Equilibrium Paths in Discounted Supergames - Kimmo Berg; Mitri Kitti (Aboa Centre for Economics (ACE), 2014)
This paper characterizes the subgame-perfect pure-strategy equilibrium paths in discounted supergames with perfect monitoring. It is shown that all the equilibrium paths are composed of fragments called elementary subpaths. This characterization result is complemented with an algorithm for finding the elementary subpaths. By using these subpaths it is possible to generate equilibrium paths and payoffs. When there are finitely many elementary subpaths, all the equilibrium paths can be represented by a directed graph. These graphs can be used in analyzing the complexity of equilibrium outcomes. In particular, it is shown that the size and the density of the equilibrium set can be measured by the asymptotic growth rate of equilibrium paths and the Hausdorff dimension of the payoff set.
Keywords: C72; C73; 330; repeated game; subgame-perfect equilibrium; equilibrium path; graph presentation of paths; complexity