmentioning

confidence: 90%

“…For instance, if the inverse demand is a decreasing concave function, and …rms' cost functions are convex, then a …rm's payo¤ is a concave function of its own output, and under standard continuity assumptions the Nash Theorem yields equilibrium existence (see Szidarovszky and Yakowitz (1977)). In general, mere quasi-concavity of each …rm's payo¤ in its own output and continuity of …rms'payo¤ functions su¢ ce to obtain existence.…”

Section: Introductionmentioning

confidence: 99%

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On the existence of Bayesian Cournot equilibrium

Einy

Haimanko

Moreno

et al. 2010

Games and Economic Behavior

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We show that when …rms have incomplete information about the market demand and their costs, a (Bayesian) Cournot equilibrium in pure strategies may not exist, or be unique. In fact, we are able to construct surprisingly simple and robust examples of duopolies with these features. However, we also …nd some su¢ cient conditions for existence, and for uniqueness, of Cournot equilibrium in a certain class of industries.More general results arise when negative prices are possible.

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Section: Cournot Competition With Incomplete Informationmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

On the existence of Bayesian Cournot equilibrium

Einy

Haimanko

Moreno

et al. 2010

Games and Economic Behavior

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“…where   is homogeneous of degree one 5 See for instance Szidarovszky and Yakowitz (1977), or Vives (1999, p.99). 6 It can be shown that condition (ii) also implies that the elasticity of aggregate output with respect to the input price is negative,…”

Section: Cournot Equilibriummentioning

confidence: 99%

Aggregation with Cournot Competition: the Le Chatelier Samuelson Principle

Koebel¹,

Laisney²

2014

Annals of Economics and Statistics

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Abstract. This paper studies the aggregate substitution and expansion effects triggered by changes in input prices in a context where firms supply a homogeneous commodity and compete in quantities à la Cournot. We derive a sufficient condition for the existence of a Cournot equilibrium and show that this condition also ensures that the Le Chatelier-Samuelson principle is satisfied in the aggregate at the Cournot equilibrium, although it may not be satisfied at the firm level.

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“…Since the Assumptions 1 and 2 ensure the existence of a unique Nash equilibrium in pure strategies 12 (see for instance Szidarovszky and Yakowitz, 1977) the first-order conditions below determine the outcome of the Cournot game.…”

Section: Propositionmentioning

confidence: 99%

Quantity-setting games with a dominant firm

Tasnádi

2010

J. Econ.

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may Abstract:We consider a possible game-theoretic foundation of Forchheimer's model of dominant-firm price leadership based on quantity-setting games with one large firm and many small firms. If the large firm is the exogenously given first mover, we obtain Forchheimer's model. We also investigate whether the large firm can emerge as a first mover of a timing game.

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A New Proof of the Existence and Uniqueness of the Cournot Equilibrium

Cited by 139 publications

References 6 publications

On the existence of Bayesian Cournot equilibrium

On the existence of Bayesian Cournot equilibrium

Aggregation with Cournot Competition: the Le Chatelier Samuelson Principle

Quantity-setting games with a dominant firm

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