Abstract
When social scientists began employing evolutionary game theory (EGT) in their disciplines, the question arose what the appropriate interpretation of the formal EGT framework would be. Social scientists have given different answer, of which I distinguish three basic kinds. I then proceed to uncover the conceptual tension between the formal framework of EGT, its application in the social sciences, and these three interpretations. First, I argue that EGT under the biological interpretation has a limited application in the social sciences, chiefly because strategy replication often cannot be sensibly interpreted as strategy bearer reproduction in this domain. Second, I show that alternative replication mechanisms imply interpersonal comparability of strategy payoffs. Giving a meaningful interpretation to such comparisons is not an easy task for many social situations, and thus limits the applicability of EGT in this domain. Third, I argue that giving a new interpretation both to strategy replication and selection solves the issue of interpersonal comparability, but at the costs of making the new interpretation incompatible with natural selection interpretations of EGT. To the extent that social scientists seek such a natural selection interpretation, they face a dilemma: either face the challenge that interpersonal comparisons pose, or give up on the natural selection interpretation. By identifying these tensions, my analysis pleas for greater awareness of the specific purposes of EGT modelling in the social sciences, and for greater sensitivity to the underlying microstructure on which the evolutionary dynamics and other EGT solution concepts supervene.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
For a historical investigation, see Grüne-Yanoff (2011).
A strategy profile is a combination of strategies s = {x 1 ,…,x n } for each of the n players, which fully specifies all actions in a game. A well-defined game has payoffs assigned to every strategy profile. I will often speak of the payoffs of a strategy x i —by which I mean the set of payoffs assigned to x i for each strategy profile s −i.
Alternative stability concepts used for static analysis—for example neutral stability (Weibull 1995, 46) or robustness against equilibrium entrants (Weibull 1995, 48)—differ in requiring that no other strategy earns a higher payoff than an incumbent, or in restrictions on the kind of other strategies; but all require inter-strategy comparisons in the same way as ESS.
There are both continuous and discrete versions of the RD, of which the continuous variant is the more prominent. The latter is discussed here.
The relation between proliferation and payoffs characterizes different classes of selection dynamics. While a linear relation characterizes the RD, wider classes are characterized by payoff positivity and payoff monotonicity, respectively (Weibull 1995, 139–152). The RD is by far the most prominent selection dynamic in EGT, and discussion therefore focuses on it.
The class of selection dynamics is not properly described and is expanding as I write. Yet all payoff-based dynamics seek to capture the relation of payoffs and strategy replication. While many of the dynamics belonging to this class can be distinguished from the RD described here by the ways how they treat this relation, and the representational frameworks they use, they all share with RD the requirement of inter-strategy comparisons of payoffs. Roughly speaking this requirement is necessitated by the need of relating payoffs to relative strategy replication, thus putting the payoffs of different strategies in a relation to each other and hence comparing them.
Indeed it would be historically more accurate to say that their theoretical concepts influenced the construction of the formal framework (cf. Grüne-Yanoff 2011).
‘The evolutionary dynamics and the conditions on payoffs characterizing equilibria discussed above all seem to require that payoffs be interpersonally comparable… When our concern is biology, and payoffs are just measures of reproductive success, this is quite appropriate. When our concern is culture, however, we should be a little more wary. It is common to regard the payoffs of these games as utilities, and the questions of whether interpersonal utility comparisons are meaningful and measurable are notoriously vexed’ (Kuhn 2004, 13).
A notable example is Axelrod (1980), the first paper in a social science journal that uses EGT. He suggests a straightforward adoption of the biological interpretation: ‘we simply have to interpret the average payoff received by an individual as proportional to that individual’s expected number of [truly-bred] offspring’ (Axelrod 1980, 398). A more recent example is Binmore et al. (1995), which interprets payoffs as the players’ probability of death.
There are important exceptions to this claim. The selection of social institutions, like firms or markets, seems to fit the biological pattern reasonably well. Interestingly enough, this is largely the playing field of evolutionary economists, while EGT has concentrated on the more complicated cases of evolution of preferences, conventions, and norms.
