Teorija igara
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Teorija igara se može definisati ili kao grana primenjene matematike koja se služi modelima za proučavanje međusobnog uticaja i dejstva formalnih impulsivnih struktura („igre”) ili kao grana ekonomske teorije koja se bavi analizom procesa odlučivanja manjeg broja aktera.[1]
Najopštije, igru može da igra i jedan igrač (poput slagalice), ali njena veza sa matematičkom teorijom nastupa kada su u igru uključena najmanje dva igrača, i kada su oni sukobljeni. Svaki od igrača bira strategiju koja će mu doneti najveću dobit, odnosno kojom će nadigrati drugog igrača.
Ono što povezuje ovu matematičku teoriju sa drugim oblastima, posebno politikom, jeste priroda čoveka da najradije projektuje i planira svoju dobit kroz gubitak drugog igrača (da kažemo preciznije: mnogi slučajevi u stvarnosti mogu da se svedu na nekooperativne igre).
Teoretičari igara definišu same igre, proučavaju i predviđaju ponašanje igrača, učesnika u igri, kao i adekvatne strategije. Naočigled različiti pristupi igri mogu proizvesti slične događaje i rezultate u okviru jedne igre.[2]
Istorija teorije igara[uredi | uredi izvor]
Džon fon Nojman i Oskar Morgenštern prvi su se bavili ovim predmetom u svojoj knjizi „Teorija igara i ekonomsko ponašanje“ iz 1944. godine.[3] Sledeći fundamentalan doprinos dao je Džon Neš definišući optimalne strategije za igre sa više igrača i pojam ravnoteže. Njena najtesnija veza sa ekonomijom je na polju istraživanja i pronalaženja racionalnih strategija u situacijama kada rezultat zavisi ne samo od sopstvene strategije i „uslova na tržištu“, već i od strategije koju su odabrali i drugi učesnici sa istim ciljevima.
Teorija se najviše razvila primenom u vojnoj strategiji. Konkretno, Nojman i Neš, su prvu primenu teorije radili za američku vojsku.
Primene teorije igara[uredi | uredi izvor]
Teorija je primenljiva u mnogim oblastima, poput ekonomije, međunarodnih odnosa, evolucionoj biologiji, političkim naukama i vojnoj strategiji. Teorija ima primenu i u operacionim istraživanjima, kolektivnom ponašanju, psihologiji.
Igre mogu biti:
- kooperativne, kada akteri sarađuju u zajedničkom interesu, i nekooperativne, oponentske, kada akteri pokušavaju da nadigraju jedni druge i zanemaruju ukupnu dobit igre;
- na igre sa fiksnom sumom, koja se deli među igračima, i sa promenljivom sumom, čija visina zavisi od odabranih strategija,
- na statičke igre, kada se sve odluke donose istovremeno, i na dinamičke, ili sekvencijalne, kada se odluke donose tokom vremena,
- na igre sa potpunim i nepotpunim informacijama itd.
Teorija igara ima sve veći uticaj i sve važniju ulogu u logici i kompjuterskim naukama. Nekoliko logičkih teorija zasnovane su na semantici igara. U kompjuterskim naukama koriste se igre kao interaktivni modeli iznalaženja rešenja. (Computability logic attempts to develop a comprehensive formal theory (logic) of interactive computational tasks and resources, formalising these entities as games between a computing agent and its environment.)*
Ova teorija može se primeniti kako na najpopularnije društvene i zabavne igre tako i na značajne oblike društvene interakcije. Zatvorenikova dilema (The prisoner's dilemma), koju je popularisao matematičar Albert Taker, predstavlja primer primene teorije u stvarnom životu; obuhvatajući prirodu ljudske saradnje, čak je postala osnova i za TV igru "Friend or Foe?".
Biolozi koriste teoriju igara u procesu razumevanja i predviđanja određenih ishoda evolucije, poput koncepta o evoluciono stabilnoj strategiji koji su postavili Džon Mejnerd Smit i Džordž Prajs u časopisu Nejčer.
Analitičari igara često koriste druge grane matematike, posebno verovatnoću, statistiku i linearno programiranje, u sadejstvu sa teorijom igara.
