Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the performance of Fictitious Play (FP), when used as a heuristic for finding an approximate Nash equilibrium of a two-player game.  exhibit a class of two-player games having payoffs in the range $$[0,1]$$ that show that FP fails to find a solution having an additive approximation guarantee significantly better than $$1/2$$ . Our construction shows that for $$n\times n$$ games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity $$1/2 - O(1/n^{1-\delta })$$ for arbitrarily small $$\delta $$ .  also show an essentially matching upper bound of $$1/2 - O(1/n)$$ . Copyright Springer-Verlag Berlin Heidelberg 2013
['Paul W. Goldberg', 'Rahul Savani', 'Troels Bjerre Sørensen', 'Carmine Ventre']
I am writing a research paper on a idea On the approximation performance of fictitious play in finite games
[{"from": "human", "value": "I am writing a research paper on a idea On the approximation performance of fictitious play in finite games"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the performance of Fictitious Play (FP), when used as a heuristic for finding an approximate Nash equilibrium of a two-player game.  exhibit a class of two-player games having payoffs in the range $$[0,1]$$ that show that FP fails to find a solution having an additive approximation guarantee significantly better than $$1/2$$ . Our construction shows that for $$n\\times n$$ games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity $$1/2 - O(1/n^{1-\\delta })$$ for arbitrarily small $$\\delta $$ .  also show an essentially matching upper bound of $$1/2 - O(1/n)$$ . Copyright Springer-Verlag Berlin Heidelberg 2013"}]