 Solution

At joint purchase, each player's gain from continuing to buy rather than deviating to $nb$ is $(t-P)/2$. Both actions are best responses exactly when this is nonnegative. ThereforeAt equality both players are indifferent to their individual unilateral deviations, which is permitted in a Nash equilibrium. The condition is less restrictive than requiring either player's action to be a weakly dominant strategy: only the opponent's actual action needs to be considered.