Nash equilibrium and minimax theorem with \(\mathcal C\)-concavity
The paper under review offers a new generalization of the Nash equilibrium theorem, which is well known in the non-cooperative game theory. Here, the generalization consists in the substitution of the linear structure of pay-offs by a modification of the concavity condition. Namely, the concept of the C-concavity generalizing both, the usual convexity and so called CF-convexity which combines continuity with a special form of concavity condition. The main result includes the proof of a new, generalized, theorem of a Nash equilibrium for non-compact generalized games. The result is applied to the proof of a new minimax theorem and of a minimax inequality.
scientific article; zbMATH DE number 5124026
scientific article