D. Monderer and L. S. Shapley. Potential games. Games and Economic Behavior, 14: 124--143, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of Proposition 2.5.1 to show the existence of a Nash equilibrium (in pure strategies) provided all r i s are equal, and exhibited a game violating this hypothesis with no Nash equilibrium. More recently, Rosenthal s work has been extended in several di#erent directions. Monderer and Shapley [127] introduced a class of atomic games they call potential games, which by definition are games for which a Nash equilibrium in pure strategies arises as the optimum solution to a related optimization problem (the objective function of which they call a potential function) Potential games strictly ....

D. Monderer and L. S. Shapley. Potential games. Games and Economic Behavior, 14:124--143, 1996.

....at a Nash Equilibrium if no user can gain by unilaterally deviating from its own policy. In this paper we focus on the load balancing problem. An interesting class of non cooperative games, which is related to load balancing, is congestion games [25] and its equivalent model exact potential games [22]. Traditionally in Computer Science research has been focused on nding a global optimum. With the emerging interest in computational issues in game theory, the coordination ratio [18] has received considerable attention [2, 8, 9, 2 Eyal Even Dar et al. 12, 18, 26] The coordination ratio is the ....

D. Monderer and L. S. Shapley, \Potential games," Games and Economic Behavior, 14, pp. 124-143, 1996.

.... games [21, 25] potential games [17] and summarization games [14] In addition, several recent papers have proposed new game theoretic ideas to better model distributed and asynchronous networks in which players have little information about their strategic environment, such as the Internet [10, 18, 27]. For further discussion and references on these topics, see [24] We make no attempt at a detailed survey of previous work on the optimal pricing of resources, and instead refer the reader to [6, 13] for recent collections of surveys on pricing by the transportation Problem Studied Linear ....

D. Monderer and M. Tennenholtz. Distributed games. Games and Economic Behavior, 28:55--72, 1999.

....Work The model of selfish routing studied in this paper was first defined in the 1950 s by Wardrop [28] and has been extensively studied ever since. It has been generalized in multiple directions that we do not explore here, such as in the literature on congestion games [21, 25] potential games [17], and summarization games [14] In addition, several recent papers have proposed new game theoretic ideas to better model distributed and asynchronous networks in which players have little information about their strategic environment, such as the Internet [10, 18, 27] For further discussion and ....

D. Monderer and L. S. Shapley. Potential games. Games and Economic Behavior, 14:124--143, 1996.

.... games [22, 26] potential games [18] and summarization games [14] In addition, several recent papers have proposed new game theoretic ideas to better model distributed and asynchronous networks in which players have little information about their strategic environment, such as the Internet [10, 19, 28]. For further discussion and references on these topics, see [25] We make no attempt at a detailed survey of previous work on the optimal pricing of resources, and instead refer the reader to [6, 13] for recent collections of surveys on pricing by the transportation science literature, and to ....

D. Monderer and M. Tennenholtz. Distributed games. Games and Economic Behavior, 28:55--72, 1999.

....Work The model of selfish routing studied in this paper was first defined in the 1950 s by Wardrop [29] and has been extensively studied ever since. It has been generalized in multiple directions that we do not explore here, such as in the literature on congestion games [22, 26] potential games [18], and summarization games [14] In addition, several recent papers have proposed new game theoretic ideas to better model distributed and asynchronous networks in which players have little information about their strategic environment, such as the Internet [10, 19, 28] For further discussion and ....

D. Monderer and L. S. Shapley. Potential games. Games and Economic Behavior, 14:124--143, 1996.

....intuitive than mixed strategy equilibria for many players; they can be easier for agents to coordinate to; as there are a finite number of pure strategy profiles in a given game, they can be easier to compute than mixed strategy equilibria. Rosenthal s work was extended by Monderer and Shapley [10] , who showed that the class of congestion games is equivalent to the class of games with potential functions. Potential functions map agents joint actions to a real number, with the property that if X and Y are strategy profiles differing only in the action choice of one agent i, P (X) P (Y ) ....

