
Accession Number : AD0717938
Title : Generally Applicable NPerson Percentile Game Theory for Case of Independently Chosen Strategies.
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 : 21 DEC 1970
Pagination or Media Count : 20
Abstract : The paper considers a discrete Nperson game theory where the players choose their strategies separately and independently. Payoff 'values' can be of a very general nature and need not be numbers. However, the totality of payoff outcomes (Ndimensional), corresponding to the possible combinations of strategies, can be ranked by each player according to their desirability to that player. A largest level of desirability (associated with one or more outcomes o sub i) occurs for the ith player such that he can assure, with probability at least a given value alpha sub i, that an outcome with at least this desirability level is obtained, and this can be done simultaneously for all the players. This game theory is of a median nature when all the alpha sub i are chosen to the 1/2. A method is given for determining o sub i and an optimum (mixed) strategy for every player. Practical aspects of applying this percentile game theory are examined. Application effort can be substantially reduced when the players have relative desirability functions for ranking the outcomes. Some elementary types of relative desirability functions are introduced. (Author)
Descriptors : (*GAME THEORY, PROBABILITY), MATRICES(MATHEMATICS), OPTIMIZATION, THEOREMS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE