GAMES ON THE UNIT-SQUARE WITH DISCRETE PAYOFF
Abstract
A few examples that were previously discussed in the literature are imbed in a fairly large class of games with a discrete payoff. After a precise definition, the results obtained are summarized. A wider class of games is defined for which a general method of solution is described. The value and the optimal strategies for both players are determined. With a suitable prescription of the game-kernel on the lines of discontinuity, the game admits a pair of optimal strategies, which are mixtures over n+2 pure strategies. InALL BUT A SINGLE CASE, BOTH PLAYERS POSSESS INFINITE SETS OF MINIMAX STRATEGIES. A natural problem which arises is concenned with the characterization of admissible minimax strategies. For each player a class of admissible optimal strategies exists and such strategies are exhibited explicitly. How far the difinition of the payoff on the lines of discontinuity can be relaxed without affecting the optimality properties of the strategies previously determined is discussed. The class of games is extended such as to allow one more value for the payoff function. A general method to obtain at least one pair of optimal strategies is indicated and a few special cases are worked out. The connection of the class of games under study with a class of matrix-games is pointed out. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 27, 1961
- Accession Number
- AD0253011
Entities
People
- Marcel F. Neuts
Organizations
- Stanford University