Fractal Geometry of Equilibrium Payoffs in Discounted Supergames
نویسندگان
چکیده
This paper examines the pure-strategy subgame-perfect equilibrium payoffs in discounted supergames with perfect monitoring. It is shown that the payoff sets are typically fractals unless they are full-dimensional, which may happen when the discount factors are large enough. More specifically, the equilibrium payoffs can be identified as subsets of self-affine sets or graph-directed self-affine sets. We propose a method to estimate the Hausdorff dimension of equilibrium payoffs and relate it to the equilibrium paths and their graph presentation.
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