Dynamic social learning under graph constraints

We introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively α-homogeneous rewards. We show that its empirical process, which can be written as a stochastic approximation recursion with Markov noise, has the same probability law as a certain vertex reinforced random walk. We use this equivalence to show that for α> 0, the asymptotic outcome concentrates around the optimum in a certain limiting sense when `annealed' by letting α\uparrow\infty slowly.