Constrained and unconstrained models of a variable-sum market game characterizing the problem of television programming are developed. Solutions are obtained through the introduction of a nonresponding pseudo-firm which turns the game into a constant-sum one. The relative values of competitive and noncompetitive models are then discussed.
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References
1.
Augustin Cournot, Researches into the Mathematical Principles of the Theory of Wealth, Nathaniel T. Bacon, trans., New York: The Macmillan Co., 1897.
2.
FellnerWilliam, Competition Among the Few, New York: Alfred A. Knopf, Inc., 1949.
3.
FriedmanLawrence, “Game Theory Models in the Allocation of Advertising Expenditures,”Operations Research6 (September 1958), 699–709. Reprinted in Frank M. Bass, et al. eds., Mathematical Models and Methods in Marketing, Homewood, Ill.: Richard D. Irwin, Inc., 1961.
4.
JamesM. Henderson, and QuandtRichard E., Microeconomic Theory: A Mathematical Approach, New York: McGraw-Hill Book Co., 1958.
5.
AlfredE. Kuehn, “A Model for Budgeting Advertising,” in BassFrank M., eds., Mathematical Models and Methods in Marketing, Homewood, Ill: Richard D. Irwin, Inc., 1961.
6.
Duncan LuceR., and RaiffaHoward, Games and Decisions: Introduction and Critical Survey, New York: John Wiley & Sons, Inc., 1957.
7.
HarlandD. Mills, “A Study in Promotional Competition,” in BassFrank M., eds., Mathematical Models and Methods in Marketing, Homewood, Ill: Richard D. Irwin, Inc., 1961.
