Electronic Resource
Springer
Journal of optimization theory and applications
50 (1986), S. 289-312
ISSN:
1573-2878
Keywords:
Semi-infinite games
;
inequality theory
;
Farkas-Minkowski systems
;
value of a game
;
optimal strategies
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper introduces a generalization of semi-infinite games. The pure strategies for player I involve choosing one function from an infinite family of convex functions, while the set of mixed strategies for player II is a closed convex setC inR n. The minimax theorem applies under a condition which limits the directions of recession ofC. Player II always has optimal strategies. These are shown to exist for player I also if a certain infinite system verifies the property of Farkas-Minkowski. The paper also studies certain conditions that guarantee the finiteness of the value of the game and the existence of optimal pure strategies for player I.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00939275
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