1) For each of the games below find the reaction function of
Player 2 and the backwards-induction outcome. 
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1) For each of the games below find the reaction function of
Player 2 and the...
2) Consider the Stackelberg Model of Duopoly in the class slides. Assume that Firm 1 and...
2) Consider the Stackelberg Model of Duopoly in the class slides. Assume that Firm 1 and Firm 2 have different marginal costs of productions—that is, Firm 1’s marginal cost of production is c1 and Firm 2’s is c2. Under this assumption, answer the following questions. i) Let Firm 1 choose its quantity first. Find Firm 2’s reaction function and the backwards-induction outcome of the game. Also, find the profit of each firm at the backwards-induction outcome. ii) Let Firm 2...
Find all pure strategy Nash Equilibria in the following games a.) Player 2 b1 b2...
Find all pure strategy Nash Equilibria in the following games a.) Player 2 b1 b2 b3 a1 1,3 2,2 1,2 a2 2,3 2,3 2,1 a3 1,1 1,2 3,2 a4 1,2 3,1 2,3 Player 1 b.) Player 2 A B C D A 1,3 3,1 0,2 1,1 B 1,2 1,2 2,3 1,1 C 3,2 2,1 1,3 0,3 D 2,0 3,0 1,1 2,2 Player 1 c.) Player 2 S B S 3,2 1,1 B 0,0 2,3
FInd all the Nash Equilibria in these games. 10) Player 1 chooses row Player 2 chooses...
FInd all the Nash Equilibria in these games.
10) Player 1 chooses row Player 2 chooses column Player 3 chooses matrix 3.-2.-1 10.a) 1.2.3) 1.-2.-3 3.-2.-1
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated...
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? Player 2 Lett Center Right Top 0.2 4, 3 3,1 Player1 Middle 1, 2 2,0 2, Bottom 2,4 36 0,3 Player 2 Left Center Right Top 1, 3 ,4 ,2 Player 1 Middle 2,2 2 3,1 Bottom 3, 5 43 1, 4
Monitoring: An employee (player 1) who works for a boss (player 2) can either work (W)...
Monitoring: An employee (player 1) who works for a boss (player 2) can either work (W) or shirk (S), while his boss can either monitor the employee (M) or ignore him (I). As in many employee-boss relationships, if the em- ployee is working then the boss prefers not to monitor, but if the boss is not monitoring then the employee prefers to shirk. The game is represented by the following matrix: Player 2 M 1 1,1 1, 2 w Player...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of player 2's strategies. (2 points) (ii) Construct a payoff matrix and identify all Nash equilibria to the game. (2 points) (iii) Use backwards induction to find all subgame perfect equilibria of the game. (2 points)
Game consists of: • It costs $2 for the player to enter • Each round, the player announces a single number: {1, 2, 3, 4,...
Game consists of: • It costs $2 for the player to enter • Each round, the player announces a single number: {1, 2, 3, 4, 5, 6} • Two fair six-sided dices are rolled • For each die that shows the number announced, the player wins $1. For example, the player pays $2 to enter the game and announces the number 2. If the outcome of the roll is 3, 2, 2, then the player gets back $2. However, if...
5. Consider the game given in the adjoining (Figure 1). Player l's actions in the initial...
5. Consider the game given in the adjoining (Figure 1). Player l's actions in the initial node o are X and E. At the node c, player 1 has two actions 1 and r. Player 2's actions at the node a are li and r1. Player 2's available actions at the node b are l2 and r2. The payoffs are given in the terminal nodes. The first entry in any payoff vector corresponds to the paoff to player 1, and...
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated...
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? What are the Nash equilibria of these games? (a) Player 2 Left 0,2 1,3 2,4 Top Middle Bottom Center 4,3 2,4 1,5 Right 3, 4 2, 3 4,6 Player 1 (b) Player 2 Left 2,4 3,3 4,6 Top Middle Bottom Center 6,5 4,3 5,4 Player 1 Right 5,3 4, 2 2,5
Game consists of: • It costs $2 for the player to enter • Each round, the...
Game consists of: • It costs $2 for the player to enter • Each round, the player announces a single number: {1, 2, 3, 4, 5, 6} • Two fair six-sided dices are rolled • For each die that shows the number announced, the player wins $1. For example, the player pays $2 to enter the game and announces the number 2. If the outcome of the roll is 3, 2, 2, then the player gets back $2. However, if...
FInd all the Nash Equilibria in these games.
10) Player 1 chooses row Player 2 chooses column Player 3 chooses matrix 3.-2.-1 10.a) 1.2.3) 1.-2.-3 3.-2.-1
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? Player 2 Lett Center Right Top 0.2 4, 3 3,1 Player1 Middle 1, 2 2,0 2, Bottom 2,4 36 0,3 Player 2 Left Center Right Top 1, 3 ,4 ,2 Player 1 Middle 2,2 2 3,1 Bottom 3, 5 43 1, 4
Monitoring: An employee (player 1) who works for a boss (player 2) can either work (W) or shirk (S), while his boss can either monitor the employee (M) or ignore him (I). As in many employee-boss relationships, if the em- ployee is working then the boss prefers not to monitor, but if the boss is not monitoring then the employee prefers to shirk. The game is represented by the following matrix: Player 2 M 1 1,1 1, 2 w Player...
1. Consider the following extensive game: F G 2,1 3,1 0,2 2,3 (i) List all of player 2's strategies. (2 points) (ii) Construct a payoff matrix and identify all Nash equilibria to the game. (2 points) (iii) Use backwards induction to find all subgame perfect equilibria of the game. (2 points)
5. Consider the game given in the adjoining (Figure 1). Player l's actions in the initial node o are X and E. At the node c, player 1 has two actions 1 and r. Player 2's actions at the node a are li and r1. Player 2's available actions at the node b are l2 and r2. The payoffs are given in the terminal nodes. The first entry in any payoff vector corresponds to the paoff to player 1, and...
Q1 Elimination of strictly-dominated strategies In each of the following two-player games, what strategies survive iterated elimination of strictly- dominated strategies? What are the Nash equilibria of these games? (a) Player 2 Left 0,2 1,3 2,4 Top Middle Bottom Center 4,3 2,4 1,5 Right 3, 4 2, 3 4,6 Player 1 (b) Player 2 Left 2,4 3,3 4,6 Top Middle Bottom Center 6,5 4,3 5,4 Player 1 Right 5,3 4, 2 2,5
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