2. (Finitely Repeated Game). Consider the following simultaneous move game as depicted below is played twice. The players observe the actions chosen in the first stage of the game prior to the second stage. What are the pure strategy subgame perfect Nash equilibria of this game? Player 2 B1 B2 B3 Player A1 10, 10 2,12 0,13 1 A2 12,2 5,5 0,0 A3 13,0 0,0 1,1
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- 1. Consider the following normal-form game: Player 2 Left Right 30,20 10,10 10,30 20,20 Player 1 How many pure-strategy Nash Equilibria are there in this game? (a) 0 (b) 1 Up Down (c) 2 (d) 3 (e) 4 (f) None of the above Answer: 1b. The only Nash Equilirbium is (Up,Left).1. Consider the following simultaneous move game Player 2 C D Player 1 A 4,3 4,-2 B 2,2 3,-1 C 3,0 4,0 d) Suppose the game is now played sequentially where Player 1 chooses first, player 2 observes 1’s choice and then makes his own choice. What are the Nash equilibria of this sequential game?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; $3B
- 15) 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 3,64. Suppose that Anne and Bob must simultaneously name a number in the set {1,2, ..., 10}. If they name the same number, the each get a payoff of 1; if they name different num- bers, they each get a payoff of 0. (a) Find all (pure and mixed strategy) Nash equilibria of this game. (b) How many are there? Explain why. (Hint: there are a lot of them!)3. 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.
- Consider the following two player extensive form game. メ (2,5) (4,) (3,5) a. Find the induced normal form of the given extensive form game using the pure strategies of the players. Find out all the possible Nash Equilibrium of this game. b. From the Nash Equilibrium you are getting in part a., which one is subgame perfect Nash Equilibrium? Explain with appropriate reasons. c. Explain why the NE in part b. is credible. (Use maximum 3 sentences):1. Find all mixed strategy Nash Equilibria for the games below. How many Nash Equilibria do these games have (including both pure and mixed strategy)? Player 2 A) R Player 1 2,2 4,1 E 1.4 3,3 B) Player 2 X y a 4,0 2,1 3,2 Player 1 b 2,2 3,4 0,1 2,2 1,2 0,3 c) Player 3: A Player 2 X y a 2,0,4 1,1,1 1,2,3, Player 1 3,2,3 0,1,0 2,1,3 b 1,0,2 0,0,3 3,1,1 Player 3: B Player 2 X y 2,0,3 4,1,2 1,2,2 a Player 1 b 1,3,2 2,2,2 0,4,0 0,0,0 3,0,3 2,1,05. Consider the following Extended Form game where P1 stands for Player one and P2 stands for player two with A, B and A', B' being their respective strategies. A' (1,1) P2 B' (2,3) P1 A' B (4,5) P2 What is the set of Nash Equilibria? Clearly explain your answer. Full-screen Snip B' (6,7)
- 9. Find all of the Nash equilibria for the three-player game here. Player 1 a b Player 3: A Player 2 X y Z 1,1,0 2,0,0 2,0,0 3,2,1 1,2,3 0,1,2 2,0,0 0,2,3 3,1,1 Player 1 a b C Player 1 Player 3: C X Player 2 y 2,0,0 0,1,2 0,1,1 1,2,1 3,1,2 0,1,2 a b C Player 3: B Player 2 X 2,0,0 1,2,0 0,1,2 Z 0,1,2 0,1,2 1,1,2 y 0,0,1 1,2,1 2,2,1 Z 2,1,2 1,2,1 2,1,03. 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(b) ROWENA up Answer 1: up Answer 2: In this simultaneous move game, the iterated dominance equilibrium is (Rowena's . Colin's left left Answer 3: ). This game has two Nash equilibria one of which is the iterated dominance equilibrium. The other Nash equilibrium, which is not the IDE, is (Rowena's down Colin's right down Up Down Answer 4: Left right 0,0 0,0 COLIN Right 0,0 1,1