Heterogeneous Beliefs and Multi-Population Learning in Network Games, Shuyue Hu, Harold Soh★, Georgios Piliouras, arXiv preprint, 2023
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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. Although the initial belief heterogeneity disappears in the limit, we show that it plays a crucial role for equilibrium selection in the case of coordination games as it helps select highly desirable equilibria. Contrary, in the case of network competition, the resulting limit behavior is independent of the initialization of beliefs, even when the underlying game has many distinct Nash equilibria.


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Shuyue Hu, Harold Soh★, Georgios Piliouras, “Heterogeneous Beliefs and Multi-Population Learning in Network Games”, arXiv preprint, 2023

title={Heterogeneous Beliefs and Multi-Population Learning in Network Games},
author={Hu, Shuyue and Soh, Harold and Piliouras, Georgios},
journal={arXiv preprint arXiv:2301.04929},


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Shuyue Hu