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514
Approximating GameTheoretic Optimal Strategies for Fullscale Poker
 IN INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2003
"... The computation of the first complete approximations of gametheoretic optimal strategies for fullscale poker is addressed. Several abstraction techniques are combined to represent the game of 2player Texas Hold'em, having size O(10^18), using closely related models each having size . ..."
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Cited by 127 (18 self)
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The computation of the first complete approximations of gametheoretic optimal strategies for fullscale poker is addressed. Several abstraction techniques are combined to represent the game of 2player Texas Hold'em, having size O(10^18), using closely related models each having size .
Engineering and economic applications of complementarity problems
 SIAM Review
, 1997
"... Abstract. This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions f ..."
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Cited by 126 (24 self)
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Abstract. This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions for the complementarity formulations. The goal of this documentation is threefold: (i) to summarize the essential applications of the nonlinear complementarity problem known to date, (ii) to provide a basis for the continued research on the nonlinear complementarity problem, and (iii) to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.
Advantages of a Leveled Commitment Contracting Protocol
, 1995
"... In automated negotiation systems consisting of selfinterested agents, contracts have traditionally been binding. Such contracts do not allow agents to efficiently accommodate future events. Game theory has proposed contingency contracts to solve this problem. Among computational agents, conting ..."
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Cited by 102 (29 self)
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In automated negotiation systems consisting of selfinterested agents, contracts have traditionally been binding. Such contracts do not allow agents to efficiently accommodate future events. Game theory has proposed contingency contracts to solve this problem. Among computational agents, contingency contracts are often impractical due to large numbers of interdependent and unanticipated future events to be conditioned on, and because some events are not mutually observable. This paper proposes a leveled commitment contracting protocol that allows selfinterested agents to efficiently accommodate future events by having the possibility of unilaterally decommitting from a contract based on local reasoning. A decommitment penalty is assigned to both agents in a contract: to be freed from the obligations of the contract, an agent only pays this penalty to the other party. It is shown through formal analysis of multiple contracting settings that this leveled commitment feature...
The price of routing unsplittable flow
 In Proc. 37th Symp. Theory of Computing (STOC
, 2005
"... The essence of the routing problem in real networks is that the traffic demand from a source to destination must be satisfied by choosing a single path between source and destination. The splittable version of this problem is when demand can be satisfied by many paths, namely a flow from source to d ..."
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Cited by 101 (4 self)
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The essence of the routing problem in real networks is that the traffic demand from a source to destination must be satisfied by choosing a single path between source and destination. The splittable version of this problem is when demand can be satisfied by many paths, namely a flow from source to destination. The unsplittable, or discrete version of the problem is more realistic yet is more complex from the algorithmic point of view; in some settings optimizing such unsplittable traffic flow is computationally intractable. In this paper, we assume this more realistic unsplittable model, and investigate the ”price of anarchy”, or deterioration of network performance measured in total traffic latency under the selfish user behavior. We show that for linear edge latency functions the price of anarchy is exactly 2.618 for weighted demand and exactly 2.5 for unweighted demand. These results are easily extended to (weighted or unweighted) atomic ”congestion games”, where paths are replaced by general subsets. We also show that for polynomials of degree d edge latency functions the price of anarchy is dΘ(d). Our results hold also for mixed strategies. Previous results of Roughgarden and Tardos showed that for linear edge latency functions the price of anarchy is exactly 4 3 under the assumption that each user controls only a negligible fraction of the overall traffic (this result also holds for the splittable case). Note that under the assumption of negligible traffic pure and mixed strategies are equivalent and also splittable and unsplittable models are equivalent. 1
Computing the optimal strategy to commit to
 IN PROCEEDINGS OF THE 7TH ACM CONFERENCE ON ELECTRONIC COMMERCE (ACMEC
, 2006
"... In multiagent systems, strategic settings are often analyzed under the assumption that the players choose their strategies simultaneously. However, this model is not always realistic. In many settings, one player is able to commit to a strategy before the other player makes a decision. Such models a ..."
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Cited by 89 (19 self)
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In multiagent systems, strategic settings are often analyzed under the assumption that the players choose their strategies simultaneously. However, this model is not always realistic. In many settings, one player is able to commit to a strategy before the other player makes a decision. Such models are synonymously referred to as leadership, commitment, or Stackelberg models, and optimal play in such models is often significantly different from optimal play in the model where strategies are selected simultaneously. The recent surge in interest in computing gametheoretic solutions has so far ignored leadership models (with the exception of the interest in mechanism design, where the designer is implicitly in a leadership position). In this paper, we study how to compute optimal strategies to commit to under both commitment to pure strategies and commitment to mixed strategies, in both normalform and Bayesian games. We give both positive results (efficient algorithms) and negative results (NPhardness results).
Simple Search Methods for Finding a Nash Equilibrium
 Games and Economic Behavior
, 2004
"... We present two simple search methods for computing a sample Nash equilibrium in a normalform game: one for 2player games and one for nplayer games. We test these algorithms on many classes of games, and show that they perform well against the state of the art the LemkeHowson algorithm for ..."
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Cited by 86 (3 self)
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We present two simple search methods for computing a sample Nash equilibrium in a normalform game: one for 2player games and one for nplayer games. We test these algorithms on many classes of games, and show that they perform well against the state of the art the LemkeHowson algorithm for 2player games, and Simplicial Subdivision and GovindanWilson for nplayer games.
Rational and Convergent Learning in Stochastic Games
, 2001
"... This paper investigates the problem of policy learning in multiagent environments using the stochastic game framework, which we briefly overview. We introduce two properties as desirable for a learning agent when in the presence of other learning agents, namely rationality and convergence. We e ..."
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Cited by 82 (5 self)
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This paper investigates the problem of policy learning in multiagent environments using the stochastic game framework, which we briefly overview. We introduce two properties as desirable for a learning agent when in the presence of other learning agents, namely rationality and convergence. We examine existing reinforcement learning algorithms according to these two properties and notice that they fail to simultaneously meet both criteria. We then contribute a new learning algorithm, WoLF policy hillclimbing, that is based on a simple principle: "learn quickly while losing, slowly while winning." The algorithm is proven to be rational and we present empirical results for a number of stochastic games showing the algorithm converges.
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.
Coalition formation among bounded rational agents
, 1995
"... This paper analyzes coalitions among selfinterested agents that need to solve combinatorial optimization problems to operate efficiently in the world. By colluding (coordinating their actions by solving a joint optimization problem), the agents can sometimes save costs compared to operating individ ..."
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Cited by 75 (12 self)
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This paper analyzes coalitions among selfinterested agents that need to solve combinatorial optimization problems to operate efficiently in the world. By colluding (coordinating their actions by solving a joint optimization problem), the agents can sometimes save costs compared to operating individually. A model of bounded rationality is adopted, where computation resources are costly. It is not worth solving the problems optimally: solution quality is decisiontheoretically traded off against computation cost. A normative, protocolindependent theory of coalitions among bounded rational (BR) agents is devised. The optimal coalition structure and its stability are significantly affected by the agents' algorithms' performance profiles (PPs) and the unit cost of computation. This relationship is first analyzed theoretically. A domain classification including rational and BR agents is introduced. Experimental results are presented in the distributed vehicle routing domain using real data from 5 dispatch centers; the optimal coalition structure for BR agents differs significantly from the one for rational agents. These problems are NPcomplete and the instances are so large that, with current technology, any agent's rationality is bounded by computational complexity.