Exploratory analysis and models for strategic learning towards equilibrium

Authors

DOI:

https://doi.org/10.31812/educdim.4513

Keywords:

behavioral game theory, guessing game, k-beauty contest, active learning, К, R, agent-based modeling

Abstract

This paper is about people's strategic behavior as observed through experiments. The research question posed in this paper is how players (primarily children) learn in complex strategic situations that they have never encountered before. We examine data from various games played during popular game theory lectures and present findings about players' strategic learning progress while competing with other players. Four "pick a number" games with similar-looking rules but very different properties were investigated. These games were presented to various groups of listeners. The collected data is available for replication and analysis in an open repository. In this paper, we analyze data and propose an agent-based model of a beauty pageant game to explain observed behavior. Finally, we discuss the findings, hypotheses to test, and open questions for future research.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...
Abstract views: 162 / PDF downloads: 83

References

Aumann, R., Brandenburger, A.: Epistemic Conditions for Nash Equilibrium. Econometrica 63(5), 1161–1180 (1995), http://www.jstor.org/stable/2171725 DOI: https://doi.org/10.2307/2171725

Aumann, R.J.: Backward induction and common knowledge of rationality. Games and Economic Behavior 8(1), 6–19 (1995). https://doi.org/10.1016/S0899-8256(05)80015-6 DOI: https://doi.org/10.1016/S0899-8256(05)80015-6

Bernheim, B.D.: Rationalizable strategic behavior. Econometrica 52(4), 1007–1028 (1984), https://www.jstor.org/stable/1911196 DOI: https://doi.org/10.2307/1911196

Camerer, C.F.: Behavioral game theory: Experiments in strategic interaction. The Roundtable Series in Behavioral Economics, Princeton University Press (2003)

Camerer, C.F., Ho, T.H., Chong, J.K.: Sophisticated experience-weighted attraction learning and strategic teaching in repeated games. Journal of Economic theory 104(1), 137–188 (2002). https://doi.org/10.1006/jeth.2002.2927 DOI: https://doi.org/10.1006/jeth.2002.2927

Camerer, C.F., Ho, T.H., Chong, J.K.: A cognitive hierarchy model of games. The Quarterly Journal of Economics 119(3), 861–898 (2004). https://doi.org/10.1162/0033553041502225 DOI: https://doi.org/10.1162/0033553041502225

Costa-Gomes, M., Crawford, V.P., Broseta, B.: Cognition and behavior in normal-form games: An experimental study. Econometrica 69(5), 1193–1235 (2001). https://doi.org/10.1111/1468-0262.00239 DOI: https://doi.org/10.1111/1468-0262.00239

Crawford, V.P., Costa-Gomes, M.A., Iriberri, N.: Structural models of nonequilibrium strategic thinking: Theory, evidence, and applications. Journal of Economic Literature 51(1), 5–62 (2013). https://doi.org/10.1257/jel.51.1.5 DOI: https://doi.org/10.1257/jel.51.1.5

Epstein, J.M.: Agent-based computational models and generative social science. Complexity 4(5), 41–60 (1999), https://cutt.ly/hKtpQa9 DOI: https://doi.org/10.1002/(SICI)1099-0526(199905/06)4:5<41::AID-CPLX9>3.0.CO;2-F

Fe, E., Gill, D., Prowse, V.L.: Cognitive skills, strategic sophistication, and life outcomes. Working Paper Series 448, The University of Warwick (2019), https://www.iza.org/publications/dp/13901/cognitive-skills-strategic-sophistication-and-life-outcomes DOI: https://doi.org/10.2139/ssrn.3737798

Gill, D., Prowse, V.: Cognitive ability, character skills, and learning to play equilibrium: A level-k analysis. Journal of Political Economy 124(6), 1619–1676 (2016). https://doi.org/10.1086/688849 DOI: https://doi.org/10.1086/688849

Güth, W., Kocher, M., Sutter, M.: Experimental ‘beauty contests’ with homogeneous and heterogeneous players and with interior and boundary equilibria. Economics Letters 74(2), 219–228 (2002). https://doi.org/10.1016/S0165-1765(01)00544-4 DOI: https://doi.org/10.1016/S0165-1765(01)00544-4

