Not just an empty threat: Subgame-perfect equilibrium in repeated games played by computationally bounded players

Joseph Y. Halpern*, Rafael Pass, Lior Seeman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study the problem of finding a subgame-perfect equilibrium in repeated games. In earlier work [Halpern, Pass and Seeman 2014], we showed how to efficiently find an (approximate) Nash equilibrium if assuming that players are computationally bounded (and making standard cryptographic hardness assumptions); in contrast, as demonstrated in the work of Borgs et al. [2010], unless we restrict to computationally bounded players, the problem is PPAD-hard. But it is well-known that for extensive-form games (such as repeated games), Nash equilibrium is a weak solution concept. In this work, we define and study an appropriate notion of a subgame-perfect equilibrium for computationally bounded players, and show how to efficiently find such an equilibrium in repeated games (again, making standard cryptographic hardness assumptions). As we show in the full paper, our algorithm works not only for games with a finite number of players, but also for constant-degree graphical games.

Original languageEnglish
Pages (from-to)249-262
Number of pages14
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8877
DOIs
StatePublished - 2014
Externally publishedYes

Funding

FundersFunder number
Air Force Office of Scientific Research
Army Research OfficeFA9550-08-1-0266
National Science FoundationCCF-1214844, IIS-0911036

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