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Séance TA6 - Théorie des jeux I / Game Theory I

Jour mardi, le 10 mai 2005
Salle Marie-Husny
Président Georges Zaccour

Présentations

10h30 Markov Perfect Equilibrium Advertising Allocation in a Multi-Instrument Lanchester Duopoly
  Ramla Jarrar, Greenwich University, Marketing and Operations, Old Royal Naval College Park Row, Greenwich, London, United Kingdom, SE10 9LS
Guiomar Martin-Herran, Universidad de Valladolid, Economia Aplicada, Avda. Valle Esgueva, 6, Valladolid, Valladolid, Spain, 47011

We propose a numerical approach to compute Stationary Markov perfect Nash equilibrium advertising strategies for the extended form of the Lanchester model. The proposed algorithm has the merit of considering a positive discount rate. We also propose an interesting comparison between the simple and extended form of the Lanchester model.


10h55 Pairs of Reciprocal Optimal Control Problems and Economic Applications
  Bruno Viscolani, University of Padova, Pure and Applied Mathematics, via Belzoni 7, Padova, Italy, I 35131
Luca Grosset, University of Padova, Pure and Applied Mathematics, via Belzoni 7, Padova, Italy, I 35131

We study a reciprocity principle for optimal control problems and apply the results to some classical economic models. Thus we extend some calculus of variations results on reciprocal isoperimetric problems, which have already been exploited and specified by Caputo to develop an interesting comparative dynamics analysis for Hotelling's model.


11h20 A Differential Game of a Dual Distribution Channel
  Georges Zaccour, HEC Montréal, GERAD et Marketing, 3000, ch. de la Côte-Sainte-Catherine, Montréal, Québec, Canada, H3T 2A7
Olivier J. Rubel, HEC Montréal, Marketing & GERAD, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Québec, Canada, H3T 2A7

An infinite-horizon differential game between a manufacturer and a retailer is considered. The players control their marketing efforts and the sales share of the online channel is the state of the system. The manufacturer seeks to maximize her profit made on both the indirect and direct channels and faces, aside from her marketing effort, a logistics cost of selling online. The retailer seeks to keep consumers buying offline through her effort. A feedback Nash equilibrium is identified and results are discussed.