Problem 1 (40 pts) You and a friend are spending two days at the beach; you both enjoy swimming. HOWEVER, each of you believes with probability 1': the water is infested with sharks . If sharks are present , a swimmer will surely be attacked . Each of you receives c for being attacked by a shark, 0 to sitting on the sand, and 1 to a day's worth of swimming (6 > 0). If either of you is attacked by sharks on the first day, then you both know there be sharks and whoever swims will surely be attacked on the second day, and hence won't swim, receiving 0. If at least one person swims and is not attacked on the first day then you know the water is safe for sure and will swim on the 2nd day, earning 1. If neither of you swim, then on the second day you have the same belief as the first (It), and swim only if and only if 7TC + 1 7r 2 O (i.e., your expected utility from swimming is higher than not swimming ) You will be considering ONLY what your decision on the first day will be, knowing that (as described above) it will affect your decision on the second day. Make sure when modeling to consider the utility of both. In other words , use the actions in period 1 to find the expected utility in BOTH periods, then put the sum of those expected utilities together in the 2x2 grid . We will assume 7: