nach oben

Dynamic Games and Applications

Erschienen in:

21.04.2017

Intertemporal Non-separability and Dynamic Oligopoly

verfasst von: Curtis Eberwein, Ted To

Erschienen in: Dynamic Games and Applications | Ausgabe 2/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We construct a framework for modeling dynamic Cournot oligopoly. We consider models where utility maximizing consumers give rise to demand functions that depend on current and prior period prices. Future demand depends on the current price and consumers, and firms must take this into account when making their decisions. Focusing on problems that yield dynamic demand functions that are linear in current and prior period price, we characterize the unique Markov perfect equilibrium in linear strategies. We then demonstrate the applicability of our framework through a series of practical examples.

Vorheriger Artikel Evolutionary Games with Sequential Decisions and Dollar Auctions

Nächster Artikel Potential Differential Games

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

It is straightforward to allow for heterogeneity of consumers (we provide two such examples) provided that conditions ensuring nonnegativity of consumption are satisfied.

Given quadratic utility functions, there will generally exist an equilibrium with “policy functions” that are linear in the state. We focus on such equilibria.

It is straightforward to allow for i.i.d. idiosyncratic shocks, i.e., $c_{it}={\bar{c}}+\varepsilon _{it}$. In this case, rather than taking rival outputs as given, firms must form beliefs over the distribution over rival outputs.

Note that we have specified the problem as one where in equilibrium, rival outputs are functions of the prior period price and an individual firm maximizes discounted expected profits through choice of price. Equivalently, we could invert (1) to get $p_t(x_t^i+X_t^{-i},p_{t-1})$ and specify an individual firm’s problem more traditionally as:

$$\begin{aligned} V^i(p_{t-1},c_t)=\max _{x_t^i}[(p_t(x_t^i+X_t^{-i}(p_{t-1},c_t ),p_{t-1})-c_t)x_t^i+\beta E_tV^i(p_t,c_{t+1})]. \end{aligned}$$

In equilibrium, for every $i, x_t^i$ is a best response to $X_t^{-i}$ (i.e., $x_t^i$ solves the Bellman equation) and $X_t^{-i}=\sum _{j\ne i}x_t^j$.

With more complicated shocks and additional information and behavioral assumptions to ensure solvability, prices can be shown to follow more complicated stochastic processes. We examine one such extension in “Appendix 2.”

As shown in the prior section, given linear consumer demand, expected prices will indeed have this form. Linearity of demand will be verified shortly.

This system is a subset of the system of equations used in Appendix 1 to prove Theorem 1. It is important to bear in mind that this is an artificial system of equations. For example, application of stability conditions to establish properties of the solution (i.e., the correspondence principle in macroeconomics) would be a mistake since stability in the artificial system is meaningless.

It is straightforward to introduce a cost to holding inventory. Suppose for example that inventory decays by the factor $\delta $ so that the following budget constraint becomes: $p_t(i_{t+1}-\delta i_t+y_t)+w_t\le {\bar{w}}$.

This can easily be derived from the fact that $(N-1)^2\ge 0$.

The case where $d<0$ is analogous but requires $\lambda =-\sqrt{(2q-1)/\beta }$.

Becker GS, Murphy KM (1988) A theory of rational addiction. J Polit Econ 96(4):675–700CrossRef

Bils M, Klenow PJ (2004) Some evidence on the importance of sticky prices. J Polit Econ 112(5):947–985CrossRef

Bond EW, Samuelson L (1984) Durable goods monopolies with rational expectations. RAND J Econ 15:336–345MathSciNetCrossRef

Bulow J (1982) Durable-goods monopolists. J Polit Econ 1982:314–332CrossRef

Carlton DW (1986) The rigidity of prices. Am Econ Rev 76:637–658

Caucutt EM, Ghosh M, Kelton CM (1999) Durability versus concentration as an explanation for price inflexibility. Rev Ind Organ 14:27–50CrossRef

Cooper R, Haltiwanger J (1990) Inventories and the propagation of sectoral shocks. Am Econ Rev 80(1):170–190

Driskill R (1997) Durable-goods monopoly, increasing marginal cost and depreciation. Economica 64(253):137–154CrossRef

Driskill R (2001) Durable goods oligopoly. Int J Ind Organ 19(3–4):391–413CrossRef

10.

Driskill R, McCafferty S (2001) Monopoly and oligopoly provision of addictive goods. Int Econ Rev 42(1):43–72MathSciNetCrossRef

11.

Dudine P, Hendel I, Lizzeri A (2006) Storable good monopoly: the role of commitment. Am Econ Rev 96(5):1706–1719CrossRef

12.

Fethke G, Jagannathan R (1996) Habit persistence, heterogeneous tastes, and imperfect competition. J Econ Dyn Control 20:1193–1207CrossRefMATH

13.

Hall RE (1988) Intertemporal substitution in consumption. J Polit Econ 96:339–357CrossRef

14.

Stokey N (1981) Rational expectations and durable goods pricing. Bell J Econ 12:112–128MathSciNetCrossRef

Titel: Intertemporal Non-separability and Dynamic Oligopoly
verfasst von: Curtis Eberwein
Ted To
Publikationsdatum: 21.04.2017
Verlag: Springer US
Erschienen in: Dynamic Games and Applications / Ausgabe 2/2018
Print ISSN: 2153-0785
Elektronische ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-017-0220-z

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 2/2018

Stochastic Differential Games for Which the Open-Loop Equilibrium is Subgame Perfect

Algebraic Formulation and Nash Equilibrium of Competitive Diffusion Games

Evolutionary Games with Sequential Decisions and Dollar Auctions

Simple Motion Evasion Differential Game of Many Pursuers and Evaders with Integral Constraints

Potential Differential Games

A Two-Player Zero-sum Game Where Only One Player Observes a Brownian Motion