ON THE REPLICA OF LINEAR PRODUCTION GAMES WITH NON ADDITIVE RESOURCES

Abstract. The replica of the Owen-Granot market linear production game is studied. A suitable way oí replicating is devised. The standard convergen ce oí the replica's eore to a competitive solution is obtained. The approaeh presented here could be of wide eeonomie applieability, sinee it depellds on a proper vector in the eore of resouree games. 1. INTRODUC TION. The linear production game introduced by Owen [3] is atype of market game, whieh is generated by linear prograrnming optimization problems. In this game it ls important the relation between the eore and the competitive seto The competit ive set is always contained in the core of an LP-game, but both sets are not identical. However, if the set of players is l'eplieated many times, the eore of replicated games converges to the competitive set, i.e., the vectors belonging to the core of all replicas of linear production games are the eompetitive vectors. This result can be considered a consequenee of a well-known theorem of Debreu and Scarf [ 1] whieh states this convergenee in the area of economies. Owen has also proved a special result for linear production games: the convergence after a finite number of replieations when th