Dynamic Strategic Interactions in Economic Systems

  • David W. K. Yeung
  • Leon A. Petrosyan
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)


The recent globalization and emergence of multinational corporations turned many major economic activities into dynamic interactive endeavors. The number of decision makers involved is relatively small and it leads to significant strategic interdependence. With human life being lived over time, and institutions like markets, firms, and governments changing over time, the economic system is definitely a dynamic interactive entity. Section 2.1 provides a general overview of dynamic interactive economic systems. Market outcomes under open-loop equilibria are investigated in Sect. 2.2 and those under feedback equilibria are examined in Sect. 2.3. An extension of the analysis to a stochastic framework is provided in Sect. 2.4.


Nash Equilibrium Differential Game Resource Stock Stochastic Differential Game Advertising Effort 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Basar, T.: Two general properties of the saddle-point solutions of dynamic games. IEEE Trans. Autom. Control AC-22, 124–126 (1977a) MathSciNetCrossRefGoogle Scholar
  2. Basar, T.: Existence of unique equilibrium solutions in nonzero-sum stochastic differential games. In: Roxin, E.O., Liu, P.T., Sternberg, R. (eds.) Differential Games and Control Theory II, pp. 201–228. Marcel Dekker, New York (1977b) Google Scholar
  3. Basar, T.: On the existence and uniqueness of closed-loop sampled-data Nash controls in linear-quadratic stochastic differential games in optimization techniques. In: Iracki, K., et al. (eds.) Lecture Notes in Control and information Sciences, pp. 193–203. Springer, New York (1980). Chap. 22 Google Scholar
  4. Berkovitz, L.D.: A variational approach to differential games. In: Dresher, M., Shapley, L.S., Tucker, A.W. (eds.) Advances in Game Theory, pp. 127–174. Princeton University Press, Princeton (1964) Google Scholar
  5. Case, J.H.: Equilibrium points of N-person differential games. PhD Thesis, University of Michigan, Ann Arbor, MI (1967). Department of Industrial Engineering, Tech. Report No. 1967-1 Google Scholar
  6. Case, J.H.: Toward a theory of many player differential games. SIAM J. Control Optim. 7, 179–197 (1969) MathSciNetMATHCrossRefGoogle Scholar
  7. Case, J.H.: Economics and the Competitive Process. New York University Press, New York (1979) Google Scholar
  8. Chiarella, C., Kemp, M.C., Long, N.V., Okuguchi, K.: On the economics of international fisheries. Int. Econ. Rev. 25, 85–92 (1984) MathSciNetMATHCrossRefGoogle Scholar
  9. Chintagunta, P.K.: Investigating the equilibrium profits to advertising dynamics and competitive effects. Manag. Sci. 39, 1146–1162 (1993) MATHCrossRefGoogle Scholar
  10. Chintagunta, P.K., Jain, D.: Empirical analysis of a dynamic duopoly model of competition. J. Econ. Manag. Strategy 4, 109–131 (1995) CrossRefGoogle Scholar
  11. Chintagunta, P.K., Vilcassim, N.J.: Marketing investment decision in a dynamic duopoly: a model and empirical analysis. Int. J. Res. Mark. 11, 287–306 (1994) CrossRefGoogle Scholar
  12. Clark, C.W.: Mathematical Bioeconomics: The Optimal Management of Renewable Resources, 2nd edn. Wiley, New York (1990) MATHGoogle Scholar
