Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T05:17:10.623Z Has data issue: false hasContentIssue false
  • English
  • Français

Darwin Meets the Logic of Decision: Correlation in Evolutionary Game Theory

Published online by Cambridge University Press:  01 April 2022

Brian Skyrms
Brian Skyrms*
Affiliation:
Department of Philosophy, University of California at Irvine
*
‡Send reprint requests to the author, Department of Philosophy, 500-HOB, University of California at Irvine, Irvine, CA 92717-4555, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

The proper treatment of correlation in evolutionary game theory has unexpected connections with recent philosophical discussions of the theory of rational decision. The Logic of Decision (Jeffrey 1983) provides the correct framework for correlated evolutionary game theory and a variant of “ratifiability” is the appropriate generalization of “evolutionarily stable strategy”. The resulting theory unifies the treatment of correlation due to kin, population viscosity, detection, signaling, reciprocal altruism, and behavior-dependent contexts. It is shown that (1) a strictly dominated strategy may be selected, and (2) under conditions of perfect correlation a strictly efficient strategy must be selected.

Type
Research Article
Information
Philosophy of Science , Volume 61 , Issue 4 , December 1994 , pp. 503 - 528
Copyright
Copyright © Philosophy of Science Association 1994

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.)

Footnotes

†

Earlier versions of this paper were read at colloquia at the University of California at Berkeley, Stanford University and the Center for Advanced Study in the Behavioral Sciences. I would like to thank John Harsanyi, Branden Fitelson, Bas van Fraassen, Richard Jeffrey, Paul Milgrom, Patrick Suppes, Peter Vanderschraaf and audiences at the colloquia mentioned for discussion and/or suggestions. An anonymous referee offered penetrating commentary, help with exposition, correction of errors and assistance in composing this acknowledgement. Remaining defects are the sole responsibility of the author. This paper was completed at the Center for Advanced Study in the Behavioral Sciences. I am grateful for financial support provided by the National Science Foundation, the Andrew Mellon Foundation and the University of California President's Fellowship in the Humanities.

