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For this task, we want to use decision theory to design the robots. We assume that the resources can appear in the locations at time t = 0 randomly - and if some resource appear in a location, it appears in quantity 50 units - but do not appear later on. We also assume that 1 unit of resource r1 (resp. 12, (3) is worth 10 pounds (resp. 35 pounds, 40 pounds). We remind that the resources disappear over time (if not collected) - see introduction. We assume for this task that there is no cliff on the grid. 1. For the two next questions, take the two last digits of your student's number. Say they are xy. We denote by p the probability 0.xy. Consider the following grid, where a robot is on the location at time O and where on the orange locations, r1 has probability 0.7 to appear, 12 probability p and r3 probability 0.1 at time 0 and in quantity 50 units, on the violet location, r1 has probability p to appear, r2 probability 0.5 and r3 probability 0.2 at time 0 and in quantity 50 units. On the other locations, resources have probability O to appear. 8. According to decision theory, which path should the robot follow? 2. Consider the following grid, where a robot is on the location at time 0 and where on the violet location, r1 has probability p to appear, r2 probability 0.4 and r3 probability x, at time 0 and in quantity 50, on the orange location, r1 has probability 0.6 to appear, r2 probability x and r3 probability p at time 0 and in quantity 50. According to decision theory, for which values of x the robot would start by collecting resources on the orange location before going to the violet one? 3. (a bit difficult) You are going to collect resources on the next location, but you are asked to choose which resource(s) you will collect (before knowing the content of the next location). On the next location, r1 has probability 0.5 to appear in quantity 50 units when you reach it. Resources r2 and r3 have probability 0.75 to appear in total quantity 50 units, but you do not know how many units are of r2 and how many are of r3 (but the total is 50 units). You have the two following scenario: Scenario 1: you are asked to choose between collecting resource r1 or collecting resource r3.9. Scenario 2: you are asked to choose between collecting resources r1 and r3 or collecting resources r2 and 13. Explain why, if you prefer to collect resource ri in Scenario 1, and prefer to collect r2 and 13 in Scenario 2, you would create a paradox