R Aumann. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press, 1959.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... and Rapoport, 1984; van der Linden and Verbeek, 1985; Zlotkin and Rosenschein, 1994; Charnes and Kortanek, 1966; Shapley, 1967; Wu, 1977] One way to interpret this is to consider the coalition members utilities to be the utilities they can guarantee themselves no matter what the nonmembers do [Aumann, 1959; Tohm e and Sandholm, 1999] Definition 1 Given a set of players A,autility possibility for B = b 1 , b nB #Ais a vector (u b1 , u b n B ) representing utilities that the players in B can guarantee themselves by cooperating with each other. A utility possibility set is a set of ....

R Aumann. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press, 1959.

.... characteristic function games where the utilities of the coalition members do not depend on the nonmembers actions [12, 26, 28, 4, 22, 27] One way to interpret this is to consider the coalition members utilities to be the utilities they can guarantee themselves no matter what the nonmembers do [1, 25]. Definition I Given a set of players A, a utility possibility vector u B for B = b, b, c A is a vector (Ubl, UbnB) representing utilities that the players in B can guarantee themselves by cooperating with each other. A utility possibility set is a set of utility possibility vectors ....

R Aumann. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press, 1959.

....having their own costs for the production of one barrel of oil. For obvious geographical reasons a country like Norway can not produce oil at the same costs as for example Saudi Arabia, even not in case of cooperation. Usually, oligopoly situations are modeled by means of non cooperative games. Aumann (1959) introduced two ways of converting a non cooperative game into a cooperative one. In the first approach every coalition computes the amount of money which they can guarantee themselves regardless what the players outside the coalition do. The second approach computes for every coalition the ....

.... Delta Delta c n . Corresponding to the oligopoly above the strategic oligopoly game Gamma = N; X i ) i2N ; u i ) i2N ) is defined by X i = 0; y i ] 2) for every i 2 N , and u i (x) b Gamma x(N) Delta x i Gamma c i x i (3) 5 for every i 2 N and every x = x i ) i2N 2 XN . Aumann (1959) introduced two ways of converting a non cooperative game (N; X i ) i2N ; u i ) i2N ) into a cooperative game. The first approach leads to the cooperative game (N; v ff ) which is obtained by computing for every coalition S the amount of money which the players in S can guarantee themselves ....

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Aumann, R., (1959). Acceptable points in general cooperative n-person games. In: Tucker and Luce (Eds.), Contributions to the Theory of Games IV. Annals of Mathematics Studies, vol. 40. Princeton University Press, Princeton.

....[17, 14] which guarantees stability in the sense that no agent alone is motivated to deviate from the solution given that others in the game do not deviate. Often this solution concept is too weak because subgroups of agents can deviate in a coordinated manner. The Strong Nash equilibrium [1] is a solution concept that guarantees more stability in the sense that it requires that there is no subgroup that can deviate in a manner that increases the payoff of all of its members given that nonmembers do not deviate from the original solution. The Strong Nash equilibrium is often too ....

....BR subadditivity, and the BRC are undefined, Fig. 2. Again, other solution concepts are necessary, e.g. the Nash equilibrium or some of its refinements. This is part of our current research. 6 Related DAI research on collusion Coalition formation has been widely studied in game theory [12, 2, 3, 1, 27, 18]; only the most relevant concepts were presented here. This section compares our work to other recent DAI research on coalition formation. Zlotkin and Rosenschein [30] analyze rational agents that cannot make side payments, while our agents do. Their analysis is limited to Subadditive Task ....

R. Aumann. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press, 1959.

....one could treat computational actions as part of each agent s strategy just like physical actions. However, the Nash equilibrium is often too weak because subgroups of agents can deviate in a coordinated manner. The Strong Nash equilibrium is a solution concept that guarantees more stability [3]. It requires that there is no subgroup that can deviate by changing strategies jointly in a manner that increases the payoff of all of its members given that nonmembers do not deviate from the original solution. The Strong Nash equilibrium is often too strong a solution concept because in many ....

R Aumann. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press, 1959. 54 Distributed Rational Decision Making

.... second are often called the and characteristicfunctions: A general nonemptiness result for the core, dened using the characteristic function, is obtained in Scarf [20] The core, dened by the characteristic function, is closely related to the folk theorem for repeated games (cf. Aumann [1], 4] 32 5.3. Solution concepts The characteristic function V of a game without side payments describes, for each coalition S; the set of payo vectors attainable by the members of S: Once this is given, the imputation space and dominance relations are extended to a game without side payments ....

Aumann, R. J. (1959), Acceptable points in general cooperative n-person games, Contributions to the Theory of Games Vol.4, Annals of Math. Studies 40, Princeton University Press, 287-324.

