 Then, for each player, although \(\bD\) does not strictly dominate \(\bC\), it still weakly dominates in the sense that each player always does at least as well, and sometimes better, by playing \(\bD\). Under these conditions it still seems rational to play \(\bD\), which again results in the payoff that neither player prefers. Let us call a game that meets PD2 a weak PD. Note that in a weak PD that does not satisfy PD1 mutual defection is no longer a nash equilibrium in the strict sense defined above. It is still, however, the only nash equilibrium in the weaker sense, that neither player can improve its position by unilaterally changing its move. Again, one might suppose that if there is a unique nash equilibrium of this weaker variety, rational self-interested players would reach it.