References

Aumann, R. J. (1974), “Subjectivity and Correlation in Randomized Strategies”, Journal of Mathematical Economics 1: 67–96.CrossRefGoogle Scholar
Aumann, R. J. (1987), “Correlated Equilibrium as an Expression of Bayesian Rationality”, Econometrica 55: 1–18.CrossRefGoogle Scholar
Axelrod, R. (1981), “The Emergence of Cooperation Among Egoists”, American Political Science Review 75: 306–318.CrossRefGoogle Scholar
Axelrod, R. (1984), The Evolution of Cooperation. New York: Basic Books.Google Scholar
Axelrod, R. and Hamilton, W. D. (1981), “The Evolution of Cooperation”, Science 211: 1390–1396.CrossRefGoogle ScholarPubMed
Binmore, K. and Samuelson, L. (1992), “Evolutionary Stability in Repeated Games Played by Finite Automata”, Journal of Economic Theory 57: 278–305.CrossRefGoogle Scholar
Bomze, I. (1986), “Non-Cooperative Two-Person Games in Biology: A Classification”, International Journal of Game Theory 15: 31–57.CrossRefGoogle Scholar
Boyce, W. E. and DiPrima, R. C. (1977), Elementary Differential Equations and Boundary Value Problems. 3d ed. New York: Wiley.Google Scholar
Boyd, R. and Loberbaum, J. P. (1987), “No Pure Strategy is Evolutionarily Stable in the Repeated Prisoner's Dilemma Game”, Nature 327: 59.CrossRefGoogle Scholar
Boyd, R. and Richerson, P. (1985), Culture and the Evolutionary Process. Chicago: University of Chicago Press.Google Scholar
Boylan, R. T. (1992), “Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals”, Journal of Economic Theory 57: 473–504.CrossRefGoogle Scholar
Busch, W. (1865), Max und Moritz, eine Bubengeschicte in sieben Streichen. Munchen: Braun & Schneider.Google Scholar
Cavalli-Sforza, L. L. and Feldman, M. (1981), Cultural Transmission and Evolution: A Quantitative Approach. Princeton: Princeton University Press.Google ScholarPubMed
Eells, E. (1982), Rational Decision and Causality. Cambridge, England: Cambridge University Press.CrossRefGoogle Scholar
Eells, E. (1984), “Metatickles and the Dynamics of Deliberation”, Theory and Decision 17: 71–95.CrossRefGoogle Scholar
Eshel, I. and Cavalli-Sforza, L. L. (1982), “Assortment of Encounters and the Evolution of Cooperativeness”, Proceedings of the National Academy of Sciences 79: 1331–1335.CrossRefGoogle ScholarPubMed
Fagen, R. M. (1980), “When Doves Conspire: Evolution of Nondamaging Fighting Tactics in a Nonrandom-Encounter Animal Conflict Model”, American Naturalist 115: 858–869.CrossRefGoogle Scholar
Farrell, J. and Ware, R. (1988), “Evolutionary Stability in the Repeated Prisoner's Dilemma Game”, Theoretical Population Biology 36: 161–166.CrossRefGoogle Scholar
Feldman, M. and Thomas, E. (1987), “Behavior-Dependent Contexts for Repeated Plays of the Prisoner's Dilemma II: Dynamical Aspects of the Evolution of Cooperation”, Journal of Theoretical Biology 128: 297–315.CrossRefGoogle ScholarPubMed
Foster, D. and Young, P. (1990), “Stochastic Evolutionary Game Dynamics”, Journal of Theoretical Biology 38: 219–232.CrossRefGoogle Scholar
Friedman, D. (1991), “Evolutionary Games in Economics”, Econometrica 59: 637–666.CrossRefGoogle Scholar
Fudenberg, D. and Maskin, E. (1986), “The Folk Theorem in Repeated Games with Discounting and with Complete Information”, Econometrica 54: 533–554.CrossRefGoogle Scholar
Fudenberg, D. and Maskin, E. (1990), “Evolution and Cooperation in Noisy Repeated Games”, American Economic Review 80: 274–279.Google Scholar
Gautier, D. (1986), Morals by Agreement. Oxford: Oxford University Press.Google Scholar
Gibbard, A. and Harper, W. (1981). “Counterfactuals and Two Kinds of Expected Utility”, in Harper, W., Stalnaker, R., and Pearce, G., (eds.), IFS: Conditionals, Beliefs, Decision, Chance, and Time. Dordrecht: Reidei, pp. 153–190.Google Scholar
Grim, P. (1993), “Greater Generosity Favored in a Spatialized Prisoner's Dilemma”. Unpublished manuscript.Google Scholar
Hamilton, W. D. (1963), “The Evolution of Altruistic Behavior”, American Naturalist 97: 354–356.CrossRefGoogle Scholar
Hamilton, W. D. (1964), “The Genetical Evolution of Social Behavior”, Journal of Theoretical Biology 7: 1–52.CrossRefGoogle Scholar
Hamilton, W. D. (1971), “Selection of Selfish and Altruistic Behavior in Some Extreme Models”, in Eisenberg, J. F. and Dillon, W. S., (eds.), Man and Beast. Washington: Smithsonian Institution Press, pp. 59–91.Google Scholar
Hirsch, M. W. and Smale, S. (1974), Differential Equations, Dynamical Systems and Linear Algebra. New York: Academic Press.Google Scholar
Hirshliefer, J. and Coll, J. C. Martinez (1988), “What Strategies can Support the Evolutionary Emergence of Cooperation?”, Journal of Conflict Resolution 32: 367–398.CrossRefGoogle Scholar
Hofbauer, J. and Sigmund, K. (1988), The Theory and Evolution of Dynamical Systems: Mathematical Aspects of Selection. Cambridge, England: Cambridge University Press.Google Scholar
Jeffrey, R. (1983), The Logic of Decision. 2d revised ed. Chicago: University of Chicago Press.Google Scholar
