Abstract
Game theory studies decisions by several persons in situations with significant interactions. Two features distinguish it from other theories of multi-person decisions. One is explicit consideration of each person’s available strategies and the outcomes resulting from combinations of their choices; that is, a complete and detailed specification of the ‘game’. Here a person’s strategy is a complete plan specifying his action in each contingency that might arise. In non-cooperative contexts, the other is a focus on optimal choices by each person separately. John Nash (1950; 1951) proposed that a combination of mutually optimal strategies can be characterized mathematically as an equilibrium. According to Nash’s definition, a combination is an equilibrium if each person’s choice is an optimal response to others’ choices. His definition assumes that a choice is optimal if it maximizes the person’s expected utility of outcomes, conditional on knowing or correctly anticipating the choices of others. In some applications, knowledge of others’ choices might stem from prior agreement or communication, or accurate prediction of others’ choices might derive from ‘common knowledge’ of strategies and outcomes and of optimizing behaviour. Because many games have multiple equilibria, the predictions obtained are incomplete. However, equilibrium is a weak criterion in some respects, and therefore one can refine the criterion to obtain sharper predictions (Harsanyi and Selten, 1988; Hillas and Kohlberg, 2002; Kohlberg, 1990; Kreps, 1990).
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Bibliography
Banks, J. and Sobel, J. 1987. Equilibrium selection in signaling games. Econometrica 55, 647–61.
Blume, L., Brandenburger, A. and Dekel, E. 1991a. Lexicographic probabilities and choice under uncertainty. Econometrica 59, 61–79.
Blume, L., Brandenburger, A. and Dekel, E. 1991b. Lexicographic probabilities and equilibrium refinements. Econometrica 59, 81–98.
Cho, I. and Kreps, D. 1987. Signaling games and stable equilibria. Quarterly Journal of Economics 102, 179–221.
Fudenberg, D., Kreps, D. and Levine, D. 1988. On the robustness of equilibrium refinements. Journal of Economic Theory 44, 351–80.
Fudenberg, D. and Tiro le, J. 1991. Perfect Bayesian equilibrium and sequential equilibrium. Journal of Economic Theory 53, 236–60.
Harsanyi, J. 1967–1968. Games with incomplete information played by ‘Bayesian’ players, I—III. Management Science 14, 159–82, 320–34, 486–502.
Harsanyi, J. and Selten, R. 1988. A General Theory of Equilibrium Selection in Games. Cambridge, MA: MIT Press.
Hillas, J. 1998. How much of ‘forward induction’ is implied by ‘backward induction’ and ‘ordinality’? Mimeo. Department of Economics, University of Auckland.
Hillas, J. and Kohlberg, E. 2002. The foundations of strategic equilibrium. In Handbook of Game Theory, vol. 3, ed. R. Aumann and S. Hart. Amsterdam: North-Holland/Elsevier Science Publishers.
Kohlberg, E. 1990. Refinement of Nash equilibrium: the main ideas. In Game Theory and Applications, ed. T. Ichiishi, A. Neyman and Y. Tauman. San Diego: Academic Press.
Kohlberg, E. and Mertens, J.-F. 1986. On the strategic stability of equilibria. Econometrica 54, 1003–38.
Kreps, D. 1990. Game Theory and Economic Modeling. New York: Oxford University Press.
Kreps, D. and Wilson, R. 1982. Sequential equilibria. Econometrica 50, 863–94.
Mertens, J.-F. 1989. Stable equilibria — a reformulation, Part I: definition and basic properties. Mathematics of Operations Research 14, 575–624.
Mertens, J.-F. 1992. The small worlds axiom for stable equilibria. Games and Economic Behavior 4, 553–64.
Mertens, J.-F. and Zamir, S. 1985. Formulation of Bayesian analysis for games with incomplete information. International Journal of Game Theory 14, 1–29.
Myerson, R. 1978. Refinement of the Nash equilibrium concept. International Journal of Game Theory 7, 73–80.
Nash, J. 1950. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences USA 36, 48–9.
Nash, J. 1951. Non-cooperative games. Annals of Mathematics 54, 286–95.
Selten, R. 1965. Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragetragheit. Zeitschrift fur die gesamte Staatswissenschaft 121, 301–24, 667–89.
Selten, R. 1975. Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4, 25–55.
van Damme, E. 1984. A relation between perfect equilibria in extensive form games and proper equilibria in normal form games. International Journal of Game Theory 13, 1–13.
van Damme, E. 1989. Stable equilibria and forward induction. Journal of Economic Theory 48, 476–96.
van Damme, E. 1991. Stability and Perfection of Nash Equilibria. Berlin: Springer-Verlag.
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Durlauf, S.N., Blume, L.E. (2010). Nash equilibrium, refinements of. In: Durlauf, S.N., Blume, L.E. (eds) Game Theory. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280847_25
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DOI: https://doi.org/10.1057/9780230280847_25
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