The paper studies a class of learning dynamics, termed inertial best responsedynamics, based on the Fictitious Play (FP) algorithm. A general convergenceresult is established showing that inertial best response dynamics converge,almost surely, to pure-strategy Nash equilibrium (NE). As an application of thegeneral result, the paper considers learning in a setting where (i) playershave some uncertainty about the underlying state of the world, and (ii) allinter-agent communication is restricted to a preassigned (possibly sparse)communication graph. The paper studies two particular instances of inertialbest response dynamics in this setting: FP with inertia and Joint Strategy FPwith inertia. General conditions are established under which the algorithmsconverge to pure-strategy NE, and a fully distributed variant of each algorithmis presented. Finally, numerical simulations are provided which verify thefindings.
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