Linear transformation of products: Games and economies
type: Item
instance of: scholarly article
title: Linear transformation of products: Games and economies
zbMATH Open document ID: 0962.91005
DOI: 10.1023/A:1004601509292
published in: Journal of Optimization Theory and Applications
publication date: 2001-02-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 91B54
zbMATH DE Number: 1533375
zbMATH Keywords: cooperative game
zbMATH Keywords: input-output linear model
zbMATH Keywords: Arrow-Debreu model
author: Judith Timmer
author: Peter Borm
author: Jeroen Suijs
MaRDI profile type: Publication
cites work: On the core of linear production games
cites work: Totally Balanced Games and Games of Flow
cites work: Characterization of the Owen set of linear production processes
cites work: GAMES ARISING FROM INFINITE PRODUCTION SITUATIONS
cites work: On balanced games and games with committee control
cites work: Q5588318
full work available at URL: a:1004601509292
OpenAlex ID: W1556762140
description: scientific article; zbMATH DE number 1533375