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132
Evolutionary Game Theory
, 1995
"... Abstract. Experimentalists frequently claim that human subjects in the laboratory violate gametheoretic predictions. It is here argued that this claim is usually premature. The paper elaborates on this theme by way of raising some conceptual and methodological issues in connection with the very def ..."
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Cited by 642 (9 self)
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Abstract. Experimentalists frequently claim that human subjects in the laboratory violate gametheoretic predictions. It is here argued that this claim is usually premature. The paper elaborates on this theme by way of raising some conceptual and methodological issues in connection with the very definition of a game and of players ’ preferences, in particular with respect to potential context dependence, interpersonal preference dependence, backward induction and incomplete information.
Rational Learning Leads to Nash Equilibrium
 Econometrica
, 1993
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 215 (13 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Dynamic Programming for Partially Observable Stochastic Games
 IN PROCEEDINGS OF THE NINETEENTH NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2004
"... We develop an exact dynamic programming algorithm for partially observable stochastic games (POSGs). The algorithm is a synthesis of dynamic programming for partially observable Markov decision processes (POMDPs) and iterated elimination of dominated strategies in normal form games. ..."
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Cited by 119 (23 self)
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We develop an exact dynamic programming algorithm for partially observable stochastic games (POSGs). The algorithm is a synthesis of dynamic programming for partially observable Markov decision processes (POMDPs) and iterated elimination of dominated strategies in normal form games.
Representations and Solutions for GameTheoretic Problems
 Artificial Intelligence
, 1997
"... A system with multiple interacting agents (whether artificial or human) is often best analyzed using gametheoretic tools. Unfortunately, while the formal foundations are wellestablished, standard computational techniques for gametheoretic reasoning are inadequate for dealing with realistic games. ..."
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Cited by 114 (0 self)
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A system with multiple interacting agents (whether artificial or human) is often best analyzed using gametheoretic tools. Unfortunately, while the formal foundations are wellestablished, standard computational techniques for gametheoretic reasoning are inadequate for dealing with realistic games. This paper describes the Gala system, an implemented system that allows the specification and efficient solution of large imperfect information games. The system contains the first implementation of a recent algorithm, due to Koller, Megiddo, and von Stengel. Experimental results from the system demonstrate that the algorithm is exponentially faster than the standard algorithm in practice, not just in theory. It therefore allows the solution of games that are orders of magnitude larger than were previously possible. The system also provides a new declarative language for compactly and naturally representing games by their rules. As a whole, the Gala system provides the capability for automa...
Constrained Markov Decision Processes
, 1995
"... This report presents a unified approach for the study of constrained Markov decision processes with a countable state space and unbounded costs. We consider a single controller having several objectives; it is desirable to design a controller that minimize one of cost objective, subject to inequalit ..."
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Cited by 104 (10 self)
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This report presents a unified approach for the study of constrained Markov decision processes with a countable state space and unbounded costs. We consider a single controller having several objectives; it is desirable to design a controller that minimize one of cost objective, subject to inequality constraints on other cost objectives. The objectives that we study are both the expected average cost, as well as the expected total cost (of which the discounted cost is a special case). We provide two frameworks: the case were costs are bounded below, as well as the contracting framework. We characterize the set of achievable expected occupation measures as well as performance vectors. This allows us to reduce the original control dynamic problem into an infinite Linear Programming. We present a Lagrangian approach that enables us to obtain sensitivity analysis. In particular, we obtain asymptotical results for the constrained control problem: convergence of both the value and the pol...
Fast Algorithms for Finding Randomized Strategies in Game Trees
, 1994
"... Interactions among agents can be conveniently described by game trees. In order to analyze a game, it is important to derive optimal (or equilibrium) strategies for the different players. The standard approach to finding such strategies in games with imperfect information is, in general, computation ..."
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Cited by 90 (12 self)
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Interactions among agents can be conveniently described by game trees. In order to analyze a game, it is important to derive optimal (or equilibrium) strategies for the different players. The standard approach to finding such strategies in games with imperfect information is, in general, computationally intractable. The approach is to generate the normal form of the game (the matrix containing the payoff for each strategy combination), and then solve a linear program (LP) or a linear complementarity problem (LCP). The size of the normal form, however, is typically exponential in the size of the game tree, thus making this method impractical in all but the simplest cases. This paper describes a new representation of strategies which results in a practical linear formulation of the problem of twoplayer games with perfect recall (i.e., games where players never forget anything, which is a standard assumption). Standard LP or LCP solvers can then be applied to find optimal randomized strategies. The resulting algorithms are, in general, exponentially better than the standard ones, both in terms of time and in terms of space.
Competitive Analysis of Randomized Paging Algorithms
, 2000
"... The paging problem is defined as follows: we are given a twolevel memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded but slow memory. At each given time step, a request to an item is issued. Given a request to an item p ..."
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Cited by 62 (9 self)
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The paging problem is defined as follows: we are given a twolevel memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded but slow memory. At each given time step, a request to an item is issued. Given a request to an item p,amiss occurs if p is not present in the fast memory. In response to a miss, we need to choose an item q in the cache and replace it by p. The choice of q needs to be made online, without the knowledge of future requests. The objective is to design a replacement strategy with a small number of misses. In this paper we use competitive analysis to study the performance of randomized online paging algorithms. Our goal is to show how the concept of work functions, used previously mostly for the analysis of deterministic algorithms, can also be applied, in a systematic fashion, to the randomized case. We present two results: we first show that the competitive ratio of the marking algorithm is ex...
A continuation method for Nash equilibria in structured games
 In Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI
, 2003
"... We describe algorithms for computing Nash equilibria in structured game representations, including both graphical games and multiagent influence diagrams (MAIDs). The algorithms are derived from a continuation method for normalform and extensiveform games due to Govindan and Wilson; they follow a ..."
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Cited by 45 (0 self)
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We describe algorithms for computing Nash equilibria in structured game representations, including both graphical games and multiagent influence diagrams (MAIDs). The algorithms are derived from a continuation method for normalform and extensiveform games due to Govindan and Wilson; they follow a trajectory through the space of perturbed games and their equilibria. Our algorithms exploit game structure through fast computation of the Jacobian of the game's payoff function. They are guaranteed to find at least one equilibrium of the game and may find more. Our approach provides the first exact algorithm for computing an exact equilibrium in graphical games with arbitrary topology, and the first algorithm to exploit finegrain structural properties of MAIDs. We present experimental results for our algorithms. The running time for our graphical game algorithm is similar to, and often better than, the running time of previous approximate algorithms. Our algorithm for MAIDs can effectively solve games that arc much larger than those that could be solved using previous methods. 1
Optimal and approximate Qvalue functions for decentralized POMDPs
 J. Artificial Intelligence Research
"... Decisiontheoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In singleagent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Qvalue functions: an optimal Qvalue functi ..."
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Cited by 39 (16 self)
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Decisiontheoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In singleagent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Qvalue functions: an optimal Qvalue function Q ∗ is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q ∗. In this paper we study whether similar Qvalue functions can be defined for decentralized POMDP models (DecPOMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Qvalue function for DecPOMDPs: one that gives a normative description as the Qvalue function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Qvalue functions that allow for efficient computation. We describe how they relate, and we prove that they all provide an upper bound to the optimal Qvalue function Q ∗. Finally, unifying some previous approaches for solving DecPOMDPs, we describe a family of algorithms for extracting policies from such Qvalue functions, and perform an experimental evaluation on existing test problems, including a new firefighting benchmark problem. 1.