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When Does Evolution Lead to Efficiency in Communication Games?

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  • Karl H. Schlag

Abstract

The object of the paper will be to investigate the effect of pre- play communication on the evolution of strategies for playing a given game. Communication is modelled as cheap talk: before the game is played, the players simultaneously exchange messages from some finite set of messages. There is no cost to exchanging these messages and hence "talk is cheap". Evolution is a dynamic concept and as such we will explicitly specify a dynamic process and analyze dynamic stability. We select two versions of the continuous replicator dynamics (Taylor and Jonker, 1978; Taylor, 1979) for our analysis, among other reasons because both of these dynamics have lately turned out to be the approximations of various individual learning models (see Binmore et al., 1993; Börgers and Sarin, 1993; Cabrales, 1993; Schlag, 1994b). The basic story behind these two dynamics is the same, a large number of agents are matched, receive a payoff (or fitness) according to an underlying game and then adapt their strategies (or reproduce) according to a given dynamic process in which growth rates are proportional to relative performance of a strategy. The difference lies in the population structure. In the version of Taylor and Jonker (1978) all agents belong to the same population (referred to as the one population setting) whereas the version of Taylor (1979) considers a conflict between two disjoint populations (which we refer to as the two population setting). There are various (more or less) static models of cheap talk that each point to the fact that communication in an evolutionary environment will select against inefficient outcomes. The object of this paper will be to pursue this stylized fact in an explicit dynamic analysis. It turns out that the modelling of the population structure and the associated matching and reproduction (learning) dynamics has a drasitc influence on the results of the analysis. In the two population setting common interest among the agents that are matched is necessary and sufficient for efficient outcomes to evolve. Moreover, without common interest, sets with minimal stability properties in the dynamic process fail to exist. In the one population setting common interest only determines whether or not efficient outcomes are stable. The existence of stable sets is independent of common interest. Especially, inefficient evolutionarily stable strategies may exist in the game with cheap talk. Due to the numerous papers in this research area we now give a brief overview of the related literature.

Suggested Citation

  • Karl H. Schlag, "undated". "When Does Evolution Lead to Efficiency in Communication Games?," ELSE working papers 026, ESRC Centre on Economics Learning and Social Evolution.
    • Handle: RePEc:els:esrcls:026
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    References listed on IDEAS

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    1. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August.
    2. Karl Schlag, 1990. "Evolutionary Stability in Games with Equivalent Strategies," Discussion Papers 912, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Sobel, Joel, 1993. "Evolutionary stability and efficiency," Economics Letters, Elsevier, vol. 42(2-3), pages 301-312.
    4. Bhaskar, V., 1998. "Noisy Communication and the Evolution of Cooperation," Journal of Economic Theory, Elsevier, vol. 82(1), pages 110-131, September.
    5. K. Schlag, 2010. "Cheap Talk and Evolutionary Dynamics," Levine's Working Paper Archive 541, David K. Levine.
    6. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
    7. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 571-595.
    8. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
    9. Cabrales, Antonio, 2000. "Stochastic Replicator Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 451-481, May.
    10. Binmore, K. & Samuelson, L. & Gale, J., 1993. "Learning to be Imperfect: The Ultimatum Game," Working papers 9325, Wisconsin Madison - Social Systems.
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    Cited by:

    1. Jean-François Laslier, 2023. "Universalization and altruism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 579-594, May.
    2. Herold, Florian & Kuzmics, Christoph, 2020. "The evolution of taking roles," Journal of Economic Behavior & Organization, Elsevier, vol. 174(C), pages 38-63.
    3. Bhaskar, V., 1994. "Noisy communication and the fast evolution of cooperation," Discussion Paper 1994-112, Tilburg University, Center for Economic Research.
    4. Sjaak Hurkens & Karl H. Schlag, 1999. "Communication, coordination and efficiency in evolutionary one-population models," Economics Working Papers 387, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Bhaskar, V., 1995. "On te generic stability of mixed strategies in asymmetric contests," Other publications TiSEM 7805032a-e121-408b-8c26-a, Tilburg University, School of Economics and Management.
    6. Banerjee, Abhijit & Weibull, Jörgen W., 1996. "Neutrally Stable Outcomes in Cheap Talk Games," Working Paper Series 450, Research Institute of Industrial Economics.
    7. Brian Skyrms, 2003. "Signals, Evolution and the Explanatory Power of Transient Information," Levine's Working Paper Archive 618897000000000799, David K. Levine.
    8. Vyrastekova, J., 2002. "Efficiency versus Risk Dominance in an Evolutionary Model with Cheap Talk," Discussion Paper 2002-6, Tilburg University, Center for Economic Research.
    9. Stefano Demichelis & Jorgen W. Weibull, 2008. "Language, Meaning, and Games: A Model of Communication, Coordination, and Evolution," American Economic Review, American Economic Association, vol. 98(4), pages 1292-1311, September.
    10. Binmore, Ken & Samuelson, Larry, 2006. "The evolution of focal points," Games and Economic Behavior, Elsevier, vol. 55(1), pages 21-42, April.
    11. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    12. Carmichael, H Lorne & MacLeod, W Bentley, 1997. "Gift Giving and the Evolution of Cooperation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 485-509, August.
    13. Bhaskar, V., 1995. "On te generic stability of mixed strategies in asymmetric contests," Discussion Paper 1995-30, Tilburg University, Center for Economic Research.

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