Modified fictitious play for solving matrix games and linear-programming problems

Abstract

We describe a modification of Brown's fictitious play method for solving matrix (zero-sum two-person) games and demonstrate its greatly improved convergence rate over Brown's original method. The modified method applied to the symmetric form of a zero-sum two-person game and of a linear-programming problem yields an approximate solution that enables us (1) to use game theoretic methods for solving symmetric matrix games that require less iterations and time, (2) to obtain simplex method Phase I crash solutions to linear-programming problems that produce a lower total iteration count than standard crash methods, and (3) to combine the game solution and an interior-point solution to select variables that tend to be in an optimal basic solution. We describe initial experiments in using the modified fictitious play method to aid in the solution of linear-programming problems.