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Cold play: Learning across bimatrix games

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  • Lensberg, Terje
  • Schenk-Hoppé, Klaus R.

Abstract

We study one-shot play in the set of all bimatrix games by a large population of agents. The agents never see the same game twice, but they can learn ‘across games’ by developing solution concepts that tell them how to play new games. Each agent’s individual solution concept is represented by a computer program, and natural selection is applied to derive stochastically stable solution concepts. Our aim is to develop a theory predicting how experienced agents would play in one-shot games.

Suggested Citation

  • Lensberg, Terje & Schenk-Hoppé, Klaus R., 2020. "Cold play: Learning across bimatrix games," MPRA Paper 99095, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:99095
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    1. Vincent P. Crawford & Uri Gneezy & Yuval Rottenstreich, 2008. "The Power of Focal Points Is Limited: Even Minute Payoff Asymmetry May Yield Large Coordination Failures," American Economic Review, American Economic Association, vol. 98(4), pages 1443-1458, September.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    3. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639.
    4. Carlsson, H. & van Damme, E.E.C., 1991. "Equilibrium selection in stag hunt games," Other publications TiSEM bd92d0ae-790f-40ad-afea-4, Tilburg University, School of Economics and Management.
    5. Mookherjee Dilip & Sopher Barry, 1994. "Learning Behavior in an Experimental Matching Pennies Game," Games and Economic Behavior, Elsevier, vol. 7(1), pages 62-91, July.
    6. Van der Heijden, Eline C. M. & Nelissen, Jan H. M. & Potters, Jan J. M. & Verbon, Harrie A. A., 1998. "The poverty game and the pension game: The role of reciprocity," Journal of Economic Psychology, Elsevier, vol. 19(1), pages 5-41, February.
    7. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    8. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
    9. Huck, Steffen & Muller, Wieland, 2005. "Burning money and (pseudo) first-mover advantages: an experimental study on forward induction," Games and Economic Behavior, Elsevier, vol. 51(1), pages 109-127, April.
    10. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
    11. Haruvy, Ernan & Stahl, Dale O., 2012. "Between-game rule learning in dissimilar symmetric normal-form games," Games and Economic Behavior, Elsevier, vol. 74(1), pages 208-221.
    12. Samuelson, Larry, 2001. "Analogies, Adaptation, and Anomalies," Journal of Economic Theory, Elsevier, vol. 97(2), pages 320-366, April.
    13. Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, vol. 62(4), pages 311-333, May.
    14. Drew Fudenberg & Annie Liang, 2019. "Predicting and Understanding Initial Play," American Economic Review, American Economic Association, vol. 109(12), pages 4112-4141, December.
    15. John Duffy & Ernest K. Lai & Wooyoung Lim, 2017. "Coordination via correlation: an experimental study," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 265-304, August.
    16. Steiner, Jakub & Stewart, Colin, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
    17. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
    18. Cooper, Russell & Douglas V. DeJong & Robert Forsythe & Thomas W. Ross, 1993. "Forward Induction in the Battle-of-the-Sexes Games," American Economic Review, American Economic Association, vol. 83(5), pages 1303-1316, December.
    19. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    20. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    21. Selten, Reinhard & Abbink, Klaus & Buchta, Joachim & Sadrieh, Abdolkarim, 2003. "How to play (3 x 3)-games.: A strategy method experiment," Games and Economic Behavior, Elsevier, vol. 45(1), pages 19-37, October.
    22. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    23. David Cooper & John Kagel, 2008. "Learning and transfer in signaling games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 415-439, March.
    24. Gilboa, Itzhak & Schmeidler, David & Wakker, Peter P., 2002. "Utility in Case-Based Decision Theory," Journal of Economic Theory, Elsevier, vol. 105(2), pages 483-502, August.
    25. LiCalzi Marco, 1995. "Fictitious Play by Cases," Games and Economic Behavior, Elsevier, vol. 11(1), pages 64-89, October.
    26. Lensberg, Terje & Schenk-Hoppé, Klaus Reiner & Ladley, Dan, 2015. "Costs and benefits of financial regulation: Short-selling bans and transaction taxes," Journal of Banking & Finance, Elsevier, vol. 51(C), pages 103-118.
    27. Arifovic, Jasmina, 1995. "Genetic algorithms and inflationary economies," Journal of Monetary Economics, Elsevier, vol. 36(1), pages 219-243, August.
    28. Grimm, Veronika & Mengel, Friederike, 2012. "An experiment on learning in a multiple games environment," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2220-2259.
    29. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    30. Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
    31. He, Simin & Wu, Jiabin, 2020. "Compromise and coordination: An experimental study," Games and Economic Behavior, Elsevier, vol. 119(C), pages 216-233.
    32. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2013. "Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications," Journal of Economic Literature, American Economic Association, vol. 51(1), pages 5-62, March.
    33. Sgroi, Daniel & Zizzo, Daniel John, 2009. "Learning to play 3×3 games: Neural networks as bounded-rational players," Journal of Economic Behavior & Organization, Elsevier, vol. 69(1), pages 27-38, January.
    34. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    35. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
    36. Stahl, Dale O., 2000. "Rule Learning in Symmetric Normal-Form Games: Theory and Evidence," Games and Economic Behavior, Elsevier, vol. 32(1), pages 105-138, July.
    37. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    38. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    39. David Cooper & John H. Kagel, 2003. "Lessons Learned: Generalizing Learning Across Games," American Economic Review, American Economic Association, vol. 93(2), pages 202-207, May.
    40. Stahl, Dale O., 2001. "Population rule learning in symmetric normal-form games: theory and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 45(1), pages 19-35, May.
    41. Russell Cooper & Douglas V. DeJong & Robert Forsythe & Thomas W. Ross, 1989. "Communication in the Battle of the Sexes Game: Some Experimental Results," RAND Journal of Economics, The RAND Corporation, vol. 20(4), pages 568-587, Winter.
    42. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
    43. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    44. COOPER, R. & DEJONG, D.V. & FORSYTHE, R. & Tom Ross, 1989. "Communication In The Battle Of The Sexes Game," Carleton Industrial Organization Research Unit (CIORU) 89-03, Carleton University, Department of Economics.
    45. Arifovic, Jasmina, 1996. "The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economies," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 510-541, June.
    46. Dale O. Stahl, 1999. "Evidence based rules and learning in symmetric normal-form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 111-130.
    47. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
    48. 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.
    49. Basu, Kaushik, 1994. "The Traveler's Dilemma: Paradoxes of Rationality in Game Theory," American Economic Review, American Economic Association, vol. 84(2), pages 391-395, May.
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    Keywords

    One-shot games; solution concepts; genetic programming; evolutionary stability.;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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

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