COMPETITIVE TWO-PERSON PERCENTILE GAME THEORY WITH DIRECT CONSIDERATION OF PAYOFF MATRICES.
Abstract
Considered is discrete two-person 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 ai-optimum solution occurs for player i when he can be simultaneously ai-protective and ai-vindictive. 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 11, 1970
- Accession Number
- AD0708672
Entities
People
- Grace J. Kelleher
- John E. Walsh
Organizations
- Southern Methodist University