Resumen de On the Balancedness of Semi-infinite Sequencing Games
In these last years several classes of TU games were extended to the semiinfinite case. Preserving a finite number of players and bounded values for the characteristic function other elements were supposed to have a countable cardinality. The aim of this paper is to study the balancedness in the semiinfinite case of the class of sequencing games, introduced by Curiel, Pederzoli, Tijs (1989), considering a countable number of jobs and a finite number of players. Curiel, Pederzoli and Tijs show that sequencing games are convex and, consequently, balanced; moreover it is possible to determine a core allocation without computing the characteristic function of the game. They propose to share equally between two players the gain produced by their switch and call this rule the Equal Gain Splitting Rule.
We redefine some elements of a sequencing situation in order to include the case in which each agent may own more jobs. We suppose that if an agent owns several jobs, he pays the cost of each one until it is completed. Given a multiple-job sequencing situation it is easy to define a multiple-job sequencing game, that results to be convex. Finally we add the condition that the set of jobs has a countable cardinality. When this happens it is possible that the cost of an order and consequently the values of the characteristic function, is unbounded. In order to avoid this situation we introduce suitable hypotheses on the total service time and on the costs of the jobs. We prove that in these hypotheses the corresponding semi-infinite sequencing game is balanced.
Finally we propose some possible future developments modifying the characteristic function for the multiple-job case and considering an infinite sequence of jobs in which only a finite number of them can be exchanged.
