H. Moulin. Cooperative Microeconomics: A GameTheoretic Introduction. Princeton University Press, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....do share the cost: c # (J) Unfortunately for many games of interest, cross monotonic competitive and cost recovering cost sharing methods do not exist. It is well known that such methods provide cost allocations that lie in the core, a well studied concept in the game theory literature [28], and that the core is empty for these games. Motivated by the research effort on approximate core (e.g. 12, 7, 14] we relax the last property to # approximate cost recovery: j#J #J, j c # (J) #, that is, the users are only required to recover an 1 # fraction of the cost. Our Results. ....

....In the corresponding games users are trying to decide on the set J of users who should participate in the network, so that the participants can (approximately) share the cost. Related work. There is a large body of literature on cooperative games, mostly focused on fair cost allocation (see e.g. [28]) A cost allocation is a vector x assigning each user i U her share. It is fair, if no subset of users I is charged more than the optimum cost, i.e. x(j) c # (I) for every I U . If it also recovers or approximately recovers the cost, it is said to be in the core or approximate core. ....

H. Moulin. Cooperative Microeconomics: A Game-Theoretic Introduction. Princeton University Press. 1995

....in [12] do not provide buyers with any means to declare and match their preferences or to calculate the division of the surplus in a stable manner. This may prevent buyers from forming a large coalition. Concepts of coalition formation and its stability have been investigated in game theory [4, 5]. Some research on multi agent systems [7, 8, 10, 9] has applied the concepts from game theory to multi agent cooperation, and developed algorithms to form stable and beneficial agent coalitions. Some of those algorithms are theoretically applicable to buyer coalition formation, but they cannot be ....

....In section 4 we describe the coalition formation scheme in detail. Section 5 analyzes the stability of the coalition formation scheme. Section 6 describes the experimental results. Finally, we conclude our discussion in section 7. 2. PRIOR WORK Works in game theory and microeconomics such as [4, 5] have provided concepts of coalition and its stability. A coalition is a set of agents which cooperate to achive a common goal, and the stability requirement is that the outcome of a coalition be immune to deviations by individual agents or subsets of agents. Those concepts are important as ....

H. Moulin. Cooperative Microeconomics: A Game-Theoretic Introduction. Princeton University Press, 1995.

.... theory, for example, has been criticized that to answer the question, which mechanisms effectuate an equilibrium state, it has contributed only little and unsatisfyingly [4] Generally spoken, markets describe the exchange and production of commodities in the private property regime [20]. In other words, the purpose of the market is the realization of a dynamic, distributed resource allocation mechanism. Economics is thus essentially all about the coordination of systems consisting of utility maximizing agents, who satisfy their needs using some mechanism for solving a ....

Moulin, H. Cooperative microeconomics - a game-theoretic introduction. London: Prentice Hall, 1995.

....1, g 1 = 0, 1 and g 2 = 0, 2 , 2, 1 . Note that g 1 # g 2 = #. Supermodularity is violated since v 1 (g 1 ) v 1 (g 2 ) 2V v 1 (#) v 1 (g 1 # g 2 ) V . Note that agent 1 gets a utility of V 0 if he is connected to the source and zero otherwise. Remark 8 Moulin [9] shows that the induced TU game in a single excludable public good economy with quasi linear preferences is convex under very weak assumptions. He also shows that this is not true when there are multiple public goods even when the preferences are convex and the cost function has constant marginal ....

....good economy with quasi linear preferences is convex under very weak assumptions. He also shows that this is not true when there are multiple public goods even when the preferences are convex and the cost function has constant marginal costs. In the multiple public goods scenario, Moulin 17 [9] shows that the supermodularity of the utility functions and the submodularity of the cost function constitute su#cient condition for the convexity of the induced TU game. The conditions used in Lemma 4 are direct analogues to Moulin s conditions for the case of network formation. We end this ....

H. Moulin, Cooperative Microeconomics: A Game-Theoretic Introduction, Princeton University Press, Princeton, New Jersey, USA, 1995.

....in a fair way. This is known as the cost allocation problem. For example, towns would pay for the building of libraries, or sports complexes, but they don t want to pay more than their fair share of the total cost, whatever that means. In the area of cooperative game theory, see for example [12], fairness means that no group of customers, or coalition, has any incentive to break apart and obtain the service on their own. In other words, if v j denotes the price being paid by customer j, we would like that j2S v j 6 OPT(S) where S is any subset of customers and OPT(S) represents the cost ....

....v j = OPT(N) j2S v j 6 OPT(S) for all S Ng (1.1) and a central question in cooperative game theory is whether the core is non empty, and if so, how to find an allocation vector in the core. Traditionally, the non vacuity of the core is established by showing that the game is balanced (see [12] for definitions) In linear programming terms, this boils down to showing that any extreme point of the dual to max j2N v j subject to (1.1) has value at least OPT(N) It is well known and easy to check that, for a submodular function OPT( the core is non empty and the Shapley value (cf. 12] ....

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H. Moulin. Cooperative Microeconomics: A Game-Theoretic Introduction. Princeton University Press, 1995.

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H. Moulin. Cooperative Microeconomics: A GameTheoretic Introduction. Princeton University Press, 1995.

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