A weakened form of fictitious play in two-person zero-sum games (Q2743765)

Fictitious play is used for computing the value and the optimal strategies of a two-person zero-sum game since its requirement for computer storage is modest, even though the convergence is slow. In this paper the author proposes a weakened form of fictitious play. This form of play does not require the players to use their best choice against the total of the past choices of the other player, but only an increasingly better one. Bounds for the convergence are derived. It is also shown that the proposed form can speed up the convergence considerably. It is argued that the proposed form can be used in games where better estimates of the pay-off matrix iself can be obtained at each stage as the fictitious play progresses.