Heterogeneous Beliefs and Multi-Population Learning in Network Games

Understand

The effect of population heterogeneity in multi-agent learning is practically relevant but remains far from being well-understood.

• Motivated by this, we introduce a model of multi-population learning that allows for heterogeneous beliefs within each population and where agents respond to their beliefs via smooth fictitious play (SFP).We show that the system state -- a probability distribution over beliefs -- evolves according to a system of partial differential equations akin to the continuity equations that commonly desccribe transport phenomena in physical systems.
• We establish the convergence of SFP to Quantal Response Equilibria in different classes of games capturing both network competition as well as network coordination.
• We also prove that the beliefs will eventually homogenize in all network games.