Competitive two person zero-sum game with linear increment function

Abstract

We analyze the competition of two firms with increment function of the first firm c(x) = kx +1 an analogue to that in [1] with the increment c = 1.
The optimal strategies X^*, Y^* and the value v of the game in explicit form are obtained, their parameters a, α, C₀, C₁ being the solutions of the equation system.
The values of the game parameters for various k are presented in graphic form.