3. Vin Diesel (VD) is deciding whether to upgrade his car prior to a race with...

  

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3. Vin Diesel (VD) is deciding whether to upgrade his car prior to a race with his nemesis, Paul Walker (PW). VD currently drives a Honda. Similar to the example from class, VD and PW compete by sequentially choosing to drive fast (f) or slow (s). VD chooses for s first, and PW then chooses f or s second after observing VD's choice. If both drive slow, they both earn R = 200. If one drives fast and the other slow, the driver who goes fast earns R = 1000 and the one that goes slow earns R = 100. If both drive fast and finish the race, they earn R = 500. However, if both drive fast, with probability p=0.1, they both crash and earn R = 0. Further suppose that prior to racing, VD has an initial choice whether to upgrade his car from a Honda to a Toyota. The cost of the upgrade to VD is C = 200. VD's benefit from upgrading to a Toyota is that he never crashes when racing this car. If VD and PW drive fast, with probability p = 0.1 only PW will crash. In this case, if PW crashes VD earns R 3500 and PW earns R = 0. Assume that all other payoffs to the game if VD buys a Toyota are analogous to the case where VD drives a Honda. (a) Determine whether information is perfect or imperfect in this game. Briefly ex- plain. (b) Present this game using a game tree. (c) Solve for the SPNE. Characterise the SPNE strategies, path(s), and payoffs. (d) For what value of C would VD be indifferent between upgrading to a Toyota and simply staying with a Honda? 3. Vin Diesel (VD) is deciding whether to upgrade his car prior to a race with his nemesis, Paul Walker (PW). VD currently drives a Honda. Similar to the example from class, VD and PW compete by sequentially choosing to drive fast (f) or slow (s). VD chooses for s first, and PW then chooses f or s second after observing VD's choice. If both drive slow, they both earn R = 200. If one drives fast and the other slow, the driver who goes fast earns R = 1000 and the one that goes slow earns R = 100. If both drive fast and finish the race, they earn R = 500. However, if both drive fast, with probability p=0.1, they both crash and earn R = 0. Further suppose that prior to racing, VD has an initial choice whether to upgrade his car from a Honda to a Toyota. The cost of the upgrade to VD is C = 200. VD's benefit from upgrading to a Toyota is that he never crashes when racing this car. If VD and PW drive fast, with probability p = 0.1 only PW will crash. In this case, if PW crashes VD earns R 3500 and PW earns R = 0. Assume that all other payoffs to the game if VD buys a Toyota are analogous to the case where VD drives a Honda. (a) Determine whether information is perfect or imperfect in this game. Briefly ex- plain. (b) Present this game using a game tree. (c) Solve for the SPNE. Characterise the SPNE strategies, path(s), and payoffs. (d) For what value of C would VD be indifferent between upgrading to a Toyota and simply staying with a Honda?

Answer rating: 100% (QA)

a Information is imperfect in this game because the players do not have complete information about t... View the full answer