  13. Clemhout, S., Wan, H.Y. Jr.: Environmental problem as a common-property resource game. In: Ehtamo, H., Hämäläinen, R.P. (eds.) Dynamic Games in Economic Analysis, pp. 132–154. Springer, New York (1985a) Google Scholar
  14. Clemhout, S., Wan, H.Y. Jr.: Dynamic common-property resources and environmental problems. J. Optim. Theory Appl. 46, 471–481 (1985b) MathSciNetMATHCrossRefGoogle Scholar
  15. Clemhout, S., Wan, H.Y. Jr.: Differential games-economic applications. In: Aumann, R.J., Hart, S. (eds.) Handbook of Game Theory with Economic Applications II, pp. 801–825. Amsterdam, Elsevier (1994) Google Scholar
  16. Deal, K.: Optimizing advertising expenditure in a dynamic duopoly. Oper. Res. 27, 682–692 (1979) MATHCrossRefGoogle Scholar
  17. Dockner, E.J.: A dynamic theory of conjectural variations. J. Ind. Econ. 40, 377–395 (1992) CrossRefGoogle Scholar
  18. Dockner, E.J., Jørgensen, S.: Optimal pricing strategies for new products in dynamic oligopolies. Mark. Sci. 7, 315–334 (1988) CrossRefGoogle Scholar
  19. Dockner, E.J., Jørgensen, S.: New product advertising in dynamic oligopolies. ZOR, Z. Oper.-Res. 36, 459–473 (1992) MATHCrossRefGoogle Scholar
  20. Dockner, E.J., Kaitala, V.: On efficient equilibrium solutions in dynamic games of resource management. Resour. Energy 11, 23–34 (1989) CrossRefGoogle Scholar
  21. Dockner, E.J., Feichtinger, G., Mehlmann, A.: Noncooperative solutions for a differential game model of fishery. J. Econ. Dyn. Control 13, 1–20 (1989) MathSciNetMATHCrossRefGoogle Scholar
  22. Dockner, E.J., Jørgensen, S., Long, N.V., Sorger, G.: Differential Games in Economics and Management Science. Cambridge University Press, Cambridge (2000) MATHGoogle Scholar
  23. Erickson, G.: A model of advertising competition. J. Mark. Res. 22, 297–304 (1985) CrossRefGoogle Scholar
  24. Erickson, G.: Empirical analysis of closed-loop duopoly advertising strategies. Manag. Sci. 38, 1732–1749 (1992) MATHCrossRefGoogle Scholar
  25. Erickson, G.: Offensive and defensive marketing: closed-loop duopoly strategies. Mark. Lett. 4, 285–295 (1993) CrossRefGoogle Scholar
  26. Erickson, G.: Differential game models of advertising competition. Cent. Eur. J. Oper. Res. 83, 431–438 (1995) MATHGoogle Scholar
  27. Erickson, G.: Dynamic conjectural variation in a Lanchester duopoly. Manag. Sci. 43, 1603–1608 (1997) MATHCrossRefGoogle Scholar
  28. Feichtinger, G., Dockner, E.J.: A note to Jorgensen’s logarithmic advertising game. ZOR, Z. Oper.-Res. 28, 133–153 (1984) MathSciNetMATHGoogle Scholar
  29. Feichtinger, G., Hartl, R.F., Sethi, S.P.: Dynamic optimal control models in advertising, recent developments. Manag. Sci. 40, 195–226 (1994) MATHCrossRefGoogle Scholar
  30. Fershtman, C.: Goodwill and market shares in oligopoly. Economica 51, 271–281 (1984) CrossRefGoogle Scholar
  31. Fershtman, C., Muller, E.: Capital accumulation games of infinite duration. J. Econ. Theory 33, 322–339 (1984) MathSciNetMATHCrossRefGoogle Scholar
  32. Fershtman, C., Muller, E.: Turnpike properties of capital accumulation games. J. Econ. Theory 38, 167–177 (1986) MathSciNetMATHCrossRefGoogle Scholar
  33. Fischer, R., Mirman, L.: Strategic dynamic interaction. J. Econ. Dyn. Control 16, 267–287 (1992) MATHCrossRefGoogle Scholar
