The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy (Dover Books on Mathematics)

In zero-sum games the payoffs represent strictly an exchange of assets; one player wins the quantity that the other loses. We have compromised this principle somewhat in games played against Nature (used as examples here and there), where we have computed strategies for the personal player as if he were playing against an opponent who shared his va

This is an important concept in Game Theory, that of mixed strategies: the concept that a player should sometimes use one pure strategy, sometimes another, and that the decision on each particular play should be governed by a suitable chance device. We can anticipate that this will be a feature of most games, that it will fail to appear only when c

However, one-person games (including Solitaire) may be regarded as a special kind of two-person game in which you are one of the players and Nature is the other.

One should always look first for a saddle-point; the process is painless and concludes the work if there is one. Recall that we inspect each row to find its minimum, select the greatest of these, and then inspect the columns to find the maxima, selecting the least of these. If the two numbers (called, incidentally, the maxmin and minmax) are equal,

In this chapter we shall describe a method, called the pivot method, which is powerful enough to ferret out all solutions, and which is efficient enough to be practical; that is, it usually reaches the exact solution in a few steps. The method is more complicated—particularly to describe—than the methods discussed earlier, but we believe the carefu

Thus we come to believe it is significant. to count the number of sets of opposing interests around the table, rather than the bodies.

Generally, when the larger of the row minima is equal to the smaller of the column maxima, the game is said to have a saddle-point; and the players should stick to the strategies which intersect at the saddle-point. To discover that there is a saddle-point, each player must examine the game both from his own and the enemy’s point of view. He lists

The Theory of Games is a method of analyzing a conflict, according to the following abstraction: The conflict is a situation in which there are two sets of opposing interests; it may be regarded as a game between two players, each of whom represents one set of interests. Each player has a finite set of strategies from which he may, on any given pla

The above two cases illustrate a fundamental distinction among games: It is important to know whether or not the sum of the payoffs, counting winnings as positive and losses as negative, to all players is zero. If it is, the game is known as a zero-sum game. If it is not, the game is known (mathematicians are not very imaginative at times) as a non

Game Theory is very similar in spirit to the Theory of Gravitation. Both attempt to treat broad classes of events according to abstract models. Neither tries to model all the complexities present in any situation.