| Title | COMPETITIVE ADVERTISING IN A DUOPOLY: A STOCHASTIC DIFFERENTIAL GAME APPROACH |
| Publication Type | Journal Article |
| Year of Publication | 2009 |
| Authors | MEDHIN, NG, WAN, WEI |
| Secondary Title | Communications in Applied Analysis |
| Volume | 13 |
| Issue | 2 |
| Start Page | 245 |
| Pagination | 270 |
| Date Published | 04/2009 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 91A15, 91A23, 91A80, 91B50, 91B60 |
| Abstract | We can not neglect the randomness in the dynamics of market competition. This paper develops a stochastic differential game model which incorporates advertising effects for two companies introducing a new brand of product, competing for the market share and optimizing the budget. Our model is formulated as a stochastic, two-player, noncooperative differential game. As to the choice of basic dynamics, because of the special sale growing style in the introductory period, our model disagrees with the simple decay factor in Vidale-Wolfe model, but is based on the combination of Lanchester combat model and Logistic growth model. The solution concept is Nash Equilibrium. We derive optimality necessary conditions for Nash Equilibrium from dynamic programming, which is a Stochastic Partial Differential Equation(SPDE). The typical work in this field is from Prasad A. (2004), where he analytically solved his model because of the special form of the model. We choose to solve the optimality conditions, which is SPDE system numerically. Management strategy and discussions based on practical considerations will be given based on numerical results.
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| URL | http://www.acadsol.eu/en/articles/13/2/7.pdf |
| Short Title | COMPETITIVE ADVERTISING IN A DUOPOLY |
| Refereed Designation | Refereed |
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