Feedback advertising strategies in a two-firm differential game: a numerical investigation

References

• Apostol, T. M. (1969). Mathematical analysis. Reading, MA: Addison-Wesley.
   Google Scholar
• Bazaraa, M. S., & Shetty, C. M. (1979). Nonlinear programming: Theory and algorithms. New York: John Wiley.
   Google Scholar
• Bellman, R. (1957). Dynamic programming. Princeton, NJ: Princeton University Press.
   Google Scholar
• Bensoussan, A., Hurst, E. G., & Näslund, B. (1974). Management applications of modern control theory. Amsterdam: North-Holland.
   Google Scholar
• Bertsekas, D. P. (1995). Dynamic programming and optimal control Belmont, MA: Athena Scientific. (Vol. I).
   Google Scholar
• Breitner, M. H. (2005). The genesis of differential games in light of Isaacs' contributions. Journal of Optimization Theory and Applications, 124(3), 523–559. doi: 10.1007/s10957-004-1173-0
   Web of Science ®Google Scholar
• Case, J. (1971). A differential game in economics. Management Science, 17(7), 394–410. doi: 10.1287/mnsc.17.7.394
   Web of Science ®Google Scholar
• Case, J. H. (1969). Toward a theory of many player differential games. SIAM Journal on Control, 7(2), 179–197. doi: 10.1137/0307013
   Google Scholar
• Chou, F.-S., & Parlar, M. (2006). Optimal control of a revenue management system with dynamic pricing facing linear demand. Optimal Control Applications and Methods, 27(6), 323–347. doi: 10.1002/oca.785
   Web of Science ®Google Scholar
• Deal, K. R. (1979). Optimizing advertising expenditures in a dynamic duopoly. Operations Research, 27(4), 682–692. doi: 10.1287/opre.27.4.682
   Web of Science ®Google Scholar
• Deal, K., Sethi, S. P., & Thompson, G. L. (1979). A bilinear-quadratic differential game in advertising. In P.-T. Liu & J. G. Sutinen (Eds.), Control theory in mathematical economics (pp. 91–109). New York: Marcel Dekker.
   Google Scholar
• Deal, K. R., & Zionts, S. (1973). A differential game solution to the problem of determining the optimal timing of advertising expenditures. In Proceedings of the second annual conference. Kingston, RI: American Institute of Decision Sciences.
   Google Scholar
• Gibbons, R. (1992). Game theory for applied economists. Princeton, NJ: Princeton University Press.
   Google Scholar
• Hartl, R. F., Sethi, S. P., & Vickson, R. G. (1995). A survey of the maximum principles for optimal control problems with state constraints. SIAM Review, 37(2), 181–218. doi: 10.1137/1037043
   Web of Science ®Google Scholar
• Huang, J., Leng, M., & Liang, L. (2012). Recent developments in dynamic advertising research. European Journal of Operational Research, 220(3), 591–609. doi: 10.1016/j.ejor.2012.02.031
   Web of Science ®Google Scholar
• Isaacs, R. (1954). Differential games I, II, III and IV (Technical report RM-1391, RM-1399, RM-1411, RM-1486). Santa Monica, CA: RAND Corporation.
   Google Scholar
• Isaacs, R. (1965). Differential games. New York: John Wiley and Sons.
   Google Scholar
• Isaacs, R. (1969). Differential games: Their scope, nature, and future. Journal of Optimization Theory and Applications, 3(5), 283–295. doi: 10.1007/BF00931368
   Google Scholar
• Kamien, M. I., & Schwartz, N. L. (1991). Dynamic optimization: The calculus of variations and optimal control in economics and management. Amsterdam: Elsevier.
   Google Scholar
• Kirk, D. E. (1970). Optimal control theory. Englewood Cliffs, NJ: Prentice-Hall.
   Google Scholar
• Nash, J. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36, 48–49. doi: 10.1073/pnas.36.1.48
   PubMed Web of Science ®Google Scholar
• Parlar, M. (1984). Optimal dynamic service rate control in time dependent M/M/S/N queues. International Journal of Systems Science, 15(1), 107–118. doi: 10.1080/00207728408926548
   Web of Science ®Google Scholar
• Pindyck, R. (1977). Optimal economic stabilization policies under decentralized control and conflicting objectives. IEEE Transactions on Automatic Control, 22(4), 517–530. doi: 10.1109/TAC.1977.1101557
   Web of Science ®Google Scholar
• Roberts, S. M., & Shipman, J. S. (1972). Two-point boundary value problems: Shooting methods. New York: American Elsevier.
   Google Scholar
• Sethi, S. P. (1973). Optimal control of the Vidale-Wolfe advertising model. Operations Research, 21, 998–1013. doi: 10.1287/opre.21.4.998
   Web of Science ®Google Scholar
• Sethi, S. P., & Thompson, G. L. (1981). Optimal control theory: Applications to management science. Boston: Martinus Nijhoff Publishing.
   Google Scholar
• Sethi, S. P., & Thompson, G. L. (2000). Optimal control theory: Applications to management science and economics (2nd ed.). New York: Springer.
   Google Scholar
• Starr, A. W., & Ho, Y. -C. (1969a). Further properties of nonzero-sum differential games. Journal of Optimization Theory and Applications, 3(4), 207–219. doi: 10.1007/BF00926523
   Google Scholar
• Starr, A. W., & Ho, Y. -C. (1969b). Nonzero-sum differential games. Journal of Optimization Theory and Applications, 3(3), 184–206. doi: 10.1007/BF00929443
   Google Scholar
• Vidale, M. L., & Wolfe, H. B. (1957). An operations research study of sales response to advertising. Operations Research, 5, 370–381. doi: 10.1287/opre.5.3.370
   Web of Science ®Google Scholar
• Wu, H., & Parlar, M. (2011). Games with incomplete information: A simplified exposition with inventory management applications. International Journal of Production Economics, 133, 562–577. doi: 10.1016/j.ijpe.2011.06.004
   Web of Science ®Google Scholar