.4 ¡Á 3 Game Continuous Convergence Of The Virtual Action

Most research about the Fictitious Play process has focused on the key question of whether the FP approaches equilibrium.In the book of《Cooperation:Game Theretic Approaches》,it said "Learning in Games:Fictitious Play Dynamics" (Krishna Vijay and Sj(?)str(?)m Tomas),the author proved that they do converge, if the game satisfies strategic complementarities and decreasing marginal returns. After that,the author also has been conjecture that they do converge,if the game satisfies strategic complementarities.Hahn Sunku(1999)[3]proved "The Conver-gence of Fictitious Play in 3×3 Games with Strategic Complementarities".This paper,from games,firstly introduces something about games,then the Fictitious Play.The main problem discussed is "The Convergence of 4×3 games".The result is "The continuous time formulation of fictitious play in 4×3 nondegenerate games with strategic complementarities always converges".Lastly I will put this result to m×n games.