# Two Player Game Useless Strategy

Let's consider the variant of dominated strategy which is the pure strategy that is not a best response to any mixed strategy of the opponent (two player game). Intuitively it sounds like more stronger notion of dominated strategy, because in this case all mixed strategies of the opponent is taken into account, lets call this kind of dominated strategy as "useless strategy".

Obviously "useless strategy" doesn't participate in mixed strategy of the player, therefore it can be safely excluded from the game.

Is there any algorithm to detect "useless strategies"?

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Thank you very much for the answer! Two questions: 1) is never best response is equivalent to useless strategy? Intuitively it seems so, but formally I don't see that it is equivalent (in useless strategy we compare against every mixed strategy of the opponent). 2)How to find the useless strategy? Should we convert to game $G'$ and check that $min_{m_2} max_{a_i} v_1(a_i,m_2) > 0$ like it was suggested in the proof (I am not sure is polynomial time algorithm) or there is another method? – fog Apr 26 '13 at 19:33