- Multiple steady states, limit cycles and chaotic attractors in evolutionary games with Logit Dynamics
- CeNDEF working paper
- Number of pages
- Universiteit van Amsterdam
- Document type
- Working paper
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
This paper investigates, by means of simple, three and four strategy games, the occurrence of periodic and chaotic behaviour in a smooth version of the Best Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cycles, do occur under the Logit Dynamics, even for three strategy games. Moreover, we show that the Logit Dynamics displays another bifurcation which cannot to occur under the Replicator Dynamics: the fold catastrophe. Finally, we find, in a four strategy game, a period-doubling route to chaotic dynamics under a 'weighted' version of the Logit Dynamics.
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