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When Does Evolution Lead to Efficiency in Communication Games?

Listed author(s):
  • Karl H. Schlag

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.

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Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 026.

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Handle: RePEc:els:esrcls:026
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  1. Warneryd, Karl, 1991. "Evolutionary stability in unanimity games with cheap talk," Economics Letters, Elsevier, vol. 36(4), pages 375-378, August.
  2. Schlag,Karl, "undated". "Cheap talk and evolutionary dynamics," Discussion Paper Serie B 242, University of Bonn, Germany.
  3. Karl Schlag, 1990. "Evolutionary Stability in Games with Equivalent Strategies," Discussion Papers 912, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  5. Sobel, Joel, 1993. "Evolutionary stability and efficiency," Economics Letters, Elsevier, vol. 42(2-3), pages 301-312.
  6. Bhaskar, V., 1998. "Noisy Communication and the Evolution of Cooperation," Journal of Economic Theory, Elsevier, vol. 82(1), pages 110-131, September.
  7. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
  8. Karl H. Schlag & Dieter Balkenborg, 2001. "Evolutionarily stable sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 571-595.
  9. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
  10. 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.
  11. Akihiko Matsui, 1989. "Cheap Talk and Cooperation in the Society," Discussion Papers 848, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. Karl H. Schlag, 1994. "Evolution in Partnership Games,an Equivalence Result," Discussion Paper Serie B 298, University of Bonn, Germany.
  13. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  14. 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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