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- 1. Solve for the mixed strategy Nash equilibrium of the game above. Explain carefully how you solve for it. 2. In the equilibrium you calculated above, what is the probability that both consoles are released in October? In December? What are the expected payoffs of firm A and of firm B in equilibrium?1. Describe all the pure and mixed strategy Nash equilibria in the game below. ABC A 1, 1 2,1 0,0 B 1,2 2,2 4, 1 с 0,0 1,4 0,011. What are the subgame perfect equilibria of the following game? Out In T B 7,21 L R L/R 9,3 1,1 1,1 3,9 (a) (InT, L), (OutB, R) and (OutT+OutB, L + R). (b) (InT, L) and (OutB, R). (c) Out and (InT, L). (d) (InT, L), (OutB, R) and (OutT+OutB, L + R). (e) (InT, L). 2
- a) Find the pure strategy Nash Equilibrium for the subgame starting at player l's second decision node. b) Find the Subgame Perfect Nash Equilibria for the entire game. 1 Withdraw Not 2 Withdraw Not Withdraw Not 10 2 6 2 10 Not Withdraw 2 Withdraw Not Withdraw Not 15 20 10 15 15 10 20 15 4915) Find all Nash equilibria (both pure and mixed strategy) in the following game Player 2 Left Right Player 1 Up 10,8 0,5 Down 4,0 3,6Question Completion Status: Consider Game 3: -10 -20 -20 3. 30 -30 -10 Write a normal form for this game. How many pure-strategy Nash Equilibria are there in this game? OA. 1 O8.2 OC3 O0.4 OE. 5 OF More than 5
- Q2 Hand written plz Find any Nash equilibria in the following normal form game and indicate which Nash equilibria, if any, are strict. Player 2 b a W 3,5 1, -3 Player 1 x 2,-4 1,2 5,2 1, 1 7,1 5,2 Y 2 d C 2,5 -1,4 3,4 0,3 -2,5 3,2 0,2 3,21. Find all of the pure strategy Nash Equilibrium to the following simultaneous move game. Show all of your work. Row a b C d e A 9,4 14,8 7,8 15,0 20,18 B 12,10 3,10 6,8 7,4 2,9 Column C 15,7 12,18 20,10 14.2 10,14 D 2,8 4,7 3,12 5.3 3,7 E 15,5 20,12 15,9 9,1 19,203. 1 2 J K 2 1 2 0 0 K 3 3 E/ 1.1 2.2 B G 2 -2 a.) How many Subgames does this Game have? b.) Convert this Game Tree into matrix form. c.) Find all Pure Strategy Nash Equilibria of this Game. d.) Find all Subgame Perfect Nash Equilibria of this Game. (Pure and Mixed) 2 2.2
- 1. Consider a repeated game in which the following stage game is played in each of two periods and there is no discounting. U Player 1 M D L 5,5 0,0 0,12 Player 2 C 0,0 2,2 0,0 R 12,0 0,0 10, 10 a) Find the Nash equilibrium that maximises the players' final payoffs, i.e. the sum of their payoffs from each period. I b) Discuss the intuition of this equilibrium.Costco Spend $1B on advertising Spend $1.5B on advertising Spend $1B on advertising $3.5B; $2.7B $4.2; $2.2B Target Spend $1.5B on advertising $3.2B; $3.4B $4B; $3B3. Player 1 and Player 2 are going to play the following stage game twice: Player 1 Top Bottom Left 4,3 0,0 Player 2 Middle 0,0 2,1 Right 1,4 0,0 There is no discounting in this problem and so a player's payoff in this repeated game is the sum of her payoffs in the two plays of the stage game. (a) Find the Nash equilibria of the stage game. Is (Top, Left) a Nash of the stage game? (b) Find a subgame perfect Nash equilibrium of the repeated game where the first time they play the stage game Player 1 chooses Top and Player 2 chooses Left.