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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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Bibliographic Info

Paper provided by Department of Economics, UC Santa Cruz in its series Santa Cruz Department of Economics, Working Paper Series with number qt6947v2f5.

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Date of creation: 19 Jul 2012
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Handle: RePEc:cdl:ucscec:qt6947v2f5

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

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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. Dan Friedman, 2010. "Equilibrium in Evolutionary Games: Some Experimental Results," Levine's Working Paper Archive 393, David K. Levine.
  3. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
  4. Cason, Timothy N. & Friedman, Daniel & Hopkins, Ed H, 2009. "Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria," Santa Cruz Department of Economics, Working Paper Series qt8kp6c049, Department of Economics, UC Santa Cruz.
  5. 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.
  6. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
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