A monopolist maximizes a well defined objective function, monetary pro
fit. In a competitive industry, although each individual pursues selfi
sh objectives, the market behaves as if an agent were maximizing an ob
jective 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? Nece
ssary and sufficient conditions for Nash equilibria of static and stat
e-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.