Concluding Remarks

Concluding Remarks

Copyright: © 2014 |Pages: 15
DOI: 10.4018/978-1-4666-6050-2.ch017

Abstract

The main purpose of this chapter is to present a broad brush picture of the many areas of game theory researches and applications that have come into being. Therefore, this chapter can serve only as a minimal guide to the study of game theory and offer pointers towards future research. Although the discussion here has been primarily concerned with the present and future, it is desirable to have at least some understanding of the past. In addition, a rich reference is provided to help readers more fully appreciate the game theory developments of today.
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Reading Lists For Key Issues In Game Theory

Since the1950s, a broad coverage of game theory has successfully been extended. There are many subdisciplines in game theory. The breakneck speed of development of game theory calls for an appreciation of both the many realities of conflict, coordination and cooperation and the abstract investigation of all of them. Therefore, the boundaries among them are not firm, and there is a considerable mix involving, substantive areas (Shubik, 2011).

The purpose in this subsection is to present a broad brush picture of the many areas of game theory that have come into being. Some of the game theory developments may take place with many thousands of books and articles. They can be a minimal guide to key issues and main fields of game theory. The topics and fileds noted below touch on areas where formal models already exist, and special results have been obtained. Although the distinction is not tight all of the topics and fileds and the range of topics are clearly eclectic and sparse, we classify the main ideas of game theory into 19 topics. With no attempt at an in-depth discourse on the proliferation of subspecializations, a broad sketch of many of the current areas of game theory and reading lists are given as follows. In each instance one or a few references in reading lists are noted as early papers or exemplars of work in that specialty.

Introduction to Game Theory

  • Brown, G., & von Neumann J. (1950). Solutions of games by differential equations. Annals of Mathematical Studies, 24, 73-79.

  • Fort, M. (1950). Essential and non-essential fixed points. American Journal of Mathematics, 72, 315-322.

  • Fudenberg, D., & Tirole, J. (1991). Game Theory. MIT Press.

  • Goeree, J., & Holt, C. (2001). Ten little treasures of game theory and ten intuitive contradictions. American Economic Review, 91, 1402-1422.

  • Hart, S. (2002). Evolutionary dynamics and backward induction. Games and Economic Behavior, 41, 227-264.

  • Hart, S., & Mas-Colell, A. (2003). Uncoupled dynamics do not lead to Nash equilibrium. American Economic Review, 1830-1836.

  • Josephson, J. (2008). Stochastic better-reply dynamics in finite games. Economic Theory, 35, 381-389.

  • Josephson, J., & Matros, A. (2003). Stochastic imitation in finite games. Games and Economic Behavior, 49, 244-259.

  • Kohlberg E., & Mertens, J. F. (1986). On the strategic stability of equilibria. Econometrica, 54, 1003-1037.

  • Nagel, R. (1995). Unravelling in guessing games: An experimental study. American Economic Review, 85, 1313-1326.

  • Nash, J. (1950a). Non-cooperative games (Ph D thesis). Department of Mathematics, Princeton University.

  • Nash, J. (1950b). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences (USA), 36, 48-49.

  • Nash, J. (1950c). The bargaining problem. Econometrica, 18, 155-162.

  • Osborne, M., & Rubinstein, A. (1994). A Course in Game Theory. MIT Press.

  • Ritzberger, K. (2002). Foundations of Non-Cooperative Game Theory. Oxford: University Press.

  • Rosenthal, R. (1981). Games of perfect information, predatory pricing and the chain-store paradox. Journal of Economic Theory, 25, 92-100.

  • Ross, D. (2008). Classical game theory, socialization and the rationalization of conventions. Topoi, 27: 57–72.

  • Sigmund, K. (1993). Games of Life. Oxford: Oxford University Press.

  • Sobel, J. (2005). Interdependent preferences and reciprocity. Journal of Economic Literature, 43, 392-436.

  • Tucker, A. W., & Luce, R. D. (1959). Contributions to the Theory of Games, Volume IV (Annals of Mathematics Studies, 40). Princeton: Princeton University Press.

  • Weibull, J. (2004). Testing game theory, in S. Huck (ed.), Advances in Understanding Strategic Behaviour: Game Theory, Experiments, and Bounded Rationality: Essays in Honour of Werner Guth. Palgrave.

  • Winter, S. (1971). Satisficing, selection, and the innovating remnant. Quarterly Journal of Economics, 85, 237-261.

  • Wu, W., & Jian, J. (1962). Essential equilibrium points of n-person non-cooperative games. Science Sinica, 11, 1307-1322.

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