Kitcher, P. (1993), “The Evolution of Human Altruism”, The Journal of Philosophy 10: 497–516.CrossRefGoogle Scholar
Lewis, D. (1979), “Prisoner's Dilemma is a Newcomb Problem”, Philosophy and Public Affairs 8: 235–240.Google Scholar
Lewis, D. (1981), “Causal Decision Theory”, Australasian Journal of Philosophy 58: 5–30.CrossRefGoogle Scholar
Lumsden, C. and Wilson, E. O. (1981), Genes, Mind, and Culture: The Coevolutionary Process. Cambridge, MA: Harvard University Press.Google Scholar
Maynard Smith, J. (1982), Evolution and the Theory of Games. Cambridge, England: Cambridge University Press.CrossRefGoogle Scholar
Maynard Smith, J. and Parker, G. R. (1976), “The Logic of Asymmetric Contests”, Animal Behavior 24: 159–175.CrossRefGoogle Scholar
Maynard Smith, J. and Price, G. R. (1973), “The Logic of Animal Conflict”, Nature 146: 15–18.CrossRefGoogle Scholar
Michod, R. and Sanderson, M. (1985), “Behavioral Structure and the Evolution of Cooperation”, in Greenwood, J., Harvey, P., and Slatkin, M., (eds.), Evolution: Essays in Honour of John Maynard Smith. Cambridge, England: Cambridge University Press, pp. 95–104.Google Scholar
Myerson, R. B.; Pollock, G. B.; and Swinkels, J. M. (1991), “Viscous Population Equilibria”, Games and Economic Behavior 3: 101–109.CrossRefGoogle Scholar
Nachbar, J. (1990), “‘Evolutionary’ Selection Dynamics in Games: Convergence and Limit Properties”, International Journal of Game Theory 19: 59–89.CrossRefGoogle Scholar
Nowak, M. A. and May, R. M. (1992), “Evolutionary Games and Spatial Chaos”, Nature 359: 826–829.CrossRefGoogle Scholar
Nowak, M.A. and May, R. M. (1993), “The Spatial Dilemmas of Evolution”, International Journal of Bifurcation and Chaos 3: 35–78.CrossRefGoogle Scholar
Nozick, R. (1970), “Newcomb's Problem and Two Principles of Choice”, in Rescher, N., (ed.), Essays in Honor of C. G. Hempel: A Tribute on the Occasion of his Sixty- Fifth Birthday. Dordrecht: Reidel, pp. 114–146.Google Scholar
Pollock, G. B. (1989), “Evolutionary Stability in a Viscous Lattice”, Social Networks 11: 175–212.CrossRefGoogle Scholar
Robson, A. (1990), “Efficiency in Evolutionary Games: Darwin, Nash and the Secret Handshake”, Journal of Theoretical Biology 144: 379–396.CrossRefGoogle ScholarPubMed
Savage, L. J. (1954), The Foundations of Statistics. New York: Wiley.Google Scholar
Schuster, P. and Sigmund, K. (1983), “Replicator Dynamics”, Journal of Theoretical Biology 100: 535–538.CrossRefGoogle Scholar
Skyrms, B. (1980), Causal Necessity: A Pragmatic Investigation of the Necessity of Laws. New Haven: Yale University Press.Google Scholar
Skyrms, B. (1984), Pragmatics and Empiricism. New Haven: Yale University Press.Google Scholar
Skyrms, B. (1990a), The Dynamics of Rational Deliberation. Cambridge, MA: Harvard University Press.Google Scholar
Skyrms, B. (1990b), “Ratifiability and the Logic of Decision”, in French, P. A.; Uehling, T. E. Jr.; and Wettstein, H. K., (eds.), Midwest Studies in Philosophy. Vol. 15, The Philosophy of the Human Sciences. Notre Dame: University of Notre Dame Press, pp. 44–56.Google Scholar
Skyrms, B. (1992), “Chaos in Game Dynamics”, Journal of Logic, Language and Information 1: 111–130.CrossRefGoogle Scholar
Skyrms, B. (1993), “Chaos and the Explanatory Significance of Equilibrium: Strange At-tractors in Evolutionary Game Dynamics”, in PSA 1992, vol. 2. East Lansing, MI: Philosophy of Science Association, pp. 374–394.Google Scholar
Sober, E. (1992), “The Evolution of Altruism: Correlation, Cost and Benefit”, Biology and Philosophy 7: 177–187.CrossRefGoogle Scholar
Stalnaker, R. (1981), “Letter to David Lewis”, in Harper, W., Stalnaker, R., and Pearce, G., (eds.), IFS: Conditionals, Beliefs, Decision, Chance, and Time. Dordrecht: Reidel, pp. 151–152.Google Scholar
Taylor, P. and Jonker, L. (1978), “Evolutionarily Stable Strategies and Game Dynamics”, Mathematical Biosciences 40: 145–156.CrossRefGoogle Scholar
Trivers, R. (1971), “The Evolution of Reciprocal Altruism”, Quarterly Review of Biology 46: 35–57.CrossRefGoogle Scholar
van Damme, E. (1987), Stability and Perfection of Nash Equilibria. Berlin: Springer.CrossRefGoogle Scholar
von Neumann, J. and Morgenstern, O. (1947), Theory of Games and Economic Behavior. Princeton: Princeton University Press.Google Scholar
Wilson, D. S. (1980), The Natural Selection of Populations and Communities. Menlo Park, CA: Benjamin/Cummings.Google Scholar
Wright, S. (1921), “Systems of Mating. III. Assortative Mating Based on Somatic Resemblance”, Genetics 6: 144–161.CrossRefGoogle ScholarPubMed
Wright, S. (1945), “Tempo and Mode in Evolution: A Critical Review”, Ecology 26: 415–419.CrossRefGoogle Scholar
Zeeman, E. C. (1980), “Population Dynamics from Game Theory”, in Niteek, Z. and Robinson, C., (eds.), Global Theory of Dynamical Systems: Proceedings of an International Conference Held at Northwestern University. Berlin: Springer Verlag, pp. 471–497.CrossRefGoogle Scholar