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GAME THEORY 2017-2018 5 cfu 2 Games in extensive form and combinatorial games 2.1 Games in extensive form Exercise 7. Consider the following two games: 1. The popular game of Rock-Paper-Scissors. 2. Job offer in Paris : Anne and Mark are working together in Milan. Anne is offered a job in Paris. If she accepts the offer, Mark has to decide whether to stay in Milan or to go to Paris with his girlfriend. Anne prefers to be in Paris rather than in Milan. Mark prefers to be in Paris with her rather than in Milan. How would you represent the two games? Exercise 8. Do the trees in Figure 1a and 1b represent games? Why (or why not)? c d a e f g b I II II 1 2 3 4 5 (a) Exercise 8 c d a e f g b I II II 1 2 3 4 5 (b) Exercise 8 Figure 1: Exercise 8 Exercise 9. Sharing Game A father wants to give something to his daughter Alice: Alice has to make her brother Bob an offer to share what the father gave her. If Bob does not accept the offer, Alice and Bob will receive nothing. Consider the previous game in these three different situations: 1. The father wants to give Alice two identical objects. 2. The father wants to give Alice one valuable object. 1 3. The father wants to give Alice 100 euro. Draw the trees for these three games and discuss the possible outcomes. Exercise 10. Apply backward induction to the graph in Figure 2. c g h d a i l e f b I II II (1,2) I I (2,1) (0,0) (0,0) (1,2) (2,3) Figure 2: Exercise 10 Exercise 11. Consider the game in extensive form in Figure 3. Solve the game using backward induction. g h 1/3 i l 2/3 a 1/2 1/2 b I N N II II (1,3) (3,1) (2,2)(1,2) (3,0) (3,2) Figure 3: Exercise 11 Exercise 12. Exam 9 February 2015 Consider the zero sum game in extensive form in Figure 4. Write all the strategies of the two players, solve the game using backward induction…