TY - JOUR

T1 - How long to equilibrium? The communication complexity of uncoupled equilibrium procedures

AU - Hart, Sergiu

AU - Mansour, Yishay

N1 - Funding Information:
We thank Fabrizio Germano, Adam Kalai, Eyal Kushilevitz, Andreu Mas-Colell, Noam Nisan, and the anonymous referees for useful discussions and suggestions, and the Institute for Advanced Studies at the Hebrew University of Jerusalem where some of this work was done. The research was partially supported by grants of the Israel Science Foundation (Hart, Mansour) and by an IBM faculty award (Mansour).

PY - 2010/5

Y1 - 2010/5

N2 - 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.

AB - 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.

KW - Communication complexity

KW - Correlated equilibrium

KW - Nash equilibrium

KW - Speed of convergence

KW - Uncoupled dynamics

UR - http://www.scopus.com/inward/record.url?scp=77951634170&partnerID=8YFLogxK

U2 - 10.1016/j.geb.2007.12.002

DO - 10.1016/j.geb.2007.12.002

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AN - SCOPUS:77951634170

VL - 69

SP - 107

EP - 126

JO - Games and Economic Behavior

JF - Games and Economic Behavior

SN - 0899-8256

IS - 1

ER -