Ex. 1 A decision maker (DM) has to make a decision a without knowing the underlying state 6. Suppose the DM has preference u(a,f) = (a #)?, and her prior belief is that 6 follows a normal distribution with mean #; and variance og. The DM receives a signal s = + about 6, 2 - where is normally distributed with mean 0 and variance o 1. What is DM's optimal decision a when receiving a signal s? 2. Now suppose that there are two decision makers i = 1, 2 choosing actions sequentially. Before making decisions, DM 7 only observers her signal s;, but you can observe DM 1's action a; before DM 2 makes the decision. Signal s; = #+ ; where ; is independently and identically distributed following a normal distribution with mean 0 and variance o2. Suppose DM 2 has preference u(a,f) = (a #)> m, where m is the money paid. Then what is the highest price you could charge by selling the data of a; to DM 27 3. In the above question, suppose there is another DM 3 who has the same preference and signal distribution as DM 2. After selling to DM 2, what is the highest price you could charge by selling the data of a; to DM 37 4. The above question implies that you can repeatedly benefit from selling the data of a;. What phenomenon or business model might be consistent with this