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GAME THEORY 2017-2018 5 cfu 1 Introductory examples Exercise 1. Ultimatum game The professor offers you four candies, to be shared with your favourite coursemate. The deal is that you have to give at least one candy to him/her, otherwise the offer will be withdrawn. How many candies would you offer to your friend? Exercise 2. Exam Bonus The day before the exam, you have the chance to gain some extra points. You are given the following two options: “give me 1 extra point” or “give to my colleague 3 extra points”. Which of the two would you choose? Exercise 3. Take-Away Game Two players. A pile of 12 chips. A move consists in removing 1, 2, or 4 chips. The players alternate moving and the one who removes the last chip wins. Would you like to be the first or second player? Exercise 4. Cows & Candies Three farmers share 12 fields in order to graze their cows. Each morning a farmer decides how many fields he want to occupy; at the end of the day he milk the cows and get as many litres of milk as the number of fields he occupied times the number of empty fields for that day. For instance, if farmer I occupies 2 fields, farmer II occupies 5 fields and farmer III occupies 1 field, then there are four empty fields and farmer I gets 8 litres of milk, farmer II 20 litres and farmer III 4 litres. If you were a farmer, how many cows would you graze? If you had to make a deal together with the other farmers, how many cows would you graze? Exercise 5. Taxi ride Three friends want to share a taxi ride to go back home. Alice and Bob by themselves will spend 10 Euro, Carol instead will spend 14. If Alice and Bob go together the ride will cost 12 Euro, if Carol will go with either Alice or Bob the cost is 18 Euro. If they go all together they will spend 20 Euro. Find a way to fairly share the cost…