Abstract
A computational procedure, Simulated Fictitious Play (SFP), is introduced to approximate equilibrium solutions for n-person, non-cooperative games with large strategy spaces. A variant of the iterative solution process fictitious play (FP), SFP is first demonstrated on several small n-person games with known solutions. In each case, SFP solutions are compared to those obtained through analytical methods. Sensitivity analyses are presented that examine the effects of iterations (repetitions of the stage game) and number of sample outcomes generated within each iteration on measures of convergence. The algorithm is then used to approximate the solution of a 20-player game, in which each player has 601 pure strategies. The resulting strategy space, 60120, or 3.78 × 1055, has proved virtually unmanageable for existing solution methods and computer software packages that employ numerical methods. The paper discusses the origins and theoretical development of FP, as well as interest in FP as a model of learning. It concludes with a discussion of both the potential and limitations of SFP.
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