 Solution

When neither buys, X's unilateral deviation gains $2t/3-P$, while Y's gains $t/3-P$. For both to be nonpositive, $P$ must exceed the larger threshold. HenceEquality is included because a zero-gain deviation does not violate a Nash equilibrium. Consequently both joint-purchase and joint-nonpurchase Nash equilibria exist throughout $2t/3\le P\le t$, a coordination region.