
Accession Number : AD0708672
Title : COMPETITIVE TWOPERSON PERCENTILE GAME THEORY WITH DIRECT CONSIDERATION OF PAYOFF MATRICES.
Descriptive Note : Technical rept.,
Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
Personal Author(s) : Walsh,John E. ; Kelleher,Grace J.
Report Date : 11 JUN 1970
Pagination or Media Count : 21
Abstract : Considered is discrete twoperson game theory where the players behave competitively and choose their strategies separately and independently. Payoffs can be of a very general nature and need not be numbers. Within each matrix, the payoffs can be ranked according to increasing desirability level. This is done separately by each player and these rankings are not necessarily related. Separately, player i, (i = 1,2), selects and applies a percentile criterion 100ai to each matrix. A largest desirability level Pi(ai) occurs in the matrix for player i such that, when acting protectively, he can assure with probability at least ai that his payoff is at least this desirable (to him). Also, a smallest desirability level (P'j)(ai), according to the ranking by player i, occurs in the matrix for the other player (designated as j) such that player i, when acting vindictively, can assure with probability at least ai that the payoff to player j has at most this desirability (to player i). An aioptimum solution occurs for player i when he can be simultaneously aiprotective and aivindictive. Median game theory occurs when a1=a2=1/2. Percentile game theory occurs when more, or less, assurance is desired than occurs for the median case. (Author)
Descriptors : (*GAME THEORY, MATHEMATICAL MODELS), STATISTICAL ANALYSIS, COSTS, OPTIMIZATION, DECISION THEORY, MATRICES(MATHEMATICS), DECISION MAKING
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE