Learning in the Santa Fe Bar Problem

This paper investigates learning in the Santa Fe (El Farol) bar problem (sfbp). It is argued that rationality together with belief-based learning (e.g., Bayesian updating) yields unstable behavior in this game. More specifically, two conditions normally sufficient for convergence to Nash equilibrium, namely rationality and predictivity, are shown to be incompatible. Low-rationality learning algorithms, however, converge to the symmetric Nash equilibrium in sfbp. Although it is fair, this equilibrium is suboptimal—the expected utility of the collective is near zero. This paper therefore proposes a simple modification to sfbp, whereby agents that attend the bar are charged an entry fee that is divided equally among those agents who do not attend the bar. In this modified scenario, low-rationality algorithms, which once again learn Nash equilibrium strategies, approximate Pareto-optimal behavior: individual rationality coincides with collective rationality.

[1]  J. Robinson.  AN ITERATIVE METHOD OF SOLVING A GAME , 1951, Classics in Game Theory.

[2]  Michael Bächle,et al.  Social Software , 2006, Informatik-Spektrum.

[3]  William A. Sethares,et al.  Coordination failure as a source of congestion in information networks , 2003, IEEE Trans. Signal Process..

[4]  Dean P. Foster,et al.  Regret in the On-Line Decision Problem , 1999 .

[5]  Roni Even.  Distributed intelligence with bounded rationality: Applications to economies and networks , 1999 .

[6]  A. Greenwald.  Learning to Play Network Games , 1998 .

[7]  Eric J. Friedman,et al.  Learning and Implementation on the Internet , 1997 .

[8]  E. Friedman.  Dynamics and Rationality in Ordered Externality Games , 1996 .

[9]  Yoav Freund,et al.  Game theory, on-line prediction and boosting , 1996, COLT '96.

[10]  John Nachbar.  Prediction, optimization, and learning in repeated games , 1997 .

[11]  Nicolò Cesa-Bianchi,et al.  Gambling in a rigged casino: The adversarial multi-armed bandit problem , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[12]  Ariel Orda,et al.  The designer's perspective to noncooperative networks , 1995, Proceedings of INFOCOM'95.

[13]  S. Shenker.  Making greed work in networks: a game-theoretic analysis of switch service disciplines , 1994, SIGCOMM.

[14]  W. Arthur.  Inductive Reasoning and Bounded Rationality , 1994 .

[15]  E. Kalai,et al.  Rational Learning Leads to Nash Equilibrium , 1993 .

[16]  T. Schelling.  Micromotives and Macrobehavior , 1978 .

[17]  G. Hardin,et al.  The Tragedy of the Commons , 1968, Green Planet Blues.

[18]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .