Linear transformation of products: Games and economies

In this paper, we introduce situations involving the linear transformation of products (LTP). LTP situations are production situations where each prod ucer has a single linear transformation technique. First, we approach LTP s ituations from a (cooperative) game theoretical point of view. We show that the corresponding LTP games are totally balanced. By extending an LTP situ ation to one where a producer may have more than one linear transformation technique, we derive a new characterization of (nonnegative) totally balanc ed games: each totally balanced game with nonnegative values is a game corr esponding to such an extended LTP situation. The second approach to LTP sit uations is based on a more economic point of view. We relate (standard) LTP situations to economies in two ways and we prove that the economies are st andard exchange economies (with production). Relations between the equilibr ia of these economies and the cores of cooperative LTP games are investigat ed.