A Solution Technique for Complex Matrix Games.
AERONAUTICAL RESEARCH LABS MELBOURNE (AUSTRALIA)
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The concept of a zero sum two person game in complex space was introduced previously. Complex analogues of payoffs, probability vectors and strategy sets were defined and a minimax theorem established. A simpler proof of a more general minimax theorem was subsequently given in another document. Both of the above papers provided numerical examples of 2x2 matrix games in complex space and their solutions. Solution of matrix games in complex space has so far been quite difficult, even for 2x2 matrices. In this note a method is derived for transforming a matrix game in complex space into a matrix game in real space having the same value. This latter game can then be solved by the standard techniques involving linear programming. Optimal strategies for the original game in complex space are easily obtained from the optimal strategies computed for the game in real space. The technique outlined in this note can be used to solve any feasible matrix game in complex space. The only constraint on the size of the game matrix which can be accommodated is that which is imposed by the computer or linear programming package to be used.
- Theoretical Mathematics