By Anatol Rapoport
N-person online game thought analyzes contests during which there are greater than units of conflicting pursuits, e.g. a hand of poker or wide-scale war. during this sequel to his Two-Person video game conception, the writer introduces the mandatory mathematical notation (mainly set theory), offers simple recommendations, discusses a number of versions, and offers functions to social events.
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Additional info for N-Person Game Theory: Concepts and Applications
While the result says little that is of interest to Chess players, the attempt to answer similar questions in the context of non-constantsum games reveals another "dimension of complexity," as it were. For example, it raises questions concerning what one can say about (non-constant-sum) games which are not "solvable" even though they possess equilibria. For, even assuming that rational players will choose strategies containing equilibria (even this assumption is open to question), we cannot be sure that the outcome will be an equilibrium.
53) Reading from left to right, we first encounter V' (S), which (as appears from the text) is a value of a characteristic function of a certain game. The double prime should alert us to the likelihood that this function was obtained from another characteristic function. And so it was, as denoted by cv ( S ); namely by multiplying all the values v ( S) by the same number c. Also the values v( S) were obtained from the original values v( S) by adding to each value v( S) a sum of numbers ab each being associated with the players in the coalition S, as indicated by i E: S under the summation.
The domain of this function may be taken as the set of all real numbers, since every real number has a square. On the other hand, if real numbers are taken as the domain, the range of the function will be only the positive real numbers and zero, since the square of every negative number is positive. Functions will be denoted by letters followed by empty parentheses. Just as in algebra a letter may stand for any number, so a letter may designate any function which, recall, is not a number but a correspondence rule.
N-Person Game Theory: Concepts and Applications by Anatol Rapoport