Za svoj rad na teoriji igara nobelove nagrade za ekonomiju dobili su:
- Džon Neš, Rajnhard Zelten i Džon Haršanji u 1994. godini i
- Robert Auman i Tomas Šeling u 2005. godini.
Vidi još[uredi | uredi izvor]
Reference[uredi | uredi izvor]
- ^ Myerson, Roger B. (1991). Game Theory: Analysis of Conflict, Harvard University Press, p. 1. Chapter-preview links, pp. vii–xi.
- ^ Neumann, J. v. (1928), „Zur Theorie der Gesellschaftsspiele”, Mathematische Annalen, 100 (1): 295—320, doi:10.1007/BF01448847 English translation: Tucker, A. W.; Luce, R. D., ur. (1959), „On the Theory of Games of Strategy”, Contributions to the Theory of Games, 4, str. 13—42
- ^ Mirowski, Philip (1992). „What Were von Neumann and Morgenstern Trying to Accomplish?”. Ur.: Weintraub, E. Roy. Toward a History of Game Theory. Durham: Duke University Press. str. 113—147. ISBN 978-0-8223-1253-6.
Literatura[uredi | uredi izvor]
- Stojanović, Božo Teorija igara: elementi i primena (Službeni glasnik i Institut za evropske studije, 2005)
Udžbenici i opšte reference[uredi | uredi izvor]
- Aumann, Robert J (1987), „game theory”, The New Palgrave: A Dictionary of Economics, 2, str. 460—82.
- Camerer, Colin (2003), „Introduction”, Behavioral Game Theory: Experiments in Strategic Interaction, Russell Sage Foundation, str. 1—25, ISBN 978-0-691-09039-9, Arhivirano iz originala 14. 05. 2011. g., Pristupljeno 13. 07. 2019, Description.
- Dutta, Prajit K. (1999), Strategies and games: theory and practice, MIT Press, ISBN 978-0-262-04169-0. Suitable for undergraduate and business students.
- Fernandez, L F.; Bierman, H S. (1998), Game theory with economic applications, Addison-Wesley, ISBN 978-0-201-84758-1. Suitable for upper-level undergraduates.
- Gibbons, Robert D. (1992), Game theory for applied economists, Princeton University Press, ISBN 978-0-691-00395-5. Suitable for advanced undergraduates.
- Published in Europe as Gibbons, Robert (2001), A Primer in Game Theory, London: Harvester Wheatsheaf, ISBN 978-0-7450-1159-2.
- Gintis, Herbert (2000), Game theory evolving: a problem-centered introduction to modeling strategic behavior, Princeton University Press, ISBN 978-0-691-00943-8
- Green, Jerry R.; Mas-Colell, Andreu; Whinston, Michael D. (1995), Microeconomic theory, Oxford University Press, ISBN 978-0-19-507340-9. Presents game theory in formal way suitable for graduate level.
- Joseph E. Harrington (2008) Games, strategies, and decision making, Worth, . ISBN 0-7167-6630-2. Tekst „pages” ignorisan (pomoć); Nedostaje ili je prazan parametar
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(pomoć). Textbook suitable for undergraduates in applied fields; numerous examples, fewer formalisms in concept presentation. - Howard, Nigel (1971), Paradoxes of Rationality: Games, Metagames, and Political Behavior, Cambridge, MA: The MIT Press, ISBN 978-0-262-58237-7
- Isaacs, Rufus (1999), Differential Games: A Mathematical Theory With Applications to Warfare and Pursuit, Control and Optimization, New York: Dover Publications, ISBN 978-0-486-40682-4
- Miller, James H. (2003), Game theory at work: how to use game theory to outthink and outmaneuver your competition, New York: McGraw-Hill, ISBN 978-0-07-140020-6. Suitable for a general audience.
- Osborne, Martin J. (2004), An introduction to game theory, Oxford University Press, ISBN 978-0-19-512895-6. Undergraduate textbook.
- Osborne, Martin J.; Rubinstein, Ariel (1994), A course in game theory, MIT Press, ISBN 978-0-262-65040-3. A modern introduction at the graduate level.
- Shoham, Yoav; Leyton-Brown, Kevin (2009), Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, New York: Cambridge University Press, ISBN 978-0-521-89943-7, Pristupljeno 8. 3. 2016
- Webb, James N. (2007), Game theory: decisions, interaction and evolution, Undergraduate mathematics, Springer, ISBN 978-1-84628-423-6 Consistent treatment of game types usually claimed by different applied fields, e.g. Markov decision processes.
Istorijski važni tekstovi[uredi | uredi izvor]
- Aumann, R.J. and Shapley, L.S. (1974), Values of Non-Atomic Games, Princeton University Press
- Cournot, A. Augustin (1838), „Recherches sur les principles mathematiques de la théorie des richesses”, Libraire des Sciences Politiques et Sociales
- Edgeworth, Francis Y. (1881), Mathematical Psychics, London: Kegan Paul
- Farquharson, Robin (1969), Theory of Voting, Blackwell (Yale U.P. in the U.S.), ISBN 978-0-631-12460-3
- Luce, R. Duncan; Raiffa, Howard (1957), Games and decisions: introduction and critical survey, New York: Wiley
- reprinted edition: R. Duncan Luce ; Howard Raiffa (1989), Games and decisions: introduction and critical survey, New York: Dover Publications, ISBN 978-0-486-65943-5
- Maynard Smith, John (1982), Evolution and the theory of games, Cambridge University Press, ISBN 978-0-521-28884-2
- Maynard Smith, John; Price, George R. (1973), „The logic of animal conflict”, Nature, 246 (5427): 15—18, Bibcode:1973Natur.246...15S, doi:10.1038/246015a0
- Nash, John (1950), „Equilibrium points in n-person games”, Proceedings of the National Academy of Sciences of the United States of America, 36 (1): 48—49, Bibcode:1950PNAS...36...48N, PMC 1063129
, PMID 16588946, doi:10.1073/pnas.36.1.48
- Shapley, L.S. (1953), A Value for n-person Games, In: Contributions to the Theory of Games volume II, H. W. Kuhn and A. W. Tucker (eds.)
- Shapley, L.S. (1953), Stochastic Games, Proceedings of National Academy of Science Vol. 39, pp. 1095–1100.
- von Neumann, John (1928), „Zur Theorie der Gesellschaftsspiele”, Mathematische Annalen, 100 (1): 295—320, doi:10.1007/bf01448847 English translation: "On the Theory of Games of Strategy," in A. W. Tucker and R. D. Luce, ed. (1959), Contributions to the Theory of Games, v. 4, p. 42. Princeton University Press.
- von Neumann, John; Morgenstern, Oskar (1944), Theory of games and economic behavior, Princeton University Press
- Zermelo, Ernst (1913), „Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels”, Proceedings of the Fifth International Congress of Mathematicians, 2: 501—4
Ostale reference[uredi | uredi izvor]
- Ben David, S.; Borodin, Allan; Karp, Richard; Tardos, G.; Wigderson, A. (1994), „On the Power of Randomization in On-line Algorithms” (PDF), Algorithmica, 11 (1): 2—14, doi:10.1007/BF01294260
- Downs, Anthony (1957), An Economic theory of Democracy, New York: Harper
- Gauthier, David (1986), Morals by agreement, Oxford University Press, ISBN 978-0-19-824992-4
- Allan Gibbard, "Manipulation of voting schemes: a general result", Econometrica, Vol. 41, No. 4 (1973), pp. 587–601.
- Grim, Patrick; Kokalis, Trina; Alai-Tafti, Ali; Kilb, Nicholas; St Denis, Paul (2004), „Making meaning happen”, Journal of Experimental & Theoretical Artificial Intelligence, 16 (4): 209—243, doi:10.1080/09528130412331294715
- Harper, David; Maynard Smith, John (2003), Animal signals, Oxford University Press, ISBN 978-0-19-852685-8
- Lewis, David (1969), Convention: A Philosophical Study, ISBN 978-0-631-23257-5 (2002 edition)
- McDonald, John (1950—1996), Strategy in Poker, Business & War, W. W. Norton, ISBN 978-0-393-31457-1. A layman's introduction.
- Papayoanou, Paul (2010), Game Theory for Business: A Primer in Strategic Gaming, Probabilistic, ISBN 978-0964793873.
