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AWESOME: A general multiagent learning algorithm that converges in selfplay and learns a best response against stationary opponents
, 2003
"... A satisfactory multiagent learning algorithm should, at a minimum, learn to play optimally against stationary opponents and converge to a Nash equilibrium in selfplay. The algorithm that has come closest, WoLFIGA, has been proven to have these two properties in 2player 2action repeated games— as ..."
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Cited by 81 (5 self)
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A satisfactory multiagent learning algorithm should, at a minimum, learn to play optimally against stationary opponents and converge to a Nash equilibrium in selfplay. The algorithm that has come closest, WoLFIGA, has been proven to have these two properties in 2player 2action repeated games— assuming that the opponent’s (mixed) strategy is observable. In this paper we present AWESOME, the first algorithm that is guaranteed to have these two properties in all repeated (finite) games. It requires only that the other players ’ actual actions (not their strategies) can be observed at each step. It also learns to play optimally against opponents that eventually become stationary. The basic idea behind AWESOME (Adapt When Everybody is Stationary, Otherwise Move to Equilibrium) is to try to adapt to the others’ strategies when they appear stationary, but otherwise to retreat to a precomputed equilibrium strategy. The techniques used to prove the properties of AWESOME are fundamentally different from those used for previous algorithms, and may help in analyzing other multiagent learning algorithms also.
Interdomain routing and games
 In STOC ’08
"... We present a gametheoretic model that captures many of the intricacies of interdomain routing in today’s Internet. In this model, the strategic agents are source nodes located on a network, who aim to send traffic to a unique destination node. The interaction between the agents is dynamic and compl ..."
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Cited by 32 (10 self)
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We present a gametheoretic model that captures many of the intricacies of interdomain routing in today’s Internet. In this model, the strategic agents are source nodes located on a network, who aim to send traffic to a unique destination node. The interaction between the agents is dynamic and complex – asynchronous, sequential, and based on partial information. Bestreply dynamics in this model capture crucial aspects of the only interdomain routing protocol de facto, namely the Border Gateway Protocol (BGP). We study complexity and incentiverelated issues in this model. Our main results are showing that in realistic and wellstudied settings, BGP is incentivecompatible. I.e., not only does myopic behaviour of all players converge to a “stable ” routing outcome, but no player has motivation to unilaterally deviate from the protocol. Moreover, we show that even coalitions of players of any size cannot improve their routing outcomes by collaborating. Unlike the vast majority of works in mechanism design, our results do not require any monetary transfers (to or by the agents).
The communication complexity of uncoupled Nash equilibrium procedures
 Games and Economic Behavior
, 2006
"... 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 trans ..."
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Cited by 21 (1 self)
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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.
Computational Aspects of Mechanism Design
, 2005
"... ions (Conitzer, Derryberry, & Sandholm 2004). It also introduces an expressive bidding protocol for matching donations to charities (Conitzer & Sandholm 2004e), as well as an expressive bidding protocol for general settings in which agents' actions impose externalities on the other agents (that is, ..."
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Cited by 1 (1 self)
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ions (Conitzer, Derryberry, & Sandholm 2004). It also introduces an expressive bidding protocol for matching donations to charities (Conitzer & Sandholm 2004e), as well as an expressive bidding protocol for general settings in which agents' actions impose externalities on the other agents (that is, affect the other agents' utilities). Mechanism design with strategic agents While having a good outcome optimization algorithm is necessary for preference aggregation to be successful, it is not sufficient. The reason is that generally, the agents' preferences are not known beforehand and will have to be elicited Copyright c # 2005, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. from them. Unfortunately, agents will misreport their preferences if it is in their interest to do so. This may lead to the outcome optimization algorithm choosing an outcome that is good under the reported preferences, but bad under the agents' true preferences. The soluti
The NOF Multiparty Communication Complexity of Composed Functions ⋆
"... Abstract. We study the kparty ‘number on the forehead ’ communication complexity of composed functions f ◦ g, where f: {0,1} n → {±1}, g: {0,1} k → {0,1} and for (x1,...,xk) ∈ ({0,1} n) k, f ◦g(x1,...,xk) = f (...,g(x1,i,...,xk,i),...). We show that there is an O(log 3 n) cost simultaneous protoc ..."
