Dynamic duopoly with adjustment costs: A differential game approach

Driskill, Robert; McCafferty, Stephen

doi:10.1016/0022-0531(89)90085-9

Cited by 79 publications

(54 citation statements)

References 6 publications

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“…8 This formulation implies that adjustment costs are minimized when no adjustment takes place. The per-period pro…t function for …rm i is the following concave function in its own prices:…”

Section: The Modelmentioning

confidence: 99%

“…See Maskin and Tirole (1988.b). 8 We use convex adjustment costs as in Rotemberg (1982). Quadratic price adjustment costs have been used also by Lapham and Ware (1994) and Jun and Vives (2001) because of their analytical tractability.…”

Section: The Modelmentioning

confidence: 99%

“…The presence of nonlinearity implies that we must expect many solutions for the unknown parameters, and thus, multiple Markov perfect equilibiria. 17 In order to reduce this multiplicity, we concentrate our analysis to symmetric Markov perfect equilibria that are asymptotically stable as in Driskill and McCa¤erty (1989) and Jun and Vives (2001). An asymptotically stable equilibrium is one where the equilibrium prices converge to a …nite stationary level for every feasible initial condition.…”

Section: Computation and Properties Of The Markov Perfect Equilibriummentioning

confidence: 99%

“…Fershtman and Kamien (1987), using a continuous time model with sticky prices, found that when only present matters for …rms their stationary Markov perfect equilibrium converges to the competitive outcome. On the other hand, Driskill and McCa¤erty (1989), using a similar model but with adjustment costs in quantities, found that the Markov perfect equilibrium converges to the static Nash equilibrium of the repeated game without adjustment costs. In our model, we have the following result:…”

Section: Markov Perfect Equilibrium In the Limit Gamementioning

confidence: 99%

“…However, the same result described above still hold in when these adjustment costs are considered. For example, Reynolds (1989Reynolds ( , 1991 and Driskill and McCa¤erty (1989) study a dynamic duopoly with homogenous product and quadratic capacity adjustment costs in continuous time setting. The steady state output in the subgame perfect equilibrium is found to be larger than in the Cournot static game without adjustment costs.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Price Competition with Price Adjustment Costs and Product Differentiation

Vernasca

2003

SSRN Journal

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We study a discrete time dynamic game of price competition with spatially di¤erentiated products and price adjustment costs. We characterise the Markov perfect and the open-loop equilibrium of our game. We …nd that in the steady state Markov perfect equilibrium, given the presence of adjustment costs, equilibrium prices are always higher than prices at the repeated static Nash solution, even though, adjustment costs are not paid in steady state. This is due to intertemporal strategic complementarity in the strategies of the …rms and from the fact that the cost of adjusting prices adds credibility to high price equilibrium strategies. On the other hand, the stationary open-loop equilibrium coincides always with the static solution. Furthermore, in contrast to continuous time games, we show that the stationary Markov perfect equilibrium converges to the static Nash equilibrium when adjustment costs tend to zero. Moreover, we obtain the same convergence result when adjustment costs tend to in…nity.-

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Section: The Modelmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

Section: Computation and Properties Of The Markov Perfect Equilibriummentioning

confidence: 99%

Section: Markov Perfect Equilibrium In the Limit Gamementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamic Price Competition with Price Adjustment Costs and Product Differentiation

Vernasca

2003

SSRN Journal

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Stability of a mean field game of production adjustment

Wang

Xin

2023

Asian Journal of Control

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We propose a mean field game model to study the stability of production adjustment by extending a kind of linear quadratic Gaussian game in large population systems. First, we present the model's equilibrium solutions by a backward HJB equation and a forward FPK equation. Second, we employ the local perturbation method to transform the nonlinear problem into a linear one to study the solutions' stability. Third, we use the spectrum and contraction analyses to study the stationary solutions' linear stability. At last, we validate the results by the numerical simulation. The results show that the additional cost coefficient and noise intensity affect the system's stability. If the additional cost coefficient and the noise intensity are large enough for firms to change their outputs, then firms will try to reduce their production adjustment and remain stable long‐term.

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Consistent Conjectures, Equilibria and Dynamic Games

Jean-Marie¹,

Tidball²

Dynamic Games: Theory and Applications

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Dynamic duopoly with adjustment costs: A differential game approach

Cited by 79 publications

References 6 publications

Dynamic Price Competition with Price Adjustment Costs and Product Differentiation

Dynamic Price Competition with Price Adjustment Costs and Product Differentiation

Stability of a mean field game of production adjustment

Consistent Conjectures, Equilibria and Dynamic Games

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