The equivalence of linear programs and zero-sum games

International Journal of Game Theory

Volumn 42, Issue 1, 2013, Pages 165-177

  Adler, Ilan ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Farkas' lemma; Linear programming; Minimax theorem; Strong duality; Villes' theorem; Zero sum games

Indexed keywords

EID: 84873715716     PISSN: 00207276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00182-012-0328-8     Document Type: Article

References (14)

1. Adler I, Beling PA (1997) Polynomial algorithms for linear programming over the algebraic numbers. Algorithmica 12(6): 436-457.
2. Carathodory C (1911) ber den variabilittsbereich der Fourierschen konstanten von positiven harmonischen Funktionen. Rend Circ Mat Palermo 32: 193-217.
3. Dantzig GB (1951) A proof of the equivalence of the programming problem and the game problem. In: Koopmans TC (ed) Activity analysis of production and allocation. Wiley, New York, pp 330-335.
4. Dantzig GB (1963) Linear programming and extensions. Princeton University Press, Princeton.
5. Farkas J (1902) Uber die theorie der einfachen ungleichungen. J Reine Angew Math 124: 1-24.
6. Gale D, Kuhn HW, Tucker AW (1951) Linear programming and the theory of games. In: Koopmans TC (ed) Activity analysis of production and allocation. Wiley, New York, pp 317-329.
7. Gordan P (1873) Uber die auflosung lincarer Glcichungcn mit reellen coefficienten. Math Ann 6: 23-28.
8. Luce RD, Raiffa H (1957) Games and decisions: introduction and critical survey. Wiley, New York.
9. Megiddo N (1990) On solving the linear programming problem approximately. Contemp Math 114: 35-50.
10. Raghavan TES (1994) Zero-sum two-person games. In: Aumann RJ, Hart S (eds) Handbook of game theory with economic applications, vol 2. Elsevier, Amsterdam, pp 735-760.
11. Tucker AW (1956) Dual systems of homogeneous linear relations. In: Kuhn HW, Tucker AW (eds) Linear inequalities and related systems. Annals of Mathematics Studies, vol 38. Princeton University Press, Princeton, pp 3-18.
12. Ville J (1938) Sur a theorie generale des jeux ou intervient Vhabilite des joueurs. Trait Calc Probab Appl IV 2: 105-113.
13. von Neumann J (1928) Zur theorie der gesellschaftsspiele. Math Ann 100: 295-320.
14. von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton.