If one tries to model real conflict situations with the help of non-cooperative normal form games, it may happen that strategy combinations have to be considered which are totally unrealistic in practice but which, however may be taken into account in equilibrium with positive probability. In this paper the battle of sexes paradigm is considered which is the most simple game owning this unrealistic feature. It is shown that a slight modification of the rules of this game remedies the problem: If the mixed equilibrium is agreed upon as solution of the game, and the unrealistic strategy combination would have to be chosen, the game is repeated as long as this happens. It turns out that the expected run length of this new game is only slightly larger than one. In other words, this modification removes the unrealistic feature, but changes only slightly the outcome of the game. Also the case of altruistic behavior of the players is considered. Here the strange situation occurs that if in the first step the absurd strategy combination would have to be chosen, in the second step the game will be terminated with exactly this strategy combination.    «

If one tries to model real conflict situations with the help of non-cooperative normal form games, it may happen that strategy combinations have to be considered which are totally unrealistic in practice but which, however may be taken into account in equilibrium with positive probability. In this paper the battle of sexes paradigm is considered which is the most simple game owning this unrealistic feature. It is shown that a slight modification of the rules of this game remedies the problem: If...    »