Computational Economics

, Volume 37, Issue 3, pp 267–300 | Cite as

A Class of Evolutionary Models for Participation Games with Negative Feedback

  • Pietro DindoEmail author
  • Jan Tuinstra
Open Access


We introduce a framework to analyze the interaction of boundedly rational heterogeneous agents repeatedly playing a participation game with negative feedback. We assume that agents use different behavioral rules prescribing how to play the game conditionally on the outcome of previous rounds. We update the fraction of the population using each rule by means of a general class of evolutionary dynamics based on imitation, which contains both replicator and logit dynamics. Our model is analyzed by a combination of formal analysis and numerical simulations and is able to replicate results from the experimental and computational literature on these types of games. In particular, irrespective of the specific evolutionary dynamics and of the exact behavioral rules used, the dynamics of the aggregate participation rate is consistent with the symmetric mixed strategy Nash equilibrium, whereas individual behavior clearly departs from it. Moreover, as the number of players or speed of adjustment increase the evolutionary dynamics typically becomes unstable and leads to endogenous fluctuations around the steady state. These fluctuations are robust with respect to behavioral rules that try to exploit them.


Participation games Heterogeneous behavioral rules Revision protocol Replicator dynamics Logit dynamics Nonlinear dynamics 

JEL Classification

C72 C73 



We thank Cees Diks, Cars Hommes, Bill Sandholm, Yang Zhang and an anonymous referee for constructive comments and Peter Heemeijer for providing us with the experimental data used in Sect. 2. Opinions and errors remain ours. Pietro Dindo acknowledges financial support from the European Commission 6th FP (Contract CIT3-CT-2005-513396) Project: DIME - Dynamics of Institutions and Markets in Europe.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.LEM, Scuola Superiore Sant’AnnaPisaItaly
  2. 2.Department of Quantitative Economics and CeNDEF, Faculty of Economics and BusinessUniversity of AmsterdamAmsterdamThe Netherlands

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