1. In the extensive form representation of the game between Player 1 and Player
ID: 1146408 • Letter: 1
Question
1. In the extensive form representation of the game between Player 1 and Player 2, Player 1 moves first and chooses L or R. If Player 1 chooses R the game ends, if Player 1 chooses L then Player 1 and 2 play a simultaneous move game. The game has Blank 1 pure strategy Nash equilibria and Blank 2 pure strategy Subgame Perfect Nash Equilibria (SPNE). The maximum payoff Player 2 gets in a SPNE is Blank 3. (Please, enter only numerical answers like: 1, 2, 3, ...)
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2. Four bidders participate in first price auction for a single object that is of the following value to them:
V1 = 150, V2 = 100, V3 = 90, V4 = 80
The information above is known to all (i.e., each bidder knows not only his own valuation but also that of the other bidders). If two bidders or more bidders place the same bid, one of them is selected at random to be the winner. Select all that apply
a. There's a Nash Equilibrium where the bids are: b1 = 99, b2 = 98, b3 = 90, b4 = 80
b. There's a Nash Equilibrium where the bids are: b1 = 150, b2 = 100, b3 = 90, b4 = 80.
c. There's a Nash Equilibrium where the bids are: b1 = 103, b2 = 102, b3 = 84. b4 = 74
d. There's a Nash Equilibrium where each bidder offers half of his value of the object.
e. There is a NE in which player 1 wins the object
2 (3,2) (0,0) (2,4) (5,4) (0,0)Explanation / Answer
Answer 1;
The above game has two pure strategy Nash equilibria - 2,4 and 5,4
It also has two sub game perfect Nash equilibria.
In a sub game perfect Nash equilibria, the maximum pay off that player 2 gets is 4.
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