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Part of the book series: Static & Dynamic Game Theory: Foundations & Applications ((SDGTFA))

Abstract

This chapter provides a brief overview of basic concepts in game theory. These include game formulations and classifications, games in extensive vs. in normal form, games with continuous action (strategy) sets vs. finite strategy sets, mixed vs. pure strategies, and games with uncoupled (orthogonal) vs. coupled action sets. The next section reviews basic solution concepts, among them Nash equilibria being of most relevance. The chapter is concluded with some remarks on the rationality assumption and learning in classical games. The following chapters will introduce these concepts formally.

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References

  1. Altman, E., Basar, T.: Multiuser rate-based flow control. IEEE Trans. Commun. 46(7), 940–949 (1998)

    Article  Google Scholar 

  2. Altman, E., Basar, T., Srikant, R.: Nash equilibria for combined flow control and routing in networks: asymptotic behavior for a large number of users. IEEE Trans. Autom. Control 47(6), 917–930 (2002)

    Article  MathSciNet  Google Scholar 

  3. Altman, E., Boulogne, T., El-Azouziand, R., Jimenez, T., Wynter, L.: A survey on networking games in telecommunications. Comput. Oper. Res. 33(2), 286–311 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Basar, T., Olsder, G.J.: In: Dynamic Noncooperative Game Theory. SIAM Series Classics in Applied Mathematics, 2nd edn. (1999)

    Google Scholar 

  5. Bertsekas, D.P.: Nonlinear Programming, 2nd edn. Athena Scientific, Nashua (1999)

    MATH  Google Scholar 

  6. Brown, G.W.: Activity Analysis of Production and Allocation. Wiley, New York (1951)

    Google Scholar 

  7. Fudenberg, D., Kreps, D.M.: Learning mixed equilibria. Games Econ. Behav. 5, 320–367 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fudenberg, D., Levine, D.K.: Theory of Learning in Games. MIT Press, Cambridge (1998)

    MATH  Google Scholar 

  9. Greenwald, A., Friedman, E.J., Shenker, S.: Learning in network contexts: experimental results from simulations. Games Econ. Behav. 35, 80–123 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  11. Krasovskii, N.N., Subbotin, A.I.: Game-Theoretical Control Problems. Springer, Berlin (1988)

    Book  MATH  Google Scholar 

  12. Krishna, V., Sjostrom, T.: On the convergence of fictitious play. Math. Oper. Res. 23, 479–511 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  13. Nash, J.: Equilibrium points in n-person games. Proc. Natl. Acad. Sci. USA 36(1), 48–49 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  14. Nash, J.: Non-cooperative games. Ann. Math. 54(2), 286–295 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  15. Owen, G.: Game Theory, 3rd edn. Academic Press, San Diego (1995)

    Google Scholar 

  16. Pavel, L.: A noncooperative game approach to OSNR optimization in optical networks. IEEE Trans. Autom. Control 51(5), 848–852 (2006)

    Article  MathSciNet  Google Scholar 

  17. Robinson, J.: An iterative method of solving a game. Ann. Math. 54, 296–301 (1951)

    Article  MATH  Google Scholar 

  18. Sandholm, W.H.: Population Games and Evolutionary Dynamics. Cambridge University Press, Cambridge (2009)

    Google Scholar 

  19. Saraydar, C., Mandayam, N.B., Goodman, D.J.: Pricing and power control in a multicell wireless data network. IEEE J. Sel. Areas Commun. 19(10), 1883–1892 (2001)

    Article  Google Scholar 

  20. Shamma, J.S., Arslan, G.: Dynamic fictitious play, dynamic gradient play and distributed convergence to Nash equilibria. IEEE Trans. Autom. Control 50(1), 312–326 (2005)

    Article  MathSciNet  Google Scholar 

  21. Smith, J.M.: The theory of games and the evolution of animal conflicts. J. Theor. Biol. 7, 209–221 (1974)

    Article  Google Scholar 

  22. Smith, J.M., Price, G.R.: The logic of animal conflict. Nature 246, 15–18 (1973)

    Article  Google Scholar 

  23. Vincent, T.L., Brown, J.S.: Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics. Cambridge University Press, Cambridge (2005)

    Book  MATH  Google Scholar 

  24. von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)

    MATH  Google Scholar 

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Correspondence to Lacra Pavel .

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Pavel, L. (2012). Basics of Game Theory. In: Game Theory for Control of Optical Networks. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8322-1_2

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