Download Two-Person Game Theory: The Essential Ideas by Anatol Rapoport PDF
By Anatol Rapoport
A famous specialist offers sincerely written discussions of crucial principles on the topic of the hugely worthwhile mathematical method of human habit and decision-making. His lucid, available therapy examines such strategies as "utility," "strategy," and the adaptation among "non-zero" and "zero-sum" video games. at least mathematical necessities makes it available to non-mathematicians. 1970 version.
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Additional resources for Two-Person Game Theory: The Essential Ideas
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Oij .. . Gamel ... OIM .. ONM 4. The Game Tree and the Game Matrix One of the keystone ideas of game theory is that any "well defined" game can be reduced to normal form. As we have said, a game in normal form presents to each player a choice among several alternatives called strategies. When such a choice is presented, it suffices for each player to choose one of the strategies available to him. It is essential that every player make his choice simultaneously or, what is the same thing, in ignorance of what choices are made by others.
Formally speaking, no player knows the outcome of a move made by a fictitious player called Chance, who at the beginning of each deal chooses among all the possible arrangements of the deck. Games which are not games of perfect information may not have any saddle points, and so the minimax principle in the form we have stated it need not apply to such games. In the next chapter we shall consider an extension of the minimax principle which does apply to zero-sum games without saddle points. 6. Mixed Strategy If, in the course of the game, some player's choice on a given move remains unknown to the other players after the move is made, then the game is no longer a game of perfect information.
One might, for example, choose the strategy which offers the possibility of the largest payoff. For Castor this would be the row which has the biggest entry in it. Another possible principle would be to choose the strategy with the largest average payoff (assuming that the choices of the other player are equiprobable ). It should be apparent that neither of these principles satisfies the criterion of maximizing one's own payoff under the constraints of the game. For the single crucially important constraint on the game is the rationality of the opponent.