Asymmetric Cournot duopoly: game complete analysis

Carfì, David and Perrone, Emanuele (2012): Asymmetric Cournot duopoly: game complete analysis.

Abstract

In this paper we apply the Complete Analysis of Differentiable Games (introduced by D. Carfì in [3], [6], [8], [9]; already employed by himself and others in [4], [5], [7]) and some new algorithms using the software wxMaxima 11.04.0, in order to reach a total scenario knowledge (that is the total knowledge of the payoff space of the interaction) of the classic Cournot Duopoly (1838), viewed as a complex interaction between two competitive subjects, in a particularly interesting asymmetric case. Moreover, in this work we propose a theoretical justification, for a general kind of asymmetric duopolistic interactions (which often appear in the real economic world), by considering and proposing a Cobb-Douglas perturbation of the classic linear model of production costs.

• Item Type: MPRA Paper
• Language: English
• Keywords: Asymmetric Cournot Duopoly; Normal-form Games; Software algorithms in Microeconomic Policy; Complete Analysis of a normal-form game; Pareto optima; valuation of Nash equilibriums; Bargaining solutions
• Subjects: D - Microeconomics > D2 - Production and Organizations; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory

References

1. Aubin Jean Pierre, Mathematical Methods of Game and Economic Theory (Revised Edition), (North-Holland).

2. Aubin Jean Pierre, Optima and Equilibria, (Springer Verlag, 1998).

3. Carfì David, Topics in Game Theory, (Edizioni Il gabbiano, 2010).

4. Carfì David, Schilirò Daniele, Crisis in the Euro area: coopetitive game solutions as new policy tools, TPREF - Theoretical and Practical Research in Economic Fields, Summer issue 2011

5. Carfì David, Ricciardello Angela, An algorithm for payoff space in C1 games, AAPP | Physical, Mathematical, and Natural Sciences, Vol. LXXXVIII, issue 1, 2010

6. Carfì David, Differentiable game complete analysis for tourism firm decisions, Proceedings of THE 2009 INTERNATIONAL CONFERENCE ON TOURISM and WORKSHOP on Sustainable tourism within High Risk areas of environmental crisis, Messina, April 22/25 (2009)

7. Carfì David, Globalization and Differentiable General Sum Games, Proceeding of 3rd International Symposium Globalization and convergence in economic thought, Faculty of Economics - Communication and Economic Doctrines Department - The Bucharest Academy of Economic Studies - Bucharest December 11/12 (2009)

8. Carfì David, Payoff space and Pareto boundaries of C1 Games, APPS vol. 2009

9. Carfì David, Complete study of linear infinite games, Proceedings of the International Geometry Center - Prooceeding of the International Conference “Geometry in Odessa 2009”, Odessa, 25 - 30 May 2009 - vol. 2 n. 3 (2009)

10. Carfì David, Optimal boundaries for decisions, Atti dell'Accademia Peloritana dei Pericolanti - Classe di Scienze Fisiche, Matematiche e Naturali Vol. LXXXVI, (2008)

11. Carfì David, Ricciardello Angela, Non-reactive strategies in decision-form games, AAPP | Physical, Mathematical, and Natural Sciences, Vol. LXXXVII, issue 1, pp. 1-18

12. Carfì David, Decision-form games, Proceedings of the IX SIMAI Congress, Rome, 22 - 26 September 2008, Communications to SIMAI congress, vol. 3, (2009) pp. 1-12

13. Carfì David, Reactivity in decision-form games, MPRA - paper 29001, University Library of Munich, Germany

14. Carfì David, Ricciardello Angela, Mixed Extensions of decision-form games, MPRA - paper 28971, University Library of Munich, Germany