## Learning Efficient Nash Equilibria in Distributed Systems (2010)

### Cached

### Download Links

Citations: | 8 - 1 self |

### BibTeX

@MISC{Pradelski10learningefficient,

author = {Bary S. R. Pradelski and H. Peyton Young},

title = {Learning Efficient Nash Equilibria in Distributed Systems},

year = {2010}

}

### OpenURL

### Abstract

Abstract. An individual’s learning rule is completely uncoupled if it does not depend on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient pure Nash equilibrium in all generic n-person games that possess at least one pure Nash equilibrium. In games that do not have such an equilibrium, there is a simple formula that expresses the long-run probability of the various disequilibrium states in terms of two factors: i) the sum of payoffs over all agents, and ii) the maximum payoff gain that results from a unilateral deviation by some agent. This welfare/stability trade-off criterion provides a novel framework for analyzing the selection of disequilibrium as well as equilibrium states in n-person games. JEL: C72, C73 1 1. Learning equilibrium in complex interactive systems Game theory has traditionally focussed on situations that involve a small number of players. In these environments it makes sense to assume that players know the structure of the game and can predict the strategic behavior of their opponents. But there are many situations involving huge numbers of players where these assumptions are not particularly persuasive.

### Citations

350 | Conventions
- Young
- 1995
(Show Context)
Citation Context ...time). This contrasts with many other adaptive learning procedures – including ordinary log linear learning – that select the risk dominant equilibrium in 2 x 2 games (Kandori, Mailath and Rob, 1993; =-=Young, 1993-=-; Blume, 1993, 1995, 2003). 12Example 2. Let � be a 2� 2 game with payoff matrix A B A 30,30 0, 40 B 24,23 10,20 This game has no pure Nash equilibria, so by theorem 1 the learning process selects th... |

329 | Individual Strategy and Social Structure - Young |

237 |
The Statistical Mechanics of Strategic Interactions
- Blume
- 1993
(Show Context)
Citation Context ...ontrasts with many other adaptive learning procedures – including ordinary log linear learning – that select the risk dominant equilibrium in 2 x 2 games (Kandori, Mailath and Rob, 1993; Young, 1993; =-=Blume, 1993-=-, 1995, 2003). 12Example 2. Let � be a 2� 2 game with payoff matrix A B A 30,30 0, 40 B 24,23 10,20 This game has no pure Nash equilibria, so by theorem 1 the learning process selects the combination... |

192 | Selfish Routing and the Price of Anarchy
- Roughgarden
- 2005
(Show Context)
Citation Context ...at result from particular learning rules? In the last few years the study of these issues has been developing rapidly among computer scientists and distributed control theorists (Papadimitriou, 2001; =-=Roughgarden, 2005-=-; Mannor and Shamma, 2007; Marden and Shamma, 2008; Marden, Arslan, and Shamma, 2009; Marden et al., 2009; Asadpour and Saberi, 2009; Shah and Shin, 2010). Concurrently game theorists have been invest... |

135 | Algorithms, Games and the Internet
- Papadimitriou
- 2001
(Show Context)
Citation Context ... of the equilibria that result from particular learning rules? In the last few years the study of these issues has been developing rapidly among computer scientists and distributed control theorists (=-=Papadimitriou, 2001-=-; Roughgarden, 2005; Mannor and Shamma, 2007; Marden and Shamma, 2008; Marden, Arslan, and Shamma, 2009; Marden et al., 2009; Asadpour and Saberi, 2009; Shah and Shin, 2010). Concurrently game theoris... |

67 | The statistical mechanics of best response strategy revision - Blume - 1995 |

63 | Uncoupled dynamics do not lead to Nash equilibrium
- Hart, Mas-Colell
- 2003
(Show Context)
Citation Context ...Concurrently game theorists have been investigating the question of whether decentralized rules can be devised that converge to Nash equilibrium (or correlated equilibrium) in general n-person games (=-=Hart and Mas-Colell, 2003-=-, 2006; Foster and Young, 2003, 2006; Young, 2009; Hart and Mansour, 2010). Among control theorists and computer scientists, the issue is not whether a given learning rule is descriptively accurate as... |

45 | Evolving aspirations and cooperation - Karandikar, Mookherjee, et al. - 1998 |

36 | Evolutionary Implementation and Congestion Pricing - Sandholm - 2002 |

29 | How noise matters - Blume - 2003 |

28 | Stochastic uncoupled dynamics and Nash equilibrium - Hart, Mas-Colell - 2006 |

27 | Regret testing: learning to play Nash equilibrium without knowing you have an opponent. Theoretical Econ - Foster, Young - 2006 |

25 | Revisiting log-linear learning: asynchrony, completeness and payoff-based implementation. Working Paper
- Marden, Shamma
- 2008
(Show Context)
Citation Context ... the last few years the study of these issues has been developing rapidly among computer scientists and distributed control theorists (Papadimitriou, 2001; Roughgarden, 2005; Mannor and Shamma, 2007; =-=Marden and Shamma, 2008-=-; Marden, Arslan, and Shamma, 2009; Marden et al., 2009; Asadpour and Saberi, 2009; Shah and Shin, 2010). Concurrently game theorists have been investigating the question of whether decentralized rule... |

20 | Payoff-based dynamics for multiplayer weakly acyclic games
- Marden, Young, et al.
(Show Context)
Citation Context ...loping rapidly among computer scientists and distributed control theorists (Papadimitriou, 2001; Roughgarden, 2005; Mannor and Shamma, 2007; Marden and Shamma, 2008; Marden, Arslan, and Shamma, 2009; =-=Marden et al., 2009-=-; Asadpour and Saberi, 2009; Shah and Shin, 2010). Concurrently game theorists have been investigating the question of whether decentralized rules can be devised that converge to Nash equilibrium (or ... |

