Simplified Solutions for Two-Person Percentile Games.
Abstract
Consider solution of a two-person game in which the players use percentile criteria. For player i, the stepwise procedure is to mark positions of the game outcomes (pairs of payoffs, one to each player) in his payoff matrix according to decreasing desirability level (i = 1,2). To be determined is the smallest marked set such that, for percentile 100 alpha sub i used by player i, an outcome of this set can be assured with probability at least alpha sub i. Also, an optimum mixed strategy is to be determined (for accomplishing this assurance). In general, the probability with which a marked set can be assured is evaluated by solution of a specialized zero-sum game with an expected-value basis. However, easily evaluated upper and lower bounds for this probability can be obtained from the matrix locations of the markings. Use of these bounds can substantially reduce the effort in the stepwise solution of a game. Moreover, equality of the bounds can occur. Then, the probability is determined without solution of a zero-sum game, and a corresponding optimum strategy is readily identified. The probability value is approximately determined when the bounds are nearly equal, and an approximately optimum strategy is easily identified. Indications are that many percentile games can be solved, exactly or approximately, by this simplified method. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 04, 1971
- Accession Number
- AD0717939
Entities
People
- Grace J. Kelleher
- John E. Walsh
Organizations
- Southern Methodist University