Games in continuous time with coupled populations

Equilibrium selection with coupled populations in hawk-dove games: ​Theory and experiment in continuous time
Journal of Economic Theory​ (2016)

Perturbed best response dynamics in a hawk-dove game
​Economics Letters ​(2017)
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Equilibrium selection with coupled populations in hawk-dove games:
​Theory and experiment in continuous time 

 Journal of Economic Theory 165 (2016) 472-486
​with Volker Benndorf and Hans-Theo Normann
Standard one- and two-population models for evolutionary games are the limit cases of a uniparametric family combining intra- and intergroup interactions. Our setup interpolates between both extremes with a coupling parameter κ. For the example of the hawk–dove game, we analyze the replicator dynamics of the coupled model. We confirm the existence of a bifurcation in the dynamics of the system and identify three regions for equilibrium selection, one of which does not appear in common one- and two-population models. We also design a continuous-time experiment, exploring the dynamics and the equilibrium selection. The data largely confirm the theory.

Perturbed best response dynamics in a hawk-dove game

Economics Letters 153 (2017) 61-64
​with Volker Benndorf
We examine the impact of behavioral noise on equilibrium selection in a hawk-dove game with a model that linearly interpolates between the one- and two-population structures in an evolutionary context. Perturbed best response dynamics generates two hypotheses in addition to the bifurcation predicted by standard replicator dynamics. First, when replicator dynamics suggests mixing behavior (close to the one-population model), there will be a bias against hawkish play. Second, polarizing behavior as predicted by replicator dynamics in the vicinity of the two-population model will be less extreme in the presence of behavioral noise. We find both effects in our data set.