Computing Equilibria in Discounted 2 × 2 Supergames

Kimmo Berg () and Mitri Kitti

Computational Economics, 2013, vol. 41, issue 1, 88 pages

Abstract: This article examines the subgame perfect pure strategy equilibrium paths and payoff sets of discounted supergames with perfect monitoring. The main contribution is to provide methods for computing and tools for analyzing the equilibrium paths and payoffs in repeated games. We introduce the concept of a first-action feasible path, which simplifies the computation of equilibria. These paths can be composed into a directed multigraph, which is a useful representation for the equilibrium paths. We examine how the payoffs, discount factors and the properties of the multigraph affect the possible payoffs, their Hausdorff dimension, and the complexity of the equilibrium paths. The computational methods are applied to the 12 symmetric strictly ordinal 2 × 2 games. We find that these games can be classified into three groups based on the complexity of the equilibrium paths. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Repeated game; 2 × 2 game; Subgame perfect equilibrium; Equilibrium path; Payoff set; Multigraph (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s10614-011-9308-5

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