The convergence of fictitious play in 3×3 games with strategic complementarities

Even though fictitious plays do not generally converge, Krishna (Learning in games with strategic complementarities. Harvard Business School working paper No. 92-073, 1992) proved that they do converge, if the game satisfies strategic complementarities and decreasing marginal returns. However, there has been conjecture that the assumption of decreasing marginal returns is not really necessary. This paper partially supports the conjecture by showing that in 3×3 games with strategic complementarities the fictitious play always converges.