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Cycles and Instability in a Rock-Paper-Scissors Population Game: a Continuous Time Experiment

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  • Friedman, Daniel
  • Cason, Timothy N
  • Hopkins, Ed
Abstract
We report laboratory experiments that use new, visually oriented software to explore the dynamics of 3x3 games with intransitive best responses. Each moment, each player is matched against the entire population, here 8 human subjects. A "heat map" offers instantaneous feedback on current profit opportunities. In the continuous slow adjustment treatment, we see distinct cycles in the population mix. The cycle amplitude, frequency and direction are consistent with the standard learning models. Cycles are more erratic and higher frequency in the instantaneous adjustment treatment. Control treatments (using simultaneous matching in discrete time) replicate previous results that exhibit weak or no cycles. Average play is approximated fairly well by Nash equilibrium, and an alternative point prediction, "TASP" (Time Average of the Shapley Polygon), captures some regularities that Nash equilibrium misses. Copyright 2014, Oxford University Press.
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Suggested Citation

  • Friedman, Daniel & Cason, Timothy N & Hopkins, Ed, 2012. "Cycles and Instability in a Rock-Paper-Scissors Population Game: a Continuous Time Experiment," Santa Cruz Department of Economics, Working Paper Series qt6947v2f5, Department of Economics, UC Santa Cruz.
    • Handle: RePEc:cdl:ucscec:qt6947v2f5
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    References listed on IDEAS

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    1. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    2. Cason, Timothy N. & Friedman, Daniel & Hopkins, Ed, 2010. "Testing the TASP: An experimental investigation of learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2309-2331, November.
    3. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    4. Hommes, Cars H. & Ochea, Marius I., 2012. "Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics," Games and Economic Behavior, Elsevier, vol. 74(1), pages 434-441.
    5. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
    6. Dan Friedman, 2010. "Equilibrium in Evolutionary Games: Some Experimental Results," Levine's Working Paper Archive 393, David K. Levine.
    7. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    8. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Social and Behavioral Sciences; experiments; learning; mixed equilibrium; continuous time;
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