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CSC5350-08

CSC5350-08 - P age 1 of 4 The Chinese University C ourse E...

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Page 1 of 4 !t&..;jfiJ'Ji";ff ;;r:1·H~ ~p ~ \$ rf k *- * Copyright Reserved The Chinese University of Hong Kong Course Examination 1st Term, 2008 - 2009 Course Code & Title : \::\$.\::Q~Q'O .. G.Cl,P:!.~.Th~.9..J:Y i.D.\::9..:g:.tp.~t.~r .. \$~.i.~.r.:t~~ . Time allowed : .2. hours minutes Student LD. No. . Seat No. : . Answer all four (4) questions. 1. One day, John and Mary decide to go for dinner together. There is an expensive restaurant and a cheap restaurant near their home. Each of John and Mary should independently decide whether to go to the expensive restaurant (action E) or the cheap restaurant (action C). John wants to go to the expensive restaurant as the food there is better, while Mary wants to go to the cheap restaurant as she does not want to spend too much money. However, no matter which restaurant they finally go, John is the one to pay, and Mary does not need to pay. Now suppose that if they both go to the expensive restaurant, then they will need to spend \$500; if they both go to the cheap restaurant, then they will need to spend only \$100. John's utility function is that the utility of his paying \$x is exactly -x. On the other hand, if they both go to the expensive restaurant, then John's joy of having dinner there is equivalent to a utility of 300 (as he has to pay \$100, so his 'net' utility will be 200), and Mary's will be 200; if they both go to the cheap restaurant, then John's joy of having dinner there is equivalent to a utility of 100 (as he has to pay \$100, so his 'net' utility will be 0), and Mary's will be 150. Finally, if John and Mary go to different restaurants, then both of them will be very unhappy, and both have a utility of 0 (zero). (a) Model the scenario as a strategic' game G = (N,(AJ,(uJ), where N = {1,2}, with John being Player 1 and Mary being Player 2. 1. (1 mark) Write down (AJ in the game G. 11. (2 marks) Write down the setA of outcomes in the game G. iii. (2 marks) Write down (uJ in the game G. (b) (5 marks) What are the pure strategy Nash equilibria in the game G? Justify your answer.

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CSC5350-08 - P age 1 of 4 The Chinese University C ourse E...

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