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Abstract. We study the kparty ‘number on the forehead ’ communication complexity of composed functions f ◦ g, where f: {0,1} n → {±1}, g: {0,1} k → {0,1} and for (x1,...,xk) ∈ ({0,1} n) k, f ◦g(x1,...,xk) = f (...,g(x1,i,...,xk,i),...). We show that there is an O(log 3 n) cost simultaneous protocol for SYM ◦ g when k> 1 + logn, SYM is any symmetric function and g is any function. Previously, an efficient protocol was only known for SYM ◦ g when g is symmetric and “compressible”. We also get a nonsimultaneous protocol for SYM ◦ g of cost O(n/2 k · logn + k logn) for any k ≥ 2. In the setting of k ≤ 1 + logn, we study more closely functions of the form MAJORITY ◦g, MODm ◦g, and NOR ◦g, where the latter two are generalizations of the wellknown and studied functions Generalized Inner Product and Disjointness respectively. We characterize the communication complexity of these functions with respect to the choice of g. In doing so, we answer a question posed by Babai et al. (SIAM Journal on Computing, 33:137–166, 2004) and determine the communication complexity of MAJORITY ◦ QCSBk, where QCSBk is the “quadratic character of the sum of the bits ” function. 1
A Computational Characterization of Multiagent Games with Fallacious Rewards
, 2007
"... Agents engaged in noncooperative interaction may seek to achieve a Nash equilibrium; this requires that agents be aware of others ’ rewards. Misinformation about rewards leads to a gap between the real interaction model—the explicit game—and the game that the agents perceive—the implicit game. If es ..."
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Agents engaged in noncooperative interaction may seek to achieve a Nash equilibrium; this requires that agents be aware of others ’ rewards. Misinformation about rewards leads to a gap between the real interaction model—the explicit game—and the game that the agents perceive—the implicit game. If estimation of rewards is based on modeling, agents may err. We define a robust equilibrium, which is impervious to slight perturbations, and prove that one can be efficiently pinpointed. We then relax this concept by introducing persistent equilibrium pairs—pairs of equilibria of the explicit and implicit games with nearly identical rewards—and resolve associated complexity questions. Assuming that valuations for different outcomes of the game are reported by agents in advance of play, agents may choose to report false rewards in order to improve their eventual payoff. We define the GameManipulation (GM) decision problem, and fully characterize the complexity of this problem and some variants.
On the Communication Complexity of Approximate Nash Equilibria
"... Abstract. We study the problem of computing approximate Nash equilibria, in a setting where players initially know their own payoffs but not the payoffs of other players. In order for a solution of reasonable quality to be found, some amount of communication needs to take place between the players. ..."
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Abstract. We study the problem of computing approximate Nash equilibria, in a setting where players initially know their own payoffs but not the payoffs of other players. In order for a solution of reasonable quality to be found, some amount of communication needs to take place between the players. We are interested in algorithms where the communication is substantially less than the contents of a payoff matrix, for example logarithmic in the size of the matrix. At one extreme is the case where the players do not communicate at all; for this case (with 2 players having n × n matrices) ɛNash equilibria can be computed for ɛ =3/4, while there is a lower bound of slightly more than 1/2 onthelowestɛ achievable. When the communication is polylogarithmic in n, weshowhowto obtain ɛ =0.438. For oneway communication we show that ɛ =1/2 is the exact answer. 1
unknown title
, 2006
"... www.elsevier.com/locate/geb How long to equilibrium? The communication complexity of uncoupled equilibrium procedures ✩ ..."
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www.elsevier.com/locate/geb How long to equilibrium? The communication complexity of uncoupled equilibrium procedures ✩
SIGACT News Complexity Theory Column 67
"... Warmest thanks to Arkadev and Toniann for telling the fascinating story of set disjointness. Upcoming guest articles in this column include Marius Zimand on Kolmogorov complexity extraction, Madhu Sudan on invariance in property testing, and John Watrous (topic TBA). As this issue arrives in mailbox ..."
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Warmest thanks to Arkadev and Toniann for telling the fascinating story of set disjointness. Upcoming guest articles in this column include Marius Zimand on Kolmogorov complexity extraction, Madhu Sudan on invariance in property testing, and John Watrous (topic TBA). As this issue arrives in mailboxes, a new academic year will be starting. I wish each of you