EGT under the actual play interpretation has also been employed to model individual learning. Drawing on the Bush-Mosteller reinforcement learning concept, Börgers and Sarin (1997), for example, modelled an individual agent’s learning as an adjustment of the weights of her mix strategy in proportion to her payoffs from past play. Such individual learning models of course do not require interpersonal comparisons, as they model an individual, not a social process.
See for example Alexander (2007), who calls them ‘public goods’, because they are publicly comparable.
Payoff-based dynamics are called monotone if and only if the difference between individual and average payoff has a monotone increasing effect on that strategy’s relative growth rate.
References
Alexander JM (2007) The structural evolution of morality. Cambridge University Press, Cambridge
Axelrod R (1980) More effective choice in the Prisoner’s Dilemma. J Conflict Resolut 24:379–403
Binmore KG, Samuelson L, Vaughan R (1995) Musical chairs: modelling noisy evolution. Games Econ Behav 11:1–35
Björnerstedt J, Weibull JW (1996) Nash equilibrium and evolution by imitation. In: Arrow KJ, Colombatto E, Perlman M, Schmidt C (eds) The rational foundations of economic behavior. St. Martin’s Press, New York, pp 155–181
Börgers T, Sarin R (1997) Learning through reinforcement and replicator dynamics. J Econ Theory 77:1–14
Fudenberg D, Levine DK (1998) Theory of learning in games. MIT Press, Cambridge
Gintis H (2000) Game theory evolving. Princeton University Press, Princeton
Godfrey-Smith P (2007) Conditions for evolution by natural selection. J Philos 104:489–516
Grüne-Yanoff T (2011) Models as products of interdisciplinary exchange: evidence from evolutionary game theory. Stud Hist Philos Sci 25(2):1–19
Hammond P, Fleurbaey M (2004) Interpersonally comparable utility. In: Hammond P, Barbera S, Seidl C (eds) Handbook of utility theory, Vol. 2: extensions. Kluwer Academic Publishers, Dordrecht, pp 1181–1285
Kandori M, Mailath G, Rob R (1993) Learning, mutation, and long run equilibria in games. Econometrica 61:29–56
Kuhn ST (2004) Reflections on ethics and game theory. Synthese 141:1–44
Mailath GJ (1998) Do people play nash equilibrium? Lessons from evolutionary game theory. J Econ Lit 36(3):1347–1374
Maynard Smith J (1982) Evolution and the theory of games. Cambridge University Press, Cambridge
Millstein RL (2006) Natural selection as a population-level causal process. Br J Philos Sci 57:627–653
Rosenberg A, Bouchard F (2010) Fitness. In: Zalta EN (ed) The Stanford encyclopedia of philosophy, Fall 2010 Edition. URL http://plato.stanford.edu/archives/fall2010/entries/fitness/
Samuelson L (1997) Evolution and game theory. J Econ Perspect 16(2):47–66
Schlag K (1998) Why imitate, and if so, how? A boundedly rational approach to multi-armed bandits. J Econ Theory 78(1):130–156
Sugden R (1986) The evolution of rights, cooperation, and welfare. Basil Blackwell, Oxford
Sugden R (2001) The evolutionary turn in game theory. J Econ Methodol 8:113–130
Weibull J (1995) Evolutionary game theory. MIT Press, Cambridge
Wimsatt WC (1980) Reductionistic research strategies and their biases in the units of selection controversy. In: Nickles T (ed) Scientific discovery: case studies. D. Reidel, Dordrecht, pp 159–213
Young P (1993) The evolution of conventions. Econometrica 61:57–84
Acknowledgments
Earlier versions of this paper were presented at LOFT’08 in Amsterdam on July 3rd, 2008 and at the workshop Evolution & and the Human Sciences, Helsinki, on November 13th, 2009. I thank the participants of these sessions for their comments. Particular thanks are due to Aki Lehtinen for very insightful discussions and to two anonymous referees for helpful comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grüne-Yanoff, T. Evolutionary game theory, interpersonal comparisons and natural selection: a dilemma. Biol Philos 26, 637–654 (2011). https://doi.org/10.1007/s10539-011-9273-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10539-011-9273-3