Linear transformation of products: Games and economies
An ``input-output'' model of production is formulated as a constrained optimization problem for some set of economic agents. This approach allows to bring out a cooperative game on a finite set of agents. On the other hand, the maximization of the profit for all agents may be treated as finding of the equilibrium in an exchange economy. The authors begin their investigation from a linear model of production, an agent is able to sell his initial endowment or transform it to goods in accordance with its input-output vector. This process of production gives a set of goods interdepending in quantity, such as in oil refinery. Agents may form coalitions which apply any of process of its members to united endowment. Prices in the economic system are exogenous, so a value of the characteristic function is equal to the maximal cost of goods (linear programming problem) produced by a coalition. This cooperative game has a nonempty core; besides, the authors prove that this cooperative game is balanced on every coalition, that is totally balanced. The authors prove that each totally balanced game is some extension of the game under consideration. Further, initial input-output assumptions are extended, a utility function equal to the cost of goods and resources is defined. The authors construct a model of exchange economy similar to one of Arrow-Debreu and examine it.
scientific article; zbMATH DE number 1533375