Skip to main content Accessibility help
×
Home
Hostname: page-component-768ffcd9cc-jp8mt Total loading time: 0.293 Render date: 2022-12-06T01:53:39.001Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

The Logic of Rational Play in Games of Perfect Information

Published online by Cambridge University Press:  05 December 2008

Giacomo Bonanno
Affiliation:
University of California, Davis

Extract

For the past 20 years or so the literature on noncooperative games has been centered on the search for an equilibrium concept that expresses the notion of rational behavior in interactive situations. A basic tenet in this literature is that if a “rational solution” exists, it must be a Nash equilibrium. The consensus view, however, is that not all Nash equilibria can be accepted as rational solutions. Consider, for example, the game of Figure 1.

Type
Essays
Copyright
Copyright © Cambridge University Press 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aumann, R. 1987a. “Correlated Equilibrium as an Expression of Bayesian Rationality.” Econometrica 55:118.CrossRefGoogle Scholar
Aumann, R. 1987b. “Game Theory.” In The New Palgrave: A Dictionary of Economics, edited by Eatwell, J., Milgate, M., and Newman, P.. London: Macmillan.Google Scholar
Bacharach, M. 1987. “A Theory of Rational Decision in Games.” Erkenntnis 27:1755.CrossRefGoogle Scholar
Banks, J., and Sobel, J.. 1987. “Equilibrium Selection in Signalling Games.” Econometrica 55:647–61.CrossRefGoogle Scholar
Basu, K. 1988. “Strategic Irrationality in Extensive Games.” Mathematical Social Sciences 15:247–60.CrossRefGoogle Scholar
Basu, K. 1990. “On the Non-Existence of a Rationality Definition for Extensive Games.” International Journal of Game Theory 19:3344.CrossRefGoogle Scholar
Battigalli, P. 1989. “On Rationalizability in Extensive Games.” Mimeo. Bocconi University, Milan.Google Scholar
Bernheim, D. 1984. “Rationalizable Strategic Behaviour.” Econometrica 52:1007–28.CrossRefGoogle Scholar
Bicchieri, C. 1988a. “Strategic Behavior and Counterfactuals.” Synthese 76:135–69.CrossRefGoogle Scholar
Bicchieri, C. 1988b. “Self-Refuting Theories of Strategic Interaction: A Paradox of Common Knowledge.” Erkenntnis 29:6985.Google Scholar
Bicchieri, C. 1988c. “Common Knowledge and Backward Induction: A Solution to the Paradox.” In Theoretical Aspects of Reasoning about Knowledge, edited by Vardi, M.. Los Altos: Morgan Kaufmann.Google Scholar
Binmore, K. 1984. “Equilibria in Extensive Games.” Economic Journal 95:5159.CrossRefGoogle Scholar
Binmore, K. 1987a. “Modeling Rational Players: Part I.” Economics and Philosophy 3:179214.CrossRefGoogle Scholar
Binmore, K. 1987b. “Modeling Rational Players: Part II.” Economics and Philosophy 4:955.CrossRefGoogle Scholar
Binmore, K. 1990. Essays on the Foundations of Game Theory. Oxford: Basil Blackwell.Google Scholar
Bjerring, A. K. 1978. “The Tracing Procedure.” In Foundations and Applications of Decision Theory, edited by Hooker, C. A., Leach, J. J., and McClennen, E. F.. Dordrecht: Reidel.Google Scholar
Brandenburger, A., and Dekel, E.. 1987. “Rationalizability and Correlated Equilibria.” Econometrica 55:13911402.CrossRefGoogle Scholar
Chellas, B. F. 1984. Modal Logic: An Introduction. Cambridge: Cambridge University Press.Google Scholar
Cho, I. 1987. “A Refinement of Nash Equilibrium.” Econometrica 55:1867–90.CrossRefGoogle Scholar
Cho, I., and Kreps, D.. 1987. “Signalling Games and Stable Equilibria.” Quarterly Journal of Economics 102:179221.CrossRefGoogle Scholar
Cubitt, R. 1988. “Dominance and Rationality in Noncooperative Games.” Mimeo. Oxford: The Queen's College.Google Scholar
Cubitt, R. 1989. “Refinements of Nash Equilibrium: A Critique.” Theory and Decision 26:107–31.CrossRefGoogle Scholar
Dekel, E., and Fudenberg, D.. 1987. “Rational Behavior with Payoff Uncertainty.” Mimeo. Berkeley: University of California.Google Scholar
Fudenberg, D., Kreps, D., and Levine, D.. 1988. “On the Robustness of Equilibrium Refinements.” Journal of Economic Theory 44:354–80.CrossRefGoogle Scholar
Gaerdenfors, P. 1978. “Conditionals and Changes of Belief.” Acta Philosophica Fennica 30:381404.Google Scholar
Grossman, S., and Perry, M.. 1986. “Perfect Sequential Equilibrium.” Journal of Economic Theory 39:97119.CrossRefGoogle Scholar
