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...

We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for...

We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for...

We show that in symmetric two-player exact potential games, the simple decision rule "imitate-if-better" cannot be beaten by any strategy in a repeated game by more than the maximal payoff difference of the one-period game. Our results apply to many interesting games including examples like 2x2...

In this note we study a very simple trial & error learning process in the context of a Cournot oligopoly. Without any knowledge of the payoff functions players increase, respectively decrease, their quantity by one unit as long as this leads to higher profits. We show that despite the absence of...

We report results of experiments designed to test the predictions of the best reply process. In a Cournot oligopoly with four firms, the best reply process should theoretically explode if demand and cost functions are linear. We find, however, no experimental evidence of such instability....