Equilibrium Paths in Discounted Supergames

Kimmo Berg and Mitri Kitti
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Kimmo Berg: Systems Analysis Laboratory, Aalto University School of Science
Mitri Kitti: Department of Economics, University of Turku

No 96, Discussion Papers from Aboa Centre for Economics

Abstract: 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: repeated game; subgame-perfect equilibrium; equilibrium path; graph presentation of paths; complexity (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Pages: 38
Date: 2014-12
New Economics Papers: this item is included in nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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