The Robustness of Game Dynamics under Random Perturbations
P.-L. Cauvin. Master Thesis, 2023.
In this work, we examine the robustness of game dynamics in the presence of random shocks and disturbances to the underlying system. Expanding on the microfoundations of evolution by imitation, we propose a class of stochastic imitation dynamics, and we examine the model’s long-run behavior as a function of the imitation protocol and the magnitude of the stochastic perturbations affecting the system. In particular, we derive a set of sufficient conditions that guarantee the extinction of dominated strategies and the asymptotic stability of Nash equilibria (with probability 1 and high probability respectively), as well as rates at which convergence occur. In a subsequent part, we also explain how our results can be extended to cover a stochastic variant of the exponential dynamics, which contain several important variants of the stochastic replicator dynamics, now unified under the same general framework.