2015- Working Papers: Operations Research and Decisions

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Regular cooperative balanced games with applications to line-balancing, 25 pp.
S. Anily and M. Haviv
(Working Paper No. 1/2015)
Research no.: 01230100 & 01240100

The conventional definition of a cooperative game G(N; V ) with a set of players N = {1,…, n} and a characteristic function V; is quite rigid to alterations of the set of players N. Moreover, it may necessitate a large input of size that is exponential in n. However, the characteristic function of many games allows a simple, efficient and flexible presentation of the game. Here we deal with a set of games that we call regular games, which have a simple presentation: In regular games each player is characterized by a vector of quantitative properties, and the characteristic function value of a coalition depends only on the vectors of properties of its members. We show that some regular games in which players can cooperate with respect to some of their resources and whose immediate formulation does not fit the framework of market games, can nevertheless be transformed into the form of market games and hence they are totally balanced. In particular, they lead to a core allocation based on a competitive equilibrium prices of the transformed game.

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A new sufficient condition on the total balancedness of regular centralizing aggregation games, 17 pp.
S. Anily
(Working Paper No. 4/2015)
Research no.: 01220100

We propose a new sufficient condition for total balancedness of regular cooperative games. In a regular game each player is characterized by a "vector of properties" that specifies the initial quantities of a number of resources owned by the player. The characteristic function value of a coalition depends only on the vectors of properties of its members through an algebraic expression. Within this class we focus on aggregation games, where the formation of a coalition is equivalent to aggregating its players into a single "new" player having a cost that is a kind of an average of the costs of the aggregated players. We prove that under some conditions such games are totally balanced and their nonnegative part of the core is fully identifiable. Applications in queueing and scheduling are presented.

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