Nash Equilibrium, Refinements of
This article describes ways that the definition of an equilibrium among players’ strategies in a game can be sharpened by invoking additional criteria derived from decision theory. Refinements of John Nash’s 1950 definition aim primarily to distinguish equilibria in which implicit commitments are credible due to incentives. One group of refinements requires sequential rationality as the game progresses. Another ensures credibility by considering perturbed games in which every contingency occurs with positive probability, which has the further advantage of excluding weakly dominated strategies.
KeywordsBackward induction Bayes’ rule Dynamic games Game theory Harsanyi, J. Imperfect information Nash equilibrium Nash, J. Non-cooperative games Perfect information Refinements of Nash equilibrium Sequential rationality Small-worlds criterion Subgame perfection Symmetric games
- Fudenberg, D., D. Kreps, and D. Levine. 1988. On the robustness of equilibrium refinements. Journal of Economic Theory 44: 351–380.Google Scholar
- Govindan, S. and Wilson, R. 2009b. Axiomatic theory of equilibrium selection for generic two-player games, Stanford Business School Research Paper 2021. https://gsbapps.stanford.edu/researchpapers/library/RP2021.pdf.
- Harsanyi, J. 1967–1968. Games with incomplete information played by ‘Bayesian’ players, I–III. Management Science 14: 159–82, 320–34, 486–502.Google Scholar
- Harsanyi, J., and R. Selten. 1988. A general theory of equilibrium selection in games. Cambridge, MA: MIT Press.Google Scholar
- Hillas, J. 1998. How much of ‘forward induction’ is implied by ‘backward induction’ and ‘ordinality’? Mimeo: Department of Economics, University of Auckland.Google Scholar
- Hillas, J., and E. Kohlberg. 2002. The foundations of strategic equilibrium. In Handbook of game theory, ed. R. Aumann and S. Hart, Vol. 3. Amsterdam: North-Holland/Elsevier Science Publishers.Google Scholar
- 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.Google Scholar
- Selten, R. 1965. Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragetragheit. Zeitschrift fur die gesamte Staatswissenschaft 121(301–24): 667–689.Google Scholar