Alex, who was convinced that "Football is coming home", was very excited for the World Cup last year. Unfortunately, he realized that his favourite Paul Gascoigne jersey from Euro 1996 was getting old, so he wanted to buy a new one before England's first game the following week. He could either buy a 2014 James Milner shirt from retailer A, which would make him totally happy (utility=1), or a 2006 David Beckham shirt from retailer B, which gives him a utility of 0.8. However, the shirts are not available today. There is a 50% chance that retailer A will have the shirt on the week-end, and 70% chance that retailer B will have theirs on the week-end. Due to time and work constraints, Alex can only visit one of these retailers before the tournament starts, otherwise he will have to keep his old 1996 shirt, which gives him a utility of 0.5. He can also ask his friend Nathan to check both places in the morning. But being a Welsh supporter, Nathan will not do it for free and wants some money to help his friend, although rival here. We assume that Nathan will return accurate information to Alex. What is Alex's expected utility of perfect information? Or in other words, what is the utility corresponding to the maximum amount Alex should pay Nathan to go check the retailers?
Alex, who was convinced that "Football is coming home", was very excited for the World Cup last year. Unfortunately, he realized that his favourite Paul Gascoigne jersey from Euro 1996 was getting old, so he wanted to buy a new one before England's first game the following week. He could either buy a 2014 James Milner shirt from retailer A, which would make him totally happy (utility=1), or a 2006 David Beckham shirt from retailer B, which gives him a utility of 0.8. However, the shirts are not available today. There is a 50% chance that retailer A will have the shirt on the week-end, and 70% chance that retailer B will have theirs on the week-end. Due to time and work constraints, Alex can only visit one of these retailers before the tournament starts, otherwise he will have to keep his old 1996 shirt, which gives him a utility of 0.5.
He can also ask his friend Nathan to check both places in the morning. But being a Welsh supporter, Nathan will not do it for free and wants some money to help his friend, although rival here. We assume that Nathan will return accurate information to Alex. What is Alex's expected utility of perfect information? Or in other words, what is the utility corresponding to the maximum amount Alex should pay Nathan to go check the retailers?
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