The authors consider a version of a finitely-repeated prisoner's dilemma (PD) with large but fixed average length of players' lifetimes. At each time period \(r=1,\dots,n\) every member of the population plays a game \(\text{PD}(a,r)\) where it receives \(1\) if both players use the strategies \((CC)\) and \(-a^r, 1+a^r, 0\) in the case \((CD), (DC), (DD)\) respectively; \(a\in (0,1)\). The problem is analysed for the set of strategies of the form: the strategy \(k\) prescribes to choose \(C\) in stages \(1,\dots,k-1\) and \(D\) in \(k,\dots,n\), but if the opponent chooses \(D\) in stage \(i