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Learning by (limited) forward looking players

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Author Info
Mengel, Friederike (METEOR)

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Abstract

We present a model of adaptive economic agents that are k periods forward looking. Agents in our model are randomly matched to interact in finitely repeated games. They form beliefs by relying on their past experience in the same situation (after the same recent history) and then best respond to these beliefs looking k periods ahead. We establish almost sure convergence of our stochastic process and characterize absorbing sets. These can be very different from the predictions in both the fully rational model and the adaptive, but myopic case. In particular we find that also Non-Nash outcomes can be sustained almost all the time whenever they are individually rational and satisfy an efficiency condition. We then characterize stochastically stable states in 2×2 games and show that under certain conditions the efficient action in Prisoner''s Dilemma games and Coordination games can be singled out as uniquely stochastically stable. We show that our results are consistent with typical patterns observed in experiments on finitely repeated Prisoner''s Dilemma games. Finally, if populations are composed of some myopic and some forward looking agents parameter constellations exists such that either might obtain higher average payoffs.

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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 053.

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Date of creation: 2008
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Handle: RePEc:dgr:umamet:2008053

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Keywords: Economics (Jel: A);

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  1. Wolf Ze'ev Ehrblatt & Kyle Hyndman & Erkut Y. ÄOzbay & Andrew Schotter, 2006. "Convergence: An Experimental Study," Levine's Working Paper Archive 122247000000001148, David K. Levine. [Downloadable!]
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  3. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December. [Downloadable!] (restricted)
  4. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January. [Downloadable!] (restricted)
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  5. Binmore, Ken & McCarthy, John & Ponti, Giovanni & Samuelson, Larry & Shaked, Avner, 2002. "A Backward Induction Experiment," Journal of Economic Theory, Elsevier, vol. 104(1), pages 48-88, May. [Downloadable!] (restricted)
  6. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December. [Downloadable!] (restricted)
  7. Antoine Terracol & Jonathan Vaksmann, 2007. "Dumbing down rational players : Learning and teaching in an experimental game," Documents de travail du Centre d'Economie de la Sorbonne bla07017, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne. [Downloadable!]
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  8. Jehiel, Philippe, 1998. "Learning to Play Limited Forecast Equilibria," Games and Economic Behavior, Elsevier, vol. 22(2), pages 274-298, February. [Downloadable!] (restricted)
  9. Camerer, Colin F. & Ho, Teck-Hua & Chong, Juin-Kuan, 2002. "Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games," Journal of Economic Theory, Elsevier, vol. 104(1), pages 137-188, May. [Downloadable!] (restricted)
  10. Myerson, Roger B. & Pollock, Gregory B. & Swinkels, Jeroen M., 1991. "Viscous population equilibria," Games and Economic Behavior, Elsevier, vol. 3(1), pages 101-109, February. [Downloadable!] (restricted)
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  11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  12. Drew Fudenberg & David Levine, 1987. "Reputation and Equilibrium Selection in Games With a Patient Player," Working papers 461, Massachusetts Institute of Technology (MIT), Department of Economics.
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  13. Mengel, Friederike, 2008. "Matching structure and the cultural transmission of social norms," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 608-623, September. [Downloadable!] (restricted)
  14. Watson, Joel, 1993. "A "Reputation" Refinement without Equilibrium," Econometrica, Econometric Society, vol. 61(1), pages 199-205, January. [Downloadable!] (restricted)
  15. Jehiel, Philippe, 2001. "Limited Foresight May Force Cooperation," Review of Economic Studies, Blackwell Publishing, vol. 68(2), pages 369-91, April.
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