18 | Cooperative control and potential games
- Marden, Arslan, et al.
(Show Context)
Citation Context ...tudy of these issues has been developing rapidly among computer scientists and distributed control theorists (Papadimitriou, 2001; Roughgarden, 2005; Mannor and Shamma, 2007; Marden and Shamma, 2008; =-=Marden, Arslan, and Shamma, 2009-=-; Marden et al., 2009; Asadpour and Saberi, 2009; Shah and Shin, 2010). Concurrently game theorists have been investigating the question of whether decentralized rules can be devised that converge to ... |

15 | Multi-agent learning for engineers
- Mannor, Shamma
- 2007
(Show Context)
Citation Context ...icular learning rules? In the last few years the study of these issues has been developing rapidly among computer scientists and distributed control theorists (Papadimitriou, 2001; Roughgarden, 2005; =-=Mannor and Shamma, 2007-=-; Marden and Shamma, 2008; Marden, Arslan, and Shamma, 2009; Marden et al., 2009; Asadpour and Saberi, 2009; Shah and Shin, 2010). Concurrently game theorists have been investigating the question of w... |

13 | Automata, matching and foraging behavior of bees
- Thuijsman, Peleg, et al.
- 1995
(Show Context)
Citation Context ...quilibrium in 2 x 2 games but not in general (Bowling and Veloso, 2002). Similar ideas have been used to model animal foraging behavior (Houston, Kacelnik, and McNamara, 1982; Motro and Shmida, 1995; =-=Thuijsman, Peleg, Amitai, and Shmida, 1995-=-). For example, bees tend to search in the neighborhood of the last visited flower as long as the nectar yield is high, and search widely 9for an alternative patch otherwise (this is known as a near-... |

13 | Achieving Pareto optimality through distributed learning - Marden, Young, et al. - 2011 |

11 | How long to equilibrium? The communication complexity of uncoupled equilibrium procedures
- Hart, Mansour
- 2010
(Show Context)
Citation Context ...decentralized rules can be devised that converge to Nash equilibrium (or correlated equilibrium) in general n-person games (Hart and Mas-Colell, 2003, 2006; Foster and Young, 2003, 2006; Young, 2009; =-=Hart and Mansour, 2010-=-). Among control theorists and computer scientists, the issue is not whether a given learning rule is descriptively accurate as a model of human behavior, but whether it leads to good system-wide perf... |

11 |
Some learning rules for acquiring information
- Houston, Kacelnik, et al.
- 1982
(Show Context)
Citation Context ... realized average. This approach is known to converge to Nash equilibrium in 2 x 2 games but not in general (Bowling and Veloso, 2002). Similar ideas have been used to model animal foraging behavior (=-=Houston, Kacelnik, and McNamara, 1982-=-; Motro and Shmida, 1995; Thuijsman, Peleg, Amitai, and Shmida, 1995). For example, bees tend to search in the neighborhood of the last visited flower as long as the nectar yield is high, and search w... |

8 | Global convergence of Foster and Young’s regret testing. Games Econ. Behav. 60, 135–154 - Germano, Lugosi - 2007 |

7 | Learning, mutation, and long-run equilibrium in games - Kandori, Mailath, et al. - 1993 |

5 |
Completely uncoupled dynamics and Nash equilibria. Working paper 529
- Babichenko, 2010a
(Show Context)
Citation Context ...ium with high probability. Indeed it can be shown that, for general n-person games, there exist no completely uncoupled rules with finite memory that select a Nash equilibrium in this stronger sense (=-=Babichenko, 2010-=-; see also Hart and Mas-Colell, 2003, 2006). The learning rule that we propose is related to the trial and error learning procedure of Young (2009), and more distantly related to the ‘learning by samp... |

5 | On the inefficiency ratio of stable equilibria in congestion games - Asadpour, Saberi - 2009 |

2 | Near-far search: an evolutionarily stable foraging strategy. J Theor Biol 173:15–22 - Motro, Shmida - 1995 |

1 |
On the inefficiency ratio of stable equilibria
- Asadpour, Saberi
- 2009
(Show Context)
Citation Context ...computer scientists and distributed control theorists (Papadimitriou, 2001; Roughgarden, 2005; Mannor and Shamma, 2007; Marden and Shamma, 2008; Marden, Arslan, and Shamma, 2009; Marden et al., 2009; =-=Asadpour and Saberi, 2009-=-; Shah and Shin, 2010). Concurrently game theorists have been investigating the question of whether decentralized rules can be devised that converge to Nash equilibrium (or correlated equilibrium) in ... |

1 |
Multi-agent learning with a variable learning rate
- Bowling, Veloso
- 2002
(Show Context)
Citation Context ...benchmark actions, and u is an n-vector of their benchmark payoffs. For 2 Learning rules with high and low rates of exploration have been studied in a variety of settings, including computer science (=-=Bowling and Veloso, 2002-=-) and biology (Thuijsman et al., 1995). 5simplicity we assume that each u i is consistent with some payoff in the game, that is, u � u ( a ) for some a�A. Since A is finite, it follows that the state... |

1 | Average testing and the efficient boundary. Working paper - Arieli, Babichenko - 2011 |

1 | How long to Pareto efficiency? Working paper 562 - Babichenko, 2010b |