A monopolist maximizes a well defined objective function, monetary profit. In a competitive industry, although each individual pursues selfish objectives, the market behaves as if an agent were maximizing an objective function, social welfare. Can we say the same for an oligopoly? Do firms pursuing selfish objectives and behaving strategically act as if an agent were maximizing a `fictitious'-objective function? Necessary and sufficient conditions for Nash equilibria of static and state-space games to be observationally equivalent to single optimization problems are derived. Nash equilibria of the game that are not maxima of the function are shown to be generically unstable.