To the right is a payoff matrix for a game in which each firm has three possible strategies or price levels.

   You should be able to quickly see that neither player has a dominant strategy. If you are Firm 1 and you know Firm 2 will charge the High price you would charge the Low price. If you knewFirm 2 would charge the Medium you would charge your Medium and if Firm 2 were going to charge the High price you would charge the Low. Since sometimes Firm 1 would charge Low and sometimes Medium there it has no dominant strategy.

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