ps3(2010)_soln

# ps3(2010)_soln - MS&E 246 Game Theory with Engineering...

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Unformatted text preview: MS&E 246: Game Theory with Engineering Applications Problem Set 3 1. (a) (5pts) Firm 1 chooses whether to build a plant (p) or not (n). Firm 2 chooses whether to enter (E) or not (N). MS&E 246: Game Theory with Engineering Applications Problem Set 4 February 19, 2009 1. (a) Firm 1 chooses whether to build a plant (p) or not (n). Firm 2 chooses whether to enter (E) or not (N). Nature ` h p n p n E N E N E N E N ( − 10 , 2) ( − 4 , 0) ( − 6 , 2) (0 , 0) (0 , − 4) (6 , 0) ( − 2 , − 4) (4 , 0) 1 1 2 2 2 2 Figure 1: Extensive Form. (b) For firm 1, there are four possible strategies pp, pn, nn and np . The first letter corresponds to firm’s 1 action when the cost is high, and the second one when the cost is low (e.g., np means “don’t build plant if cost is high, build plant if cost is low”). For firm 2 there are also 4 strategies EE,EN,NN and NE. The first letter corresponds to firm’s 2 action when firm 1 builds a plant, and the second one when firm 1 does not build a plant (e.g., EN means “enter the market if firm 1 builds a plant, do not enter the market if firm 1 does not build a plant”). The entries of the matrix are expected payoffs. Firm 1 Firm 2 EE EN NN NE pp pn nn np ( − 5 , − 1) ( − 5 , − 1) (1 , 0) (1 , 0) ( − 6 , − 1) ( − 3 , 1) (0 , 0) ( − 3 , − 2) ( − 4 , − 1) (2 , 0) (2 , 0) ( − 4 , − 1) ( − 3 , − 1) (0 , − 2) (3 , 0) (0 , 1) Figure 2: Normal Form. 2. (a) We first compute the bequest that the parent will choose when the child’s action is A . The (b) (5pts) When we write a strategy of firm 1, we first write the action the firm takes when the costs are high and then the action the firm takes when the costs are low. So, with strategy pn, firm 1 builds the plant only when the costs are high. For the strategies of firm 2 we first write the action that the firm takes when firm 1 builds a plant. MS&E 246: Game Theory with Engineering Applications Problem Set 4 February 19, 2009 1. (a) Firm 1 chooses whether to build a plant (p) or not (n). Firm 2 chooses whether to enter (E) or not (N)....
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ps3(2010)_soln - MS&E 246 Game Theory with Engineering...

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