  34. Fornell, C., Robinson, W.T., Wernerfelt, B.: Consumption experience and sales promotion expenditure. Manag. Sci. 31, 1084–1105 (1985) CrossRefGoogle Scholar
  35. Fruchter, G.E.: Optimal advertising strategies with market expansion. Optim. Control Appl. Methods 20, 199–211 (1999a) MathSciNetCrossRefGoogle Scholar
  36. Fruchter, G.E.: The many-player advertising game. Manag. Sci. 45, 1609–1611 (1999b) MATHCrossRefGoogle Scholar
  37. Fruchter, G.E.: Advertising in a competitive product line. Int. Game Theory Rev. 3(4), 301–314 (2001) MathSciNetMATHCrossRefGoogle Scholar
  38. Fruchter, G.E., Kalish, S.: Dynamic promotional budgeting and media allocation. Eur. J. Oper. Res. 111, 15–27 (1998) MATHCrossRefGoogle Scholar
  39. Fruchter, G.E., Erickson, G.M., Kalish, S.: Feedback competitive advertising strategies with a general objective function. J. Optim. Theory Appl. 109, 601–613 (2001) MathSciNetMATHCrossRefGoogle Scholar
  40. Fudenberg, D., Tirole, J.: Capital as a commitment: strategic investment to deter mobility. J. Econ. Theory 31, 227–250 (1983) MATHCrossRefGoogle Scholar
  41. Fudenberg, D., Tirole, J.: Dynamic Models of Oligopoly. Harwood, London (1986) Google Scholar
  42. Fudenberg, D., Tirole, J.: Game Theory. MIT Press, Cambridge (1991) Google Scholar
  43. Ho, Y.C., Bryson, A.E. Jr., Baron, S.: Differential games and optimal pursuit evasion strategies. IEEE Trans. Autom. Control AC-10, 385–389 (1965) MathSciNetCrossRefGoogle Scholar
  44. Horsky, D., Simon, L.S.: Advertising and the diffusion of new products. Mark. Sci. 2, 1–18 (1983) CrossRefGoogle Scholar
  45. Jørgensen, S.: A differential games solution to a logarithmic advertising model. J. Oper. Res. Soc. 33, 425–432 (1982) MathSciNetGoogle Scholar
  46. Jørgensen, S., Sorger, G.: Feedback Nash equilibria in a problem of optimal fishery management. J. Optim. Theory Appl. 64, 293–310 (1990) MathSciNetCrossRefGoogle Scholar
  47. Jørgensen, S., Yeung, D.W.K.: Stochastic differential game model of a common property fishery. J. Optim. Theory Appl. 90, 381–403 (1996) MathSciNetCrossRefGoogle Scholar
  48. Jørgensen, S., Yeung, D.W.K.: Inter-and intragenerational renewable resource extraction. Ann. Oper. Res. 88, 275–289 (1999) MathSciNetCrossRefGoogle Scholar
  49. Kaitala, V.: Equilibria in a stochastic resource management game under imperfect information. Eur. J. Oper. Res. 71, 439–453 (1993) MATHCrossRefGoogle Scholar
  50. Little, J.D.C.: Aggregate advertising models: the state of art. Oper. Res. 27, 629–667 (1979) MATHCrossRefGoogle Scholar
  51. Long, N.V.: A Survey of Dynamic Games in Economics. World Scientific, Singapore (2010) CrossRefGoogle Scholar
  52. Mesak, H.I., Calloway, J.A.: A pulsing model of advertising competition: a game theoretical. Part A—theoretical foundation. Eur. J. Oper. Res. 86, 231–248 (1995) MATHCrossRefGoogle Scholar
  53. Mesak, H.I., Darrat, A.F.: A competitive advertising model: some theoretical and empirical results. J. Oper. Res. Soc. 44, 491–502 (1993) MATHGoogle Scholar
  54. Mukundan, R., Elsner, W.B.: Linear feedback strategies in non-zero-sum differential games. Int. J. Syst. Sci. 6, 513–532 (1975) MathSciNetMATHCrossRefGoogle Scholar
  55. Olsder, G.J.: On open- and closed-loop bang-bang control in nonzero-sum differential games. SIAM J. Control Optim. 40(4), 1087–1106 (2001) MathSciNetMATHCrossRefGoogle Scholar