....game theoretic notion of equilibrium; That is, we are interested in protocols, in which it is irrational for an agent to deviate from its protocol, assuming the other agents stick to their protocol. More generally one may replace the concept of equilibrium with the concept of strong equilibrium [1]. In a strong equilibrium, there does not exist a group (coalition) of agents such that a joint deviation of this group can benefit each of its members. If an outcome function g is implemented by a mechanism and by an equilibrium profile b, which is also a strong equilibrium, we say that the ....

R.J. Aumann. Acceptable points in general cooperative n-person games. In A.W. Tucker and R.D. Luce, editors, Contribution to the Thoery of Games, Vol. IV (Annals of Mathematics Studies, 40), pages 287--324. 1959.

....the agent different payoffs (depending on the payoff division scheme) However, by making P high enough compared to the V (CS) values, this consideration can be made negligible compared to the risk of getting caught. 9 Related research Coalition formation has been widely studied in game theory [20, 2, 1, 3, 26, 29, 48]. However, most of that work has not taken into account the computational limitations involved. This section reviews some of the research that has been done on the computational aspects. We will discuss payoff division among agents, coalition structure generation, and optimization within each ....

R. Aumann. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press, 1959.

....that a strategy profile is a Nash equilibrium if there is no player who can increase his payo# by unilaterally deviating from it. A strategy profile is called a strong Nash equilibrium if there is no coalition of players that can strictly increase the payo#s of all its members by a joint deviation (Aumann (1959)) Consider the following example. Let (N, v) be the symmetric 3 player game with v(S) 8 : 0 if S # 1 30 if S = 2 48 if S = N . 7) The payo#s to the players for the five positions we distinguished in figure 1 are summarized in table 2. Position Payo# 1 0 2 15 1 2 c 3 ....

Aumann, R. (1959). Acceptable points in general cooperative n-person games. In: Contributions to the theory of games IV (Eds. A. Tucker and R. Luce), Princeton University Press, 287-324.

....making P high enough compared to V (CS)s, this consideration can be made negligible compared to the risk of getting caught. Related research on computational coalition formation Coalition formation has been widely studied in game theory (Kahan Rapoport 1984; Bernheim, Peleg, Whinston 1987; Aumann 1959). They address the question of how to divide V (CS ) among agents so as to achieve stability of the payoff configuration. Some also address coalition structure generation. However, most of that work has not taken into account the computational limitations involved. This section reviews some of ....

Aumann, R. 1959. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press.

....to V (CS)s, this consideration can be made negligible compared to the risk of getting caught. Related research on computational coalition formation Coalition formation has been widely studied in game theory (Kahan Rapoport 1984; Bernheim, Peleg, Whinston 1987; Bernheim Whinston 1987; Aumann 1959). They address the question of how to divide V (CS ) among agents. Some also address coalition structure generation. However, most of that work has not taken into account the computational limitations involved. This section reviews some of the work that has been done on the computational ....

Aumann, R. 1959. Acceptable points in general cooperative nperson games. volume IV of Contributions to the Theory of Games. Princeton University Press.

....Nash equilibrium [29, 24] It guarantees stability in the sense that no agent alone is motivated to deviate by changing its strategy given that others do not deviate. Often the Nash equilibrium is too weak because subgroups of agents can deviate in a coordinated manner. The Strong Nash equilibrium [1] is a solution concept for NFGs that guarantees more stability. It requires that there is no subgroup that can deviate by changing their strategies jointly in a manner that increases the payoff of all of its members given that nonmembers do not deviate from the original solution. The Strong Nash ....

.... strategic solution concepts are specific to a given interaction protocol while core based analyses are not (unless the coalition formation process itself affects the payoffs) 7 Related research on computational coalition formation Coalition formation has been widely studied in game theory [20, 2, 3, 1, 56, 32], and only the most relevant concepts were presented. Many of the solution concepts for coalition formation are static. They address the question of how to divide the payoffs among agents. Some of them also address the question of which coalition structure should form. But being static in nature, ....

R. Aumann. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press, 1959.

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R Aumann. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press, 1959.

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Aumann, R. 1959. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press.

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Aumann, R., 1959. Acceptable points in general cooperative n-person games. In: Annals of Mathematics Study 40. Vol. IV of Contributions to the Theory of Games. Princeton University Press, pp. 287--324.

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Aumann, R. 1959. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press.

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R Aumann. Acceptable points in general cooperative n-person games. volume IV of Contributions to the Theory of Games. Princeton University Press, 1959.

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Aumann, R. J. 1959 : "Acceptable Points in General Cooperative n-Person Games." In H. W. Kuhn and R. D. Luce, eds., Contributions to the Theory of Games IV. Princeton University Press.

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Aumann, R., Acceptable Points in General Cooperative n-Person Games, in Tucker,A. and Luce,D. (eds.) Contributions to the Theory of Games IV, Princeton University Press, Princeton 1959.

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Aumann, R., Acceptable Points in General Cooperative n-Person Games, in Tucker,A. and Luce,D. (eds.) Contributions to the Theory of Games IV, Princeton University Press, Princeton 1959.

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