In John Nash’s proofs for the existence of (Nash) equilibria basedon Brouwer’s theorem, an iteration mapping is used. A continuous—time analogue of the same mapping has been studied even earlier byBrown and von Neumann. This differential equation has recently beensuggested as a plausible...

A game is unprofitable if equilibrium payoffs do not exceed the maximin payoff for each player. In an unprofitable game, Nash equilibrium play has been notoriously difficult to justify. For some simple examples we analyze whether evolutionary and learning processes lead to Nash play