14fe221ps1soln - Econ 221(002 004 Winter Session Term I 2014 M Vaney Problem Set 1 Solutions 1 Show a game matrix for a 2 player game where each player

14fe221ps1soln - Econ 221(002 004 Winter Session Term I...

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Econ 221 (002 & 004) Winter Session Term I, 2014 M. Vaney Problem Set 1 - Solutions 1. Show a game matrix for a 2 player game where each player has 2 strategies to choose from and: (a) both players have strictly dominant strategies. Player 2 L R Player 1 U (12 ; 5) ° (14 ; 9) ° D (8 ; 8) (11 ; 13) ° (b) player 1 has a weakly dominant strategy, player 2 does not have either a strictly or weakly dominant strategy. Player 2 L R Player 1 U ° (12 ; 5) ° (11 ; 9) ° D (8 ; 8) ° ° (11 ; 3) (c) there are 2 pure strategy Nash equilibria to the game. Player 2 L R Player 1 U ° (12 ; 5) ° (11 ; 2) D (8 ; 8) ° (13 ; 13) ° (d) there is no pure strategy Nash equilibrium to the game. Player 2 L R Player 1 U ° (12 ; 5) (7 ; 9) ° D (8 ; 8) ° ° (11 ; 3) 2. In the following game, Player 2 w x y z a ° (3 ; 2) (1 ; 1) ° (4 ; 3) (3 ; 5) ° Player 1 b (1 ; 3) ° (3 ; 0) (2 ; 4) ° ° (4 ; 2) c (2 ; 1) (0 ; 1) (1 ; 2) ° (1 ; 0) d (1 ; 0) (2 ; 0) (2 ; 1) ° (4 ; 0) °nd any strategies that are: 1
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(a) Strictly dominant. - No strategy is strictly dominant for either player (this would require all best responses to line up along a single row for player 1 or along a single column for player 2) : (b) Strictly dominated. - For player 1 ; c is strictly dominated by a: For player 2 ; w is strictly dominated by y and x is strictly dominated by y . (c) For player 1 : a and b are the only two strategies that are best responses. For player 2 : y and z are the only two strategies that are best responses. 3. A particular street corner is a popular location for food carts to sell lunch to people working in the area. Two vendors must each decide in the morning whether to operate carts on a particular day or stay at home. One vendor operates a small size Hot Dog cart ( H ), the other vendor operates a Thai food cart ( T ). The Thai food vendor can choose to bring either a large cart or a small cart. There is a higher cost of operating the large cart (additional person), but the Thai food vendor will serve a larger share of the customers. There is °xed demand for 40 lunches at $10 each (Total market sales/revenue will be $400 ). The cost of operating a small cart is $100 (for both H and T ), while the cost of operating the large Thai food cart is $150 : When only one vendor shows up to the street corner they will get 100% of the sales. If both show up with small carts the two vendors split sales evenly. When the Thai food vendor shows up with a large cart they will get 75% of the sales ( 25% to the Hot Dog vendor). (a) Can this economic interaction be modeled as a game? If so, identify all the ele- ments that make this a well-de°ned game. Players: vendors H and T Rules: simultaneous. Strategies available to H : bring a S mall cart or N o cart (stay home). Strategies available to T : operate L arge cart, operate S mall cart or N o cart (stay home). Outcomes: all the ways that the game can be played. (6 possible outcomes). Payo/s: the pro°ts to each vendor, ° H and ° T .
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