Convex semi-infinite games (Q1065725)

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 set C in \(R^ n\). The minimax theorem applies under a condition which limits the directions of recession of C. 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.