To connect with the cyber audience, Tech Tiger Inc. is thinking about hiring EE (Ercole Enorme), an Italian YouTube star who is a bit of an enigma. In the opinion of Tech Tiger's HR manager, Heidi Hammer, his contribution is going to be worth at least 500K (with 20% likelihood), but could well be 2M (with 80% likelihood). Two competitors are potentially interested in hiring Signore Enorme as well. Each company is individually interviewing and evaluating him virtually. Heidi believes that, in similar circumstances, these competitors have a 30% likelihood of making an offer - however, if they learn that the individual is highly valuable, the likelihood of an offer increases to 60%. Tech Tiger is a relatively young firm and not really able to match what these competitors would pay.

(i) What is Tech Tiger's prior belief that EE is worth $2M?

(ii) Suppose Tech Tiger makes an offer, and it is accepted. Why should it update its prior? (What would Tech Tiger have learned in that case?)

(iii) What is the unconditional likelihood that a particular competitor does not make an offer to EE? What is the conditional likelihood of that event if EE is worth $2M?

(iv) What is Tech Tiger's posterior after having its offer accepted?

(v) What is the most Tech Tiger should offer EE based on his expected value when he accepts the offer?