How long to equilibrium? The communication complexity of uncoupled equilibrium procedures

Sergiu Hart, Yishay Mansour

Research output: Contribution to journalArticlepeer-review

Abstract

We study the question of how long it takes players to reach a Nash equilibrium in uncoupled setups, where each player initially knows only his own payoff function. We derive lower bounds on the communication complexity of reaching a Nash equilibrium, i.e., on the number of bits that need to be transmitted, and thus also on the required number of steps. Specifically, we show lower bounds that are exponential in the number of players in each one of the following cases: (1) reaching a pure Nash equilibrium; (2) reaching a pure Nash equilibrium in a Bayesian setting; and (3) reaching a mixed Nash equilibrium. We then show that, in contrast, the communication complexity of reaching a correlated equilibrium is polynomial in the number of players.

Original languageEnglish
Pages (from-to)107-126
Number of pages20
JournalGames and Economic Behavior
Volume69
Issue number1
DOIs
StatePublished - May 2010

Keywords

  • Communication complexity
  • Correlated equilibrium
  • Nash equilibrium
  • Speed of convergence
  • Uncoupled dynamics

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