Static large games with finitely many types of players and strategies

• Autorzy: Wieczorek A.

Warianty tytułu

PL

Statyczne duże gry ze skończoną liczbą typów graczy i strategii

• Języki publikacji: EN

Abstrakty

EN

The paper briefly presents a theory of games with finitely many infinite populations (types) each of whom has finitely many available strategies; the payoff of an individual player depends on the distribution of choices of strategies in all populations and his own particular choice. We give specific examples of applications of the theory in several areas: spatial allocation (of species), economic models – household economy and transportation networks. We also briefly discuss questions of computation of equilibria and relations of large games, as understood in the present paper, to ordinary matrix games, games with continuum of players and evolutionary game theory.

PL

Praca zawiera skrótowy opis gier ze skończoną liczbą nieskończonych populacji (typów), z których każda dysponuje skończoną liczbą strategii; wypłata pojedynczego gracza zależy od rozkładu wyborów strategii wszystkich populacji i jego własnego wyboru strategii. Podajemy konkretne przykłady zastosowań w kilku dziedzinach: alokacja przestrzenna (gatunków), modele ekonomiczne – model gospodarki drobnotowarowej i model ruchu drogowego. Dyskutujemy też krótko zagadnienia obliczeniowe i związki dużych gier, jak przedstawiono je w tym artykule, ze zwykłymi grami macierzowymi, grami z continuum graczy i z ewolucyją teorią gier.

Słowa kluczowe

EN

large game; equilibrium; strategy; type of player; spatial allocation; household economy; road traffic model; directed graph; Fibonacci numbers

PL

duża gra; równowaga; strategia; typ gracza; alokacja przestrzenna; gospodarka drobno-towarowa; model ruchu drogowego; graf skierowany; liczby Fibonacciego

• Wydawca: Instytut Podstaw Informatyki PAN
• Czasopismo: Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk
• Rocznik: 2016
• Tom: Nr 1037
• Strony: 1--17
• Opis fizyczny: Bibliogr. 30 poz., rys.

Twórcy

autor

Wieczorek A.

• Instytut Podstaw Informatyki PAN, 01-248 Warszawa, Jana Kazimierza 5

Bibliografia

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• Sjur D. Fläm and Andrzej Wieczorek, Core solutions and Nash equilibria in non-cooperative games with a measure space of players, in: Game Theory and Mathematical Economics, Banach Center Publications 71. A. Wieczorek. M. Malavvski and A. Wiszniewska-Matyszkiel (eds.), 2006, 115-123
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• Karl Vind. Edgeworth-allocations in an exchange economy with many traders, International Economic Review 5. 1964, 165-177
• Jorgen W. Weibull. Evolutionaiy Game Theoiy, 1995, MIT Press.
• Andrzej Wieczorek, Agnieszka Wiszniewska (Wiszniewska-Matyszkiel), A Game-Theoretic Model of Social Adaptation in an Infinite Population. Applicationes Mathematicae 25, 1999, 417-430
• Andrzej Wieczorek. Household Economies with Infinitely Many Agents: a Game-Theoretic Analysis, International Game Theory Review 4. 2002. 319-329
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• Andrzej Wieczorek. Large Games with Only Small Players and Strategy Sets in Euclidean Spaces, Applicationes Mathematicae 32, 2005, 183-193
• Andrzej Wieczorek. Fibonacci Numbers and Equilibria in "Large” Neighborhood Games, in: Advances in Dynamic Games and Their Applications, Series: Annals of the International Society of Dynamic Games 10. eds.: P. Bernhard, V. Gaitsgory. O. Pourtallier, 2009. 445-462
• Zaifu Yang. Computing Equilibria and Fixed Points, Springer, 1999

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).