Fictitious Play Algorithm

The original fictitious play algorithm is an iterative procedure developed by G. Brown to find an estimate of a solution to two-person zero-sum games (also commonly referred to as matrix games). The simplicity of the method is very appealing, but the convergence is very slow. Since its development, most of the ensuing research had focused on modifications to speed up convergence rate, identifying other classes of games where the method (or its variants) converges or fails to converge, and implementing the fictitious play concept in solving some applied problems. A complete description of the algorithm is provided, along with an example where a detailed step-by-step execution of the first few iterations is illustrated.