  56. Plourde, C., Yeung, D.: Harvesting of a transboundary replenishable fish stock: a non-cooperative game solution. Mar. Resour. Econ. 6, 57–71 (1989) Google Scholar
  57. Reinganum, J.F., Stokey, N.L.: Oligopoly extraction of a common property resource: the importance of the period of commitment in dynamic games. Int. Econ. Rev. 26, 161–173 (1985) MathSciNetMATHCrossRefGoogle Scholar
  58. Reynolds, S.S.: Capacity investment, preemption and commitment in an infinite horizon model. Int. Econ. Rev. 28, 69–88 (1987) MathSciNetMATHCrossRefGoogle Scholar
  59. Reynolds, S.S.: Dynamic oligopoly with capacity adjustment costs. J. Econ. Dyn. Control 15, 491–514 (1991) MathSciNetMATHCrossRefGoogle Scholar
  60. Sethi, S.P.: Optimal control of the Vidale–Wolfe advertising model. Oper. Res. 21, 998–1013 (1973) MathSciNetMATHCrossRefGoogle Scholar
  61. Sethi, S.P., Thompson, G.L.: Optimal Control Theory: Applications to Management Science and Economics, 2nd edn. Kluwer Academic, Boston (2000) MATHGoogle Scholar
  62. Sorger, G.: Competitive dynamic advertising: a modification of the case game. J. Econ. Dyn. Control 13, 55–80 (1989) MathSciNetMATHCrossRefGoogle Scholar
  63. Spence, A.M.: Investment strategy and growth in a new market. Bell J. Econ. 10, 1–19 (1979) CrossRefGoogle Scholar
  64. Starr, A.W., Ho, Y.C.: Further properties of nonzero-sum differential games. J. Optim. Theory Appl. 3, 207–219 (1969a) MathSciNetMATHCrossRefGoogle Scholar
  65. Starr, A.W., Ho, Y.C.: Nonzero-sum differential games. J. Optim. Theory Appl. 3, 184–206 (1969b) MathSciNetMATHCrossRefGoogle Scholar
  66. Tapiero, C.S.: A generalization of the Nerlove–Arrow model to multi-firms advertising under uncertainty. Manag. Sci. 25, 907–915 (1979) MathSciNetCrossRefGoogle Scholar
  67. Tsutsui, S., Mino, K.: Nonlinear strategies in dynamic duopolistic competition with sticky prices. J. Econ. Theory 52, 136–161 (1990) MathSciNetMATHCrossRefGoogle Scholar
  68. Wang, Q., Wu, Z.: A duopolistic model of dynamic competitive advertising. Eur. J. Oper. Res. 128, 213–226 (2001) MATHCrossRefGoogle Scholar
  69. Yeung, D.W.K.: A class of differential games which admits a feedback solution with linear value functions. Eur. J. Oper. Res. 107, 737–754 (1998) MATHCrossRefGoogle Scholar
  70. Yeung, D.W.K.: A stochastic differential game model of institutional investor speculation. J. Optim. Theory Appl. 102, 463–477 (1999) MathSciNetMATHGoogle Scholar
  71. Yeung, D.W.K.: Infinite-horizon stochastic differential games with branching payoffs. J. Optim. Theory Appl. 111, 445–460 (2001) MathSciNetMATHCrossRefGoogle Scholar
  72. Zaccour, G.: Computation of characteristic function values for linear-state differential games. J. Optim. Theory Appl. 117(1), 183–194 (2003) MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.SRS Consortium for Advanced Study in Cooperative Dynamic GamesHong Kong Shue Yan UniversityHong KongPeople’s Republic of China
  2. 2.Center of Game TheorySt. Petersburg State UniversitySaint PetersburgRussia
  3. 3.Faculty of Applied Mathematics and Control ProcessesSt. Petersburg State UniversitySaint PetersburgRussia

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