- Quine, W.v.O (1967), „Truth by Convention”, Philosophica Essays for A.N. Whitehead, Russel and Russel Publishers, ISBN 978-0-8462-0970-6
- Quine, W.v.O (1960), „Carnap and Logical Truth”, Synthese, 12 (4): 350—374, doi:10.1007/BF00485423
- Mark A. Satterthwaite, "Strategy-proofness and Arrow's Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions", Journal of Economic Theory 10 (April 1975), 187–217.
- Siegfried, Tom (2006), A Beautiful Math, Joseph Henry Press, ISBN 978-0-309-10192-9
- Skyrms, Brian (1990), The Dynamics of Rational Deliberation, Harvard University Press, ISBN 978-0-674-21885-7
- Skyrms, Brian (1996), Evolution of the social contract, Cambridge University Press, ISBN 978-0-521-55583-8
- Skyrms, Brian (2004), The stag hunt and the evolution of social structure, Cambridge University Press, ISBN 978-0-521-53392-8
- Sober, Elliott; Wilson, David Sloan (1998), Unto others: the evolution and psychology of unselfish behavior, Harvard University Press, ISBN 978-0-674-93047-6
- Thrall, Robert M.; Lucas, William F. (1963), „-person games in partition function form”, Naval Research Logistics Quarterly, 10 (4): 281—298, doi:10.1002/nav.3800100126
- Dolev, Shlomi; Panagopoulou, Panagiota; Rabie, Mikael; Schiller, Elad Michael; Spirakis, Paul (2011), „Rationality authority for provable rational behavior”, Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing, str. 289—290, ISBN 9781450307192, doi:10.1145/1993806.1993858
- Chastain, E. (2014), „Algorithms, games, and evolution”, Proceedings of the National Academy of Sciences, 111 (29): 10620—10623, Bibcode:2014PNAS..11110620C, PMC 4115542
, PMID 24979793, doi:10.1073/pnas.1406556111
Spoljašnje veze[uredi | uredi izvor]
- James Miller (2015): Introductory Game Theory Videos.
- Hazewinkel Michiel, ur. (2001). „Games, theory of”. Encyclopaedia of Mathematics. Springer. ISBN 978-1556080104.
- Paul Walker: History of Game Theory Page.
- David Levine: Game Theory. Papers, Lecture Notes and much more stuff.
- Alvin Roth:„Game Theory and Experimental Economics page”. Arhivirano iz originala 15. 8. 2000. g. Pristupljeno 13. 9. 2003. — Comprehensive list of links to game theory information on the Web
- Adam Kalai: Game Theory and Computer Science — Lecture notes on Game Theory and Computer Science
- Mike Shor: GameTheory.net — Lecture notes, interactive illustrations and other information.
- Jim Ratliff's Graduate Course in Game Theory (lecture notes).
- Don Ross: Review Of Game Theory in the Stanford Encyclopedia of Philosophy.
- Bruno Verbeek and Christopher Morris: Game Theory and Ethics
- Elmer G. Wiens: Game Theory — Introduction, worked examples, play online two-person zero-sum games.
- Marek M. Kaminski: Game Theory and Politics Arhivirano na sajtu Wayback Machine (20. oktobar 2006) — Syllabuses and lecture notes for game theory and political science.
- Websites on game theory and social interactions
- Kesten Green's Conflict Forecasting na sajtu Wayback Machine (arhivirano 2011-04-11) — See Papers for evidence on the accuracy of forecasts from game theory and other methods Arhivirano na sajtu Wayback Machine (15. septembar 2019).
- McKelvey, Richard D., McLennan, Andrew M., and Turocy, Theodore L. (2007) Gambit: Software Tools for Game Theory.
- Benjamin Polak: Open Course on Game Theory at Yale Arhivirano na sajtu Wayback Machine (3. avgust 2010) videos of the course
- Benjamin Moritz, Bernhard Könsgen, Danny Bures, Ronni Wiersch, (2007) Spieltheorie-Software.de: An application for Game Theory implemented in JAVA.
- Antonin Kucera: Stochastic Two-Player Games.
- Yu-Chi Ho: What is Mathematical Game Theory; What is Mathematical Game Theory (#2); What is Mathematical Game Theory (#3); What is Mathematical Game Theory (#4)-Many person game theory; What is Mathematical Game Theory ?( #5) – Finale, summing up, and my own view