Ho, T.H., Camerer, C., Weigelt, K.: Iterated dominance and iterated best response in experimental “p-beauty contests”. The American Economic Review 88(4), 947–969 (1998), https://www.jstor.org/stable/117013

Ignatenko, O.: Guessing games experiments in school education and their analysis. CEUR Workshop Proceedings 2732, 881–892 (2020)

Ignatenko, O.P.: Data from experiments (2021), https://github.com/ignatenko/GameTheoryExperimentData

Ignatenko, O.P.: Guessing games experiments in Ukraine. Learning towards equilibrium. In: Proceedings of the 1st Symposium on Advances in Educational Technology - Volume 2: AET. pp. 156–168. INSTICC, SciTePress (2022). https://doi.org/10.5220/0010929600003364 DOI: https://doi.org/10.5220/0010929600003364

Kuhn, H.W., Harsanyi, J.C., Selten, R., Weibull, J.W., Van Damme, E., Nash Jr., J.F., Hammerstein, P.: The work of John Nash in game theory. Journal of Economic Theory 69(1), 153–185 (1996). https://doi.org/10.1006/jeth.1996.0042 DOI: https://doi.org/10.1006/jeth.1996.0042

Ledoux, A.: Concours résultats complets. Les victimes se sont plu à jouer le 14 d’atout. Jeux & Stratégie 2(10), 10–11 (1981)

Leyton-Brown, K., Shoham, Y.: Essentials of game theory: A concise, multidisciplinary introduction. Synthesis lectures on artificial intelligence and machine learning 2(1), 1–88 (2008). https://doi.org/10.2200/S00108ED1V01Y200802AIM003 DOI: https://doi.org/10.2200/S00108ED1V01Y200802AIM003

Mauersberger, F., Nagel, R.: Levels of reasoning in Keynesian Beauty Contests: a generative framework. In: Hommes, C., LeBaron, B. (eds.) Handbook of Computational Economics, Handbook of Computational Economics, vol. 4, pp. 541–634. Elsevier (2018) DOI: https://doi.org/10.1016/bs.hescom.2018.05.002

Moulin, H.: Game theory for the social sciences. New York Univeristy Press, New York, 2nd edn. (1986)

Nagel, R.: Unraveling in guessing games: An experimental study. The American Economic Review 85(5), 1313–1326 (1995), https://www.cs.princeton.edu/courses/archive/spr09/cos444/papers/nagel95.pdf

Nagel, R., Bühren, C., Frank, B.: Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game. Mathematical Social Sciences 90, 191–207 (2017). https://doi.org/10.1016/j.mathsocsci.2016.09.001 DOI: https://doi.org/10.1016/j.mathsocsci.2016.09.001

Nichols, M.W., Radzicki, M.J.: An agent-based model of behavior in “beauty contest” games. Working Paper 07-010, University of Nevada (2007), https://www.researchgate.net/publication/23694542_An_Agent-Based_Model_of_Behavior_in_Beauty_Contest_Games

Povea, E., Citak, F.: Children in the beauty contest game: behaviour and determinants of game performance. Master’s thesis, Norwegian School of Economics (2019), https://openaccess.nhh.no/nhh-xmlui/handle/11250/2611651

Schelling, T.C.: The Strategy of Conflict: With a New Preface by The Author. Harvard University Press (1980)

Wright, J.R., Leyton-Brown, K.: Models of level-0 behavior for predicting human behavior in games. CoRR abs/1609.08923 (2016), http://arxiv.org/abs/1609.08923

Wright, J.R., Leyton-Brown, K.: Predicting human behavior in unrepeated, simultaneous-move games. Games and Economic Behavior 106, 16–37 (2017). https://doi.org/10.1016/j.geb.2017.09.009 DOI: https://doi.org/10.1016/j.geb.2017.09.009

Downloads

Published

16-06-2022

How to Cite

Ignatenko, O. (2022). Exploratory analysis and models for strategic learning towards equilibrium. Educational Dimension, 59, 94–111. https://doi.org/10.31812/educdim.4513

Issue

Section

Theories of Learning, Education and Training