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Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

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  • Timothy N. Cason
  • Daniel Friedman
  • Ed Hopkins

    ()

Abstract

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.

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Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 188.

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Length: 38
Date of creation: 16 Mar 2009
Date of revision:
Handle: RePEc:edn:esedps:188

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Keywords: games; experiments; TASP; learning; unstable; mixed equilibrium; fictitious play.;

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Cited by:
  1. 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.
  2. Martin Hahn, 2012. "An Evolutionary Analysis of Varian’s Model of Sales," Dynamic Games and Applications, Springer, vol. 2(1), pages 71-96, March.

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