All costs are known in advance here we assume that we have

Question

Question: Consider three variations of a shortest path problem:

Case I.  i.

Case III. Costs are learned after the fact. In this setting we only learn the cost on each link after the trip is finished.

Let v_i^I be the expected cost to get from node i to the destination for case I. Similarly let v_i^II and v_i^III be the expected costs for cases II and III. Show

that v_i^I = v_i^II = v_i^III