Let’s solve this problem without trying to refer to existing particular cases.
For the start, we assume that utility of A-the-thief monotonically decreases with time served; utility of B monotonically increases, and if A gives up lollipops it is increased by another constant.
Let’s graph what choices A has when B does not give up lollipops.
We may notice that in this case B will simply throw A in jail for life. Well, what happens if A is willing to cooperate a bit?
Coordination result will not be below or to the left of Pareto frontier, since otherwise it is possible to do better than that;
Coordination result will not be below or to the left of no-coordination result, since otherwise one or both parties are acting irrationally.
We may see that after these conditions, only a piece of curve “A gives up lollipops” remains. The exact bargaining point can then be found out by using ROSE values, but we can already conclude that A will likely be convicted for a long time but not for life.
Let’s solve this problem without trying to refer to existing particular cases.
For the start, we assume that utility of A-the-thief monotonically decreases with time served; utility of B monotonically increases, and if A gives up lollipops it is increased by another constant.
Let’s graph what choices A has when B does not give up lollipops.
We may notice that in this case B will simply throw A in jail for life. Well, what happens if A is willing to cooperate a bit?
Coordination result will not be below or to the left of Pareto frontier, since otherwise it is possible to do better than that;
Coordination result will not be below or to the left of no-coordination result, since otherwise one or both parties are acting irrationally.
We may see that after these conditions, only a piece of curve “A gives up lollipops” remains. The exact bargaining point can then be found out by using ROSE values, but we can already conclude that A will likely be convicted for a long time but not for life.