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The concept of a mixed-strategy equilibrium was introduced by John von Neumann and Oskar Morgenstern in their 1944 book The Theory of Games and Economic Behavior, but their analysis was restricted to the special case of zero-sum games. They showed that a mixed-strategy Nash equilibrium will exist for any zero-sum game with a finite set of ...
The main problem with these games falls into one of two categories: (1) various mixed strategies of the game are purified by different sequences of perturbed games and (2) some mixed strategies of the game involve weakly dominated strategies. No mixed strategy involving a weakly dominated strategy can be purified using this method because if ...
A well-known example of the minority game is the El Farol Bar problem proposed by W. Brian Arthur. A hybrid form of coordination and anti-coordination is the discoordination game, where one player's incentive is to coordinate while the other player tries to avoid this. Discoordination games have no pure Nash equilibria.
In game theory, fictitious play is a learning rule first introduced by George W. Brown. In it, each player presumes that the opponents are playing stationary (possibly mixed) strategies. In it, each player presumes that the opponents are playing stationary (possibly mixed) strategies.
Selected equilibrium refinements in game theory. Arrows point from a refinement to the more general concept (i.e., ESS Proper). In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the ...
Matching pennies is used primarily to illustrate the concept of mixed strategies and a mixed strategy Nash equilibrium. [1] This game has no pure strategy Nash equilibrium since there is no pure strategy (heads or tails) that is a best response to a best response. In other words, there is no pair of pure strategies such that neither player ...
A mixed strategy is an assignment of a probability to each pure strategy. When enlisting mixed strategy, it is often because the game does not allow for a rational description in specifying a pure strategy for the game. This allows for a player to randomly select a pure strategy. (See the following section for an illustration.)
We can demonstrate the same methods on a more complex game and solve for the rational strategies. In this scenario, the blue coloring represents the dominating numbers in the particular strategy. Step-by-step solving: For Player 2, X is dominated by the mixed strategy 1 / 2 Y and 1 / 2 Z.