Dynamic social learning under graph constraints
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We argue that graph-constrained dynamic choice with reinforcement can be viewed as a scaled version of a special instance of replicator dynamics. The latter also arises as the limiting differential equation for the empirical measures of a vertex reinforced random walk on a directed graph. We use this equivalence to show that for a class of positively α-homogeneous rewards, α > 0, the asymptotic outcome concentrates around the optimum in a certain limiting sense when `annealed' by letting α↑∞ slowly. We also discuss connections with classical simulated annealing.
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