Nash Equilibrium and Best Response Strategy

Dominic and Placido can choose from among High, Medium and Low prices for their pizza. The payoffs are profits from pizza sales.

Placido (Pat) conjectures that Dominic (Dom) is going to price High.  In that case Placido's best response is Medium, so we strike through High and Low for Pat.  If Placido conjectures that Dom will charge Medium, then Pat's best response is Medium, so we strike through High and Low for Pat again.  Finally, when Pat conjectures that Dom will play Low, his best response is to play High, so we strike through Medium and Low for Pat.

Now go through the best response elimination for Dom.  When you are all done you will see that the only cell in which no payoff has been struck through is the Medium, Medium strategy vector.