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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 100 (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 36 (14 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 22 (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.
How long to equilibrium? The communication complexity of uncoupled equilibrium procedures
, 2010
"... ..."
The NOF Multiparty Communication Complexity of Composed Functions
"... 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 ..."
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Cited by 1 (0 self)
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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.
Computational aspects of mechanism design
 In Proceedings of the National Conference on Artificial Intelligence (AAAI
, 2005
"... In a preference aggregation setting, a group of agents must jointly make a decision, based on the individual agents’ privately known preferences. To do so, the agents need some protocol (or mechanism) that will elicit this information from them, and make the decision. Examples of such mechanisms in ..."
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Cited by 1 (1 self)
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In a preference aggregation setting, a group of agents must jointly make a decision, based on the individual agents’ privately known preferences. To do so, the agents need some protocol (or mechanism) that will elicit this information from them, and make the decision. Examples of such mechanisms include voting protocols, auctions, and exchanges. In most realworld settings, preference aggregation is confronted with the following three computational issues. First, there is the complexity of executing the mechanism. Second, when standard mechanisms do not apply to or are suboptimal for the setting at hand, there is the complexity of designing the mechanism. Third, the agents face the complexity of (strategically) participating in the mechanism. My thesis statement is that by studying these computational aspects of the mechanism design process, we can significantly improve the generated mechanisms in a hierarchy of ways, leading to increased economic welfare. Outcome optimization Even when all the agents ’ preferences are already known, computing the optimal outcome (for example, the one that maximizes the sum of the agents ’ utilities) can be nontrivial. For example, in a combinatorial auction, bidders are allowed to place bids on any subset of the items for sale. While the expressiveness that this provides to the bidders increases economic welfare, the winner determination problem of deciding which bids to accept so as to maximize the total value is known to be NPcomplete (Rothkopf, Pekeč, & Harstad 1998), even to approximate (Sandholm 2002). My thesis work includes new work on the winner determination problem in combinatorial auctions (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
Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness
, 2014
"... We show that the deterministic numberonforehead communication complexity of set disjointness for k parties on a universe of size n is Ω(n/4k). This gives the first lower bound that is linear in n, nearly matching Grolmusz’s upper bound of O(log2(n) + k2n/2k). We also simplify Sherstov’s proof sh ..."
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Cited by 1 (0 self)
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We show that the deterministic numberonforehead communication complexity of set disjointness for k parties on a universe of size n is Ω(n/4k). This gives the first lower bound that is linear in n, nearly matching Grolmusz’s upper bound of O(log2(n) + k2n/2k). We also simplify Sherstov’s proof showing an Ω( n/(k2k)) lower bound for the randomized communication complexity of set disjointness. 1
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
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.