Abstract
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.
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References
Sethi, S.R., “Optimal Control Problems in Advertising” in “Optimal Control Theory and its Applications”, Springer Verlag Lecture Notes in Econ. and Math. Systems, no. 106, 1974, pp. 301–337.
Starr, A.W., Ho, Y.C., “Nonzero-Sum Differential Games” and “Further Properties of Nonzero-Sum Differential Games”, JOTA, vol. 9, 1969, pp. 184–219.
Leitmann, G., “Cooperative and Non-Cooperative Many Players Differential Games”, International Centre for Mechanical Sciences courses and lectures no. 190, Udine, 1974, published by Springer.
Blaquiere, A., “Dynamic Games with Coalitions and Diplomacies”, this volume.
Aubin, J.P., “Fuzzy Games”, Proceedings of the 7th IFIP Conference on Optimization Techniques, Nice, France, 1975.
Haas, E.B., “The Balance of Power: Prescription, Concept or Propaganda?”, World Politics, vol. 5, 1953, pp. 442–477.
Gately, D., “Sharing the Gains from Customs Unions among Less Developed Countries”, Journal of Development Economics 1, 1974, pp. 213–233.
Lee, E.B., Markus, L., “Foundations of Optimal Control Theory”, John Wiley, 1967.
Stalford, H., Leitmann, G., “Sufficiency Conditions for Nash Equilibria in N-Person Differential Games”, in Blaquiere, A., (ed.), “Topics in Differential Equations”, North Holland, 1973.
Blaquiere, A., Wiese, K.E., “Jeux qualitatifs multieages a N personnes, coalitions”, C.R. Acad. Sc. Paris, t.270, pp. 1280–1282 (mai 1970), Serie A.
Owen, G., “Game Theory”, Saunders, 1968,
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© 1976 Plenum Press, New York
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Olsder, G.J. (1976). Some Thoughts about Simple Advertising Models as Differential Games and the Structure of Coalitions. In: Ho, Y.C., Mitter, S.K. (eds) Directions in Large-Scale Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2259-7_12
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DOI: https://doi.org/10.1007/978-1-4684-2259-7_12
Publisher Name: Springer, Boston, MA
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