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

In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuoustime analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a plausible...

Brown and von Neumann introduced a dynamical system that converges to saddle points of zero sum games with finitely many strategies. Nash used the mapping underlying these dynamics to prove existence of equilibria in general games. The resulting Brown--von Neumann--Nash dynamics are a benchmark...

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