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Learning by (limited) forward looking players

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  • Mengel, F.

    (Microeconomics & Public Economics)

Abstract

We present a model of adaptive economic agents who are k periods forward looking. Agents in our model are randomly matched to interact in finitely repeated games. They form beliefs by learning from past behavior of others 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 whenever they satisfy a “local” efficiency condition. We then characterize stochastically stable states in a class of 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 and in particular can explain what is commonly called the “endgame effect” and the “restart effect”. Finally, if populations are composed of some myopic and some forward looking agents, parameter constellations exist such that either might obtain higher average payoffs.
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  • Mengel, F., 2008. "Learning by (limited) forward looking players," Research Memorandum 053, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2008053
    DOI: 10.26481/umamet.2008053
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    Cited by:

    1. Andrés Perea & Elias Tsakas, 2019. "Limited focus in dynamic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 571-607, June.
    2. Marco Mantovani, 2015. "Limited backward induction: foresight and behavior in sequential games," Working Papers 289, University of Milano-Bicocca, Department of Economics, revised Jan 2015.
    3. Aidas Masiliunas, 2016. "Inefficient Lock-in with Sophisticated and Myopic Players," AMSE Working Papers 1615, Aix-Marseille School of Economics, France, revised 19 Apr 2016.
    4. Charness, Gary & Feri, Francesco & Meléndez-Jiménez, Miguel A. & Sutter, Matthias, 2012. "Equilibrium Selection in Experimental Games on Networks," University of California at Santa Barbara, Economics Working Paper Series qt51v6w9hd, Department of Economics, UC Santa Barbara.
    5. Herz, Holger & Schmutzler, Armin & Volk, André, 2019. "Cooperation and mistrust in relational contracts," Journal of Economic Behavior & Organization, Elsevier, vol. 166(C), pages 366-380.
    6. Norton, Douglas A., 2015. "Killing the (coordination) moment: How ambiguity eliminates the restart effect in voluntary contribution mechanism experiments," Economics Letters, Elsevier, vol. 126(C), pages 1-5.
    7. Lahkar, Ratul & Mukherjee, Saptarshi, 2021. "Evolutionary implementation in aggregative games," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 137-151.
    8. Masiliūnas, Aidas, 2019. "Overcoming inefficient lock-in in coordination games with sophisticated and myopic players," Mathematical Social Sciences, Elsevier, vol. 100(C), pages 1-12.
    9. Yu Yvette Zhang & Rodolfo M Nayga Jr. & Dinah Pura T Depositario, 2019. "Learning and the possibility of losing own money reduce overbidding: Delayed payment in experimental auctions," PLOS ONE, Public Library of Science, vol. 14(5), pages 1-19, May.

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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

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