We introduce the algorithmic learning equations (ALEs), a set of ordinary differential equations which characterizes the finite-time and asymptotic behaviour of the stochastic interaction between state-dependent learning algorithms in dynamic games. Our framework allows for a variety of...

We characterise the stochastic interaction of independent learning algorithms as a deterministic system of ordinary differential equations and use it to understand the long-term behaviour of the algorithms in a repeated game. In a symmetric bimatrix repeated game, we prove that the dynamics of...

We propose an extension to smooth fictitious play and prove that play converges to an ε-Markov perfect equilibrium with probability one in a class of stochastic games known as Markov potential games. We then prove a partial Folk theorem for repeated games under one-period perfect monitoring. We...