Some Thoughts about Simple Advertising Models as Differential Games and the Structure of Coalitions
Two simple dynamic advertising models are discussed. In both models three companies compete through advertising for the trade of a fixed pool of customers.
Several criteria, to be maximized by the companies, are considered. Nash optimal solutions — open loop as well as closed loop — are studied.
It is assumed that two of the three companies can cooperate against the third one. Such a coalition, which can change in time, is formed according to specific rules. It is then seen that, if one allows coalitions, they do indeed appear with respect to one of the models. With respect to the other model a coalition is disadvantageous to both participants and hence will not be formed.
KeywordsOptimal Control Problem Open Loop Differential Game Optimal Control Theory Total Profit
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