 Given this new, stronger solution concept, we can ask about the solutions to the IPD. There is a significant theoretical difference on this matter between IPDs of fixed, finite length, like the one pictured above, and those of infinite or indefinitely finite length. In games of the first kind, one can prove by an argument known as backward induction that \(\bDu\), \(\bDu\) is the only subgame perfect equilibrium. Suppose the players know the game will last exactly \(n\) rounds. Then, no matter what node have been reached, at round \(n-1\) the players face an ordinary (“one-shot”) PD, and they will defect. At round \(n-2\) the players know that, whatever they do now, they will both defect at the next round. Thus it is rational for them to defect now as well. By repeating this argument sufficiently many times, the rational players deduce that they should defect at every node on the tree. Indeed, since at every node defection is a best response to any move, there can be no other subgame-perfect equilibria.