Harsanyi, J. C., and Selten, R.. 1988. A General Theory of Equilibrium Selection in Games. Cambridge, MA: MIT Press.Google Scholar
Kalai, E., and Samet, D.. 1984. “Persistent Equilibria.” International Journal of Game Theory 13:129–44.CrossRefGoogle Scholar
Kaneko, M., and Nagashima, T.. 1990a. “Game Logic I: Deductions and the Common Knowledge of Deductive Abilities.” Working Paper No. E90–03–1. Virginia Polytechnic Institute and State University.Google Scholar
Kaneko, M., and Nagashima, T.. 1990b. “Final Decisions: The Nash Equilibrium Concept and Solvability in Non-Cooperative Games with Common Knowledge of Logical Abilities.” Working Paper No. E89–12–01. Virginia Polytechnic Institute and State University.Google Scholar
Kohlberg, E., and Mertens, J. F.. 1986. “On the Strategic Stability of Equilibria.” Econometrica 54:1003–37.CrossRefGoogle Scholar
Kreps, D. 1987. “Nash Equilibrium.” In The Neiv Palgrave: A Dictionary of Economics, edited by Eatwell, J., Milgate, M., and Newman, P.. London: Macmillan.Google Scholar
Kreps, D., and Wilson, R.. 1982a. “Sequential Equilibria.” Econometrica 50:863–94.CrossRefGoogle Scholar
Luce, R. D., and Raiffa, H.. 1957. Games and Decisions. New York: Wiley.Google Scholar
McLennan, A. 1985. “Justifiable Beliefs in Sequential Equilibrium.” Econometrica 53:889904.CrossRefGoogle Scholar
Myerson, R. B. 1978. “Refinement of the Nash Equilibrium Concept.” International Journal of Game Theory 7:7380.CrossRefGoogle Scholar
Okada, A. 1981. “On Stability of Perfect Equilibrium Points.” International Journal of Game Theory 10:6773.CrossRefGoogle Scholar
Pearce, D. 1984. “Rationalizable Strategic Behaviour and the Problem of Perfection.” Econometrica 52:1029–50.CrossRefGoogle Scholar
Pettit, P., and Sugden, R.. 1989. “The Backward Induction Paradox.” The Journal of Philosophy 86:169–82.CrossRefGoogle Scholar
Reny, P. 1985. “Rationality, Common Knowledge, and the Theory of Games.” Ph.D. thesis. Princeton University.Google Scholar
Reny, P. 1988. “Backward Induction and Common Knowledge in Games of Perfect Information.” Mimeo. Department of Economics, University of Western Ontario.Google Scholar
Rosenthal, R. 1981. “Games of Perfect Information, Predatory Pricing, and the Chain-Store Paradox.” Journal of Economic Theory 25:92100.CrossRefGoogle Scholar
Samuelson, L. 1989. “Dominated Strategies and Common Knowledge.” Department of Economics Working Paper. Pennsylvania State University.Google Scholar
Selten, R. 1965. “Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragetraegheit.” Zeitschrift fuer die gesmate Staatswissenschaft 12:301–24.Google Scholar
Selten, R. 1975. “Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games.” International Journal of Came Theory 4:2555.CrossRefGoogle Scholar
Selten, R., and Leopold, U.. 1982. “Subjunctive Conditionals in Decision and Game Theory.” In Philosophy of Economics, edited by Stegmueller, W., Balzer, W., and Spohn, W.. Berlin: Springer-Verlag.Google Scholar
Shin, H. S. 1988. “Correlated Equilibrium as a Consequence of Evidential Rationality with Lessons for ‘No Trade’ Equilibria.” Mimeo. Oxford: Magdalene College.Google Scholar
Shin, H. S. 1989. “Counterfactuals and a Theory of Equilibrium in Games.” Discussion Paper No. 42. Oxford: Nuffield College.Google Scholar
Sugden, R. 1988. “Game Theory without Backward Induction.” Mimeo. School of Economic and Social Studies, University of East Anglia, U.K.Google Scholar
Tan, T., and Werlang, S.. 1984. “The Bayesian Foundations of Rationalizable Strategic Behavior and Nash Equilibrium Behavior.” Mimeo. Princeton University.Google Scholar
Van Damme, E. 1987. Stability and Perfection of Nash Equilibria. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Wu, Wen-Tsuen and Jia-He, Jiang. 1962. “Essential Equilibrium Points of n−Person Non-Cooperative Games.” Science Sinica 11:1307–22.Google Scholar
29
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

The Logic of Rational Play in Games of Perfect Information
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

The Logic of Rational Play in Games of Perfect Information
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

The Logic of Rational Play in Games of Perfect Information
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *