After removing the dominated strategies for each Firm we are left with a simple payoff matrix. In this particular case it turns out that in this reduced game each player has a dominant strategy so the outcome is easy to predict for one time play. Firm 1 will charge the Low price and Firm 2 will charge the High price.

   We can always eliminate a dominated strategy, if one exists, because such a strategy will never be used and so is irrelevant to our considerations. Even in a game where some strategies can be removed this way the resulting reduced game may not neccesarily lend itsself to easy solution. And a number of situations yield neither dominant nor dominated strategies.

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