Hidrológiai Közlöny 1976 (56. évfolyam)
10. szám - Dr. Bogárdi István–Dr. Szidarovszky Ferenc: Játékelmélet alkalmazása a vízminőség gazdálkodásban
462 Hidrológiai Közlöny 1976. 10. sz. Dr. Bogárdi I.—Dr. Szidarovszky F.: Játékelmélet alkalmazása akkor legyen G = s*, és D értékét hagyjuk változatlanul. Az intervallumfelezési eljárás elég sokszori megismétlésével az egyensúlypont koordinátáit tetszőleges pontossággal megközelíthetjük. The application of game theory in water quality management By Dr. Bogárdi, I. and Dr. Szidarovszky , F . Keeping practical applicability in mind, of the mathematical games the multi-person oligopol game is described with its potential applications in water management. In Section 2 some important domains of decision analysis in water management are reviewed in brief, where the form of the target function is suited to the use of the method developed for the oligopoly game. In Section 3 the "mathematical solution of the game is described. The solution has been developed for an arbitrary number of players and a computer programme is presented for practical computation work. In Section 4 a typical problem is considered of water quality inangement among the potential water management applications, namely pollution control on regional level, from the viewpoint of particular pollutants. The practical problem is solved by the oligopol game, the results leading to conclusions of a generalized nature. In Section 5, relying on the results the application of the oligopol game is suggested for decision analysis in water management. For practical applications the successive steps of the method are specified. The main conclusions arrived at from the residts of the study described are as follows: a ) Game theory can be applied successfully in several domains of water management for decision preparation. b ) Earlier studies of exploratory character have contributed to the development of the present method. c ) The oligopol model suggested is directly applicable to the analysis of important water management decisions. d ) The mathematical methods of the oligopol game have been developed in Hungary. e ) Computer use yields a simple and rapid solution for the oligopol game. The relevant computer programmes have been elaborated and these are available at VIKÖZ. /) The application of the oligopol game in water quality management, as described in the paper, is a novel result also on the international level. g ) The economically justified extent of treatment can be determined by the method for an arbitrary number of pollutants. /t ) The recognition and quantitative demonstration of the fact that each individual effluent producer fares best by solving his treatment problems in association with the others, is considered a result of general validity. i ) The advantages of the method warrant its further refinement by successively eliminating the simplifying assumptions. In conclusion the preferable sequence of steps in the application of the oligopol game are presented comprehensively : 1. Exact formulation of the problem (planning-, or operational model, which branch of water management, etc.). 2. identifying the number of participants in the game. 3. Observation of the loss-, or benefit function produced by all players at points, and the computation of a smooth function L(£ xi) for the points. 4. Determination of the cost function xi, or benefit function K í ( xí ) resulting from the proper production of the individual players in analogy to the preceeding point. 5. Writing the target functions for all players. 6. Solution of the game — by individual interests, — by group interests and — by combined interest. 7. The comparison of results corresponding to the different cases, sensitivity analysis, followed by suggestion concerning the preferable decision.
