Efficient learning equilibrium

Ronen I. Brafman, Moshe Tennenholtz

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


We introduce efficient learning equilibrium (ELE), a normative approach to learning in non-cooperative settings. In ELE, the learning algorithms themselves are required to be in equilibrium. In addition, the learning algorithms must arrive at a desired value after polynomial time, and a deviation from the prescribed ELE becomes irrational after polynomial time. We prove the existence of an ELE (where the desired value is the expected payoff in a Nash equilibrium) and of a Pareto-ELE (where the objective is the maximization of social surplus) in repeated games with perfect monitoring. We also show that an ELE does not always exist in the imperfect monitoring case. Finally, we discuss the extension of these results to general-sum stochastic games.

Original languageEnglish
Pages (from-to)27-47
Number of pages21
JournalArtificial Intelligence
Issue number1-2
StatePublished - 1 Jan 2004


  • Efficiency
  • Ex-post equilibrium
  • Learning equilibrium
  • Multi-agent learning
  • Repeated games
  • Stochastic games

ASJC Scopus subject areas

  • Language and Linguistics
  • Linguistics and Language
  • Artificial Intelligence


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