Task \#3. A simply merchant Dario considers establishing a small shop in a district of Palermo. He has got three alternatives: he can simply resign (which yields a zero pay-off and ends the decision problem), establish a small shop (S), establish a big shop (B). Establishing a shop will probably not be unnoticed by a local mob. S will be noticed with probability of 10%, B - with 90%. If shop is unnoticed it will bring (in a time horizon we are interested in) a profit equal to 100 for S and 150 for B. If the shop is noticed though, then Dario has got to possibilities. He can pay ransom money and continue trading. Ransom is equal to 20% of profit for S and 40% for B. Dario can also ask police for help. Officers are corrupted with probability of 40%. If they are, they will let the mob know, and shop (S or B) will be simply confiscated from Dario (yielding zero profit). If policemen are not corrupted, it will offer to Dario two alternatives: to continue trading while being protected by the policy or to try to collect some evidence against the mob. If Dario goes for the former, he will simply collect all the profit (100 for S and 150 for B ). If he tries to collect this evidence, he can succeed or not. He will succeed with probability of 80% for S, and 20% for B. Losing this game means losing the shop (hence no profit) and additional penalty from the mob giving utility of -100 for S and -150 for B. Winning this game means keeping all the profit and a reward from the police equal to 10. What should Dario do? Solve for various {0,1,,9}. What is the probability of B being noticed so that establishing S or B is equally good? What is the EVPI on police being corrupted