Is a Unique Cournot Equilibrium Locally Stable?

Dastidar, Krishnendu Ghosh

doi:10.1006/game.1999.0768

Cited by 35 publications

(20 citation statements)

References 10 publications

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“…Okuguchi and Yamazaki (2008) derive sufficient conditions for the unique equilibrium in sumaggregative games to be globally stable. Dastidar (2000) shows that there is a close relationship between local gradient stability and uniqueness of equilibria in the Cournot game. In this paper I pursue a similar question by investigating the relationship between uniqueness and local stability of the stepwise best-reply dynamics for the analytically tractable classes of sum-aggregative games and symmetric games.…”

Section: Introductionmentioning

confidence: 91%

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Local Contraction-Stability and Uniqueness

Hefti

2013

SSRN Journal

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This paper investigates the relationship between uniqueness of Nash equilibria and local stability with respect to the best-response dynamics in the cases of sum-aggregative and symmetric games. If strategies are equilibrium complements, local stability and uniqueness are the same formal properties of the game. With equilibrium substitutes, local stability is stronger than uniqueness. If players adjust sequentially rather than simultaneously, this tends towards making a symmetric equilibria of symmetric games more stable. Finally, the relationship between the stability of the Nash best-response dynamics is compared to the stability of the response-dynamics induced by aggregate-taking behavior.

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Section: Introductionmentioning

confidence: 91%

“…Dixit (1986), Vives (1999), Dastidar (2000) or Hefti (2011) for applications). s > 0 is an arbitrary speed of adjustment.…”

Section: Gradient Dynamics Sequential Adjustments and Uniquenessmentioning

confidence: 99%

Local Contraction-Stability and Uniqueness

Hefti

2013

SSRN Journal

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“…Hahn [29] established asymptotic stability of this process to the unique equilibrium of the Cournot oligopoly game under conditions which ensure decreasing replacement functions. These results were extended by Al-Nowaihi and Levine [1] and, more recently, by Dastidar [20]. Discrete best-response dynamics for aggregative games have recently been analyzed by Kukushkin [34] for finite strategy spaces and "better-response" dynamics 32 by Dindos and Mezetti [23] for interval strategy spaces.…”

Section: Stabilitymentioning

confidence: 98%

“…where MF and MC are given by (19) and (20). If ∂u i /∂c > 0, we can apply the factorization principle with φ i = MF ∂u i /∂c to divide by φ i , which gives…”

Section: Sharing Gamesmentioning

confidence: 99%

Fully aggregative games

Cornes

Hartley

2012

Economics Letters

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We study aggregative games in which players' strategy sets are convex intervals of the real line and (not necessarily differentiable) payoffs depend only on a player's own strategy and the sum of all players' strategies. We give sufficient conditions on each player's payoff function to ensure the existence of a unique Nash equilibrium in pure strategies, emphasizing the geometric nature of these conditions. These conditions are almost best possible in the sense that the requirements on one player can be slightly weakened, but any further weakening may lead to multiple equilibria. The same conditions also permit the analysis of comparative statics and the competitive limit. We discuss the application of these conditions in a range of examples, chosen to illustrate various aspects their use. We also show that all restrictions on payoffs in aggregative games that guarantee the existence of a unique equilibrium of which we are aware are covered by these conditions. When payoffs are sufficiently smooth, these conditions can be tested using derivatives of the marginal payoff and we illustrate these tests in the applications introduced earlier. We also investigate conditions under which the unique equilibrium is locally stable. These hold in particular in a symmetric game under the same conditions required to ensure the existence of a unique equilibrium.

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“…For example, Dastidar shows that in case of the symmetric Cournot game uniqueness of the equilibrium and its local stability are intimately related (Dastidar (2000), p.213). By introducing the concept of symmetric stability I show for one-dimensional games satisfying assumption 3 that local symmetric stability and the inexistence of multiple symmetric equilibria are in fact the same properties.…”

Section: Stabilitymentioning

confidence: 99%

On Uniqueness and Stability of Symmetric Equilibria in Differentiable Symmetric Games

Hefti

2011

SSRN Journal

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Higher-dimensional symmetric games become of more and more importance for applied micro-and macroeconomic research. Standard approaches to uniqueness of equilibria have the drawback that they are restrictive or not easy to evaluate analytically. In this paper I provide some general but comparably simple tools to verify whether a symmetric game has a unique symmetric equilibrium or not. I distinguish between the possibility of multiple symmetric equilibria and asymmetric equilibria which may be economically interesting and is useful to gain further insights into the causes of asymmetric equilibria in symmetric games with higher-dimensional strategy spaces. Moreover, symmetric games may be used to derive some properties of the equilibrium set of certain asymmetric versions of the symmetric game.I further use my approach to discuss the relationship between stability and (in)existence of multiple symmetric equilibria. While there is an equivalence between stability, inexistence of multiple symmetric equilibria and the unimportance of strategic effects for the comparative statics, this relationship breaks down in higher dimensions. Stability under symmetric adjustments is a minimum requirement of a symmetric equilibrium for reasonable comparative statics of symmetric changes. Finally, I present an alternative condition for a symmetric equilibrium to be a local contraction which is more general than the conventional approach of diagonal dominance and yet simpler to evaluate than the eigenvalue condition of continuous adjustment processes.

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Is a Unique Cournot Equilibrium Locally Stable?

Cited by 35 publications

References 10 publications

Local Contraction-Stability and Uniqueness

Local Contraction-Stability and Uniqueness

Fully aggregative games

On Uniqueness and Stability of Symmetric Equilibria in Differentiable Symmetric Games

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