Capital accumulation games of infinite duration

Consider a market in which firms accumulate capital according to the Nerlove-Arrow capital accumulation equation. Each player chooses a path of investment and thus an induced path of capital to maximize his total discounted profits which depend on his own capital and the capital stocks of his rivals. Existence is proved for such a nonzero sum, infinite horizon differential game and conditions under which the game converges to a particular stationary point, regardless of the initial conditions are shown. Thus, the game possesses the property of conditional global asymptotic stability.