ORIGINAL PAPER
The selling price of raw material surpluses in an n-person market game model – exemplified by copper raw materials
1
AGH University of Science and Technology in Krakow
Submission date: 2022-10-24
Final revision date: 2022-12-23
Acceptance date: 2023-01-23
Publication date: 2023-03-22
Gospodarka Surowcami Mineralnymi – Mineral Resources Management 2023;39(1):149-171
KEYWORDS
TOPICS
ABSTRACT
Mineral-resource mining is a pillar of many state economies and, in many cases, it determines the welfare of the society. The mining of mineral resources provides the market with the raw materials that are traded and drives the economic and social development of countries, although it can also be a source of tensions and crises (e.g. the “curse of wealth”, “Dutch disease”). The trade of raw materials is conducted by exchanges, bilateral deals and other forms of transactions, and is regulated by trade regulations and contract agreements, and in most cases, constitutes a source of income for exporters. In this paper, the use of game-theory modelling for creating the selling price of mineral products on the basis of Polish export quotas for refined copper raw materials is proposed. Using a characteristic function created on the basis of reported export values, possible cooperation arrangements are defined and solutions are calculated for an n-person game of hypothetical coalitions of the major (in terms of volume) recipients of refined Polish copper, i.e. Germany, Italy and France. Alternative markets and possible supplies of cheaper raw material are excluded from the analyses, while the price spread between the rates paid by the buyers is taken into consideration. Among the many possibilities, the game core, the Shapley imputation and the Gately point are arbitrarily adopted as permissible solutions to the defined system. The obtained results are used for a speculative analysis relating to the possibility of renegotiating prices between the producer and recipients of the raw material. Marginal contributions resulting from Shapley’s solution are taken into account as is the power of individual trading-participant coalitions. The paper demonstrates that the recognition and adoption of solutions based on the n-personnel game model as impartial would require the redefinition of contracts and the rates paid for the raw material.
ACKNOWLEDGEMENTS
This research and paper preparation was funded by AGH University of Science and Technology, Faculty of Geology, Geophysics and Environment Protection; subsidy number: 16.16.140.315.
METADATA IN OTHER LANGUAGES:
Polish
Cena zbytu nadwyżek surowcowych w modelu n-osobowej gry rynkowej na przykładzie surowców miedzi
obrót surowcowy, gra n -osobowa, wartość Shapleya, punkt Gatelego
Górnictwo kopalin bywa filarem gospodarek państw i decyduje niekiedy o poziomie dobrobytu społeczeństw. Produkcja górnicza, przeróbka i przetwórstwo kopalin dostarcza na rynek pożądane surowce, będące przedmiotem obrotu handlowego, warunkując rozwój gospodarczo-społeczny krajów, jakkolwiek bywa też źródłem napięć i kryzysów (np. klątwa bogactw, choroba holenderska). Obrót surowcowy, realizowany za pośrednictwem sformalizowanych rynków (giełd), wymian bilateralnych bądź innych form transakcji jest na ogół źródłem przychodów dla eksporterów i co równie ważne ujęty jest w karby regulacji handlowych i umów kontraktowych. W artykule, na bazie kwot eksportowych rafinowanych surowców miedzi z Polski, zaproponowano wykorzystanie modelowania teoriogrowego w zagadnieniu kreowania ceny sprzedaży produktów mineralnych. Za pomocą funkcji charakterystycznej, skonstruowanej na bazie raportowanych wartości eksportu, zdefiniowano możliwe układy kooperacyjne a następnie skalkulowano rozwiązania n-osobowej gry dla hipotetycznych koalicji, największych tonażowo odbiorców miedzi rafinowanej z Polski: Niemiec, Włoch i Francji. Przyjęto w analizie brak istnienia alternatywnych rynków i możliwych dostaw tańszego surowca stamtąd oraz uwzględniono rozrzut cenowy pomiędzy stawkami płaconymi przez nabywców. Spośród wielu możliwości, rdzeń gry, imputacja Shapleya oraz punkt Gatelytego zostały arbitralnie przyjęte jako dopuszczalne rozwiązania zdefiniowanego układu. Uzyskane wyniki wykorzystano do spekulatywnej analizy odnoszącej się do sposobności renegocjacji cen pomiędzy producentem a odbiorcami surowca. Uwzględniono w rozważaniach wkłady marginalne wynikające z rozwiązania Shapleya, jak również wzięto pod uwagę siłę koalicyjną poszczególnych uczestników obrotu. Wskazano, że uznanie i przyjęcie jako bezstronne rozwiązań opartych na modelu gry n-osobowej wymagałoby redefiniowania umów oraz stawek kwotowych płaconych za surowiec.
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