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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...
Persistent link: https://www.econbiz.de/10005868464
We introduce a generalized theoretical approach to study imitation andsubject it to rigorous experimental testing. In our theoretical analysiswe …nd that the different predictions of previous imitation models aredue to different informational assumptions, not to different behavioralrules. It is...
Persistent link: https://www.econbiz.de/10005868466
A well—known result from the theory of finitely repeated games statesthat if the stage game has a unique equilibrium, then there is a uniquesubgame perfect equilibrium in the finitely repeated game in which theequilibrium of the stage game is being played in every period. Here Ishow that this...
Persistent link: https://www.econbiz.de/10009248985
It is well known that the rock-paper-scissors game has no pure saddle point. Weshow that this holds more generally: A symmetric two-player zero-sum game hasa pure saddle point if and only if it is not a generalized rock-paper-scissors game.Moreover, we show that every finite symmetric...
Persistent link: https://www.econbiz.de/10009248997
We show that for many classes of symmetric two-player games, the simple decision rule \imitate-the-best" can hardly be beaten by any other decision rule. Weprovide necessary and sufficient conditions for imitation to be unbeatable and showthat it can only be beaten by much in games that are of...
Persistent link: https://www.econbiz.de/10009248998
The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this restriction is in most cases unnecessary. We give a mild condition under which the continuous time replicator dynamics are well defined for infinite strategy spaces....
Persistent link: https://www.econbiz.de/10010309877
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...
Persistent link: https://www.econbiz.de/10010310032
We show in this paper that none of the existing static evolutionary stability concepts (ESS, CSS, uninvadability, NIS) is sufficient to guarantee dynamic stability in the weak topology with respect to standard evolutionary dynamics if the strategy space is continuous. We propose a new concept,...
Persistent link: https://www.econbiz.de/10010310182
In a recent paper Bagwell (1995) pointed out that only the Cournot outcome, but not the Stackelberg outcome, can be supported by a pure Nash equilibrium when actions of the Stackelberg leader are observed with the slightest error. The Stackelberg outcome, however, remains close to the outcome of...
Persistent link: https://www.econbiz.de/10010310808
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...
Persistent link: https://www.econbiz.de/10010317631