An algorithm for two‐player repeated games with perfect monitoring. Issue 2 (2nd June 2014)

• Record Type: Journal Article
• Authors: Abreu, Dilip; Sannikov, Yuliy
• Is Part Of: Theoretical economics. Volume 9:Issue 2(2014:May)
• Page Start: 313
• Page End: 338
• Publication Date: 2014-06-02
• Subjects: Economics -- Periodicals; 330.01
• DOI: 10.3982/TE1302
• Languages: English
• ISSNs: 1933-6837

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p>Consider repeated two‐player games with perfect monitoring and discounting. We provide an algorithm that computes the set <italic>V</italic>^* of payoff pairs of all pure‐strategy subgame‐perfect equilibria with public randomization. The algorithm provides significant efficiency gains over the existing implementations of the algorithm from Abreu et al. (1990). These efficiency gains arise from a better understanding of the manner in which <italic>extreme points</italic> of the equilibrium payoff set are generated. An important theoretical implication of our algorithm is that the set of extreme points <italic>E</italic> of <italic>V</italic>^* is <italic>finite</italic>. Indeed, |<italic>E</italic>| 3|<italic>A</italic>|, where <italic>A</italic> is the set of action profiles of the stage game.</p> </abstract>