....Figure 2: Arbitrary k n = 3, 50 agents 4 Empirical Findings Section 3 shows that there are many cases in which localeffect games have pure strategy Nash equilibria. Myopic best response has been shown to be an effective technique for computing pure strategy equilibria in a variety of settings [10] . In this section we show that this simple algorithm can compute pure strategy equilibria for very large local effect games that are not covered by any of the positive results in section 3 and that do not have potential functions. We present five different graph structures with similar ....

D. Monderer and L.S. Shapley. Potential games. Games and Economic Behavior, 14:124--143, 1996.

....knowledge [12] 16] A most natural question then becomes: will the concerned parties learn Nash equilibrium over time This question also motivates the present note. Our focus is on a special class consisting of so called potential games, recently introduced and studied by Monderer and Shapley [13]. That class is admittedly narrow, but more important for economics and more frequent in practice than might first be believed [20] So, part of our motivation is to show that manifold modes of play associated with known methods of optimization will all lead to equilibrium in games of this ....

....point in this set must be a Nash equilibrium. 2 One might be tempted to think that potential games enjoy distinguished welfare properties. This is, however, far from so. Indeed, the prisoners dilemma and some Cournot oligopolies are potential games that yield ine#cient equilibrium outcomes [13]. In those and many other cases, including congestion games [20] the hidden potential should not be seen as a welfare indicator. Rather, in terms of optimization theory, it constitutes a most natural merit function, monitoring the drift towards Nash equilibrium. This will be abundantly ....

D. Monderer and L. S. Shapley, Potential games, Games and Economic Behavior 14, 124-143 (1996).

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D. Monderer and L.S. Shapley. Potential games. Games and Economic Behavior, 14:124--143, 1996.

....if and only if it is dominated by another behavior of it. In section 2 we describe bidding games, a family of games that will serve us for the illustration of the basic concepts developed in this paper. Bidding games are representatives of k price auctions, a central class of economic mechanisms [ Monderer and Tennenholtz, 2000 ] In section 3 we present a competitive analysis of bidding games. In section 4 we introduce rational competitive analysis, a new tool for normative decision making, that generalizes competitive analysis to the context of rational environments, and apply it to bidding games. In section 5 we ....

....i (s) A strategy s 2 S i is a competitive strategy for agent i if s 2 argmin t2S i max q2S Gammai Reg i (t; q) where S Gammai denotes the possible strategy profiles of players in N n fig. Third price auctions have been shown to have appealing properties in the context of Internet Auctions [Monderer and Tennenholtz, 2000]. Given the above definition we are interested in applying competitive analysis to bidding games. We now present three claims about competitive analysis of bidding games. These claims are associated with the competitive analysis of 1st,2nd, and 3rd price auctions, respectively. Claim 3.1 Given ....

D. Monderer and M. Tennenholtz. K-price auctions. Games and Economic Behavior, 31:220--244, 2000.

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D. Monderer and L. S. Shapley. Potential games. Games and Economic Behavior, 14: 124--143, 1996.

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Monderer, D., Shapley, L.: Potential Games. Games and Economic Behavior, 14:124--143, 1996.

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Monderer D,Shapley LS. Potential games. Games and Economic Behavior 1996;14:124--43.

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Monderer D. and Shapley L. Potential games. Games and Economic Behavior, 14:124--143, 1996.

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D. Monderer and M. Tennenholtz. Distributed games. Games and Economic Behavior, 28:55--72, 1999.

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D. Monderer and L. S. Shapley. Potential games. Games and Economic Behavior, 14:124--143, 1996.

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D. Monderer, L. Shapley. Potential Games. Games and Economic Behavior 14(1996), 124--143.

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D. Monderer and L. S. Shapley. Potential games. Games and Economic Behavior, 14:124-143, 1996.

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Monderer D. and Shapley L. Potential games. Games and Economic Behavior, 14:124--143, 1996.

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D. Monderer and L. S. Shapley. Potential games. Games and Economic Behavior,

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D. Monderer and L. S. Sharpley. Potential games. Games and Economic Behavior, 14:124--143, 1996.

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