Question 1 Consider the following extensive-form game. y R 2 А/ B 1,3 ay 1,-1 3,-2...
Question 2 Consider the following extensive form game. R 2 a А/ B 2,3 / 1 \ь 3, x 3,0 1, Each value of x defines a different game. 1. Solve this game by backward induction for x = 0 and for x = 2. For each of those values of x, what are the payoffs that player 2 can get in the solution? 2. Write this game in Normal form (The table can have an entry of the form...
Solve the following Extensive Form game by Backward Induction, then covert them into Normal Form and find the pure-strategy Nash equilibria in Normal Form. P1 V P2 (2, 2) P1 (1,3) B (3,4) (4,2)
Consider the extensive form game above. The game has _______ proper subgames. The strategy profile (AGJKM, CF) leads to a payoff of _______ for Player 1 and _________ for Player 2. In the backward induction equilibrium in pure strategies. Player 2 gets a payoff of ____________ (Please, enter only numerical values like: 0, 1, 2, 3,....). 2 36 8 LM 2 2 2 4 2 5
Consider the extensive form game above. The game has__________ subgames. The strategy profile (AGJKM, CE) leads to a payoff of_________ for Player 1 and____________ for Player 2. In the backward induction equilibrium in pure strategies Player 2 gets a payoff of______________ (Please, enter only numerical values like: 0, 1, 2, 3,....).
Q.1 Consider the following extensive-form game: Playxo Playr 2 o Player? 8, 6 8,5 7, 6 9, 7 Q.1.a Depict the corresponding normal form of the game. Q.1.b Identify the Nash equilibria. Q.1.c Identify the subgame-perfect Nash equilibrium by using backward induction.
1. The following is the extensive-form representation (omitting payoffs) of a game: ·N = {1, 2, 3): . H = 10, A, B, C. Ay, An, Ayy, Ayr, Any, Ann. Ba, Bb. Bc,CY.CN,CYY, CYN,CNY, CNN): ·Z = {Ayy, Ayn, Any, Ann, Ba, Bb. Bc, CYy, CYN,CNY, CNN): (1) Draw the corresponding game tree of the game; (8 points) (2) Write down the sets of strategies for each player; (7 points) (3) Suppose the information sets in this game are: (0),...
Problem 1. Consider the following extensive form game. 2 > 2,3 4,1 3,2 1.2 (a) By converting the game into normal form game (by finding the corre- sponding bimatrix game), find all Nash equilibrium in pure strategies. (b) Does player 2 have a strictly dominated strategy?
2,4 3, 6 6,7 7, 3 8, 1 9.2 4, 5 5, 4 Consider the extensive form game above. The game has for Plasyer 2. In the backward induction equilibrium in pure strategies Player 2 gets a payott of subgames. The strategy profile (AGUKM, CED) leads to a payoff of for Player 1 and (Please, enter only numerical values like: 0. 1.2,3)
4. (General Extensive Form Game ID Suppose the following general extensive-form game. Player 1 Player 2 (0, 4) (4,0 (4, 0) (0, 4) (a) Represent this game in normal form by using a matrix, and find all pure strategy (Bayesian Nash equilibrium (equilibria) b) Does a pure strategy perfect Bayesian equilibrium exist? If so, show it (or them). If not, prove it.
Game: Extensive Form. Suppose player 1 chooses G or H, and player 2 observes this choice. If player 1 chooses H, then player 2 must choose A or B. Player 1 does not get to observe this choice by player 2, and must then choose X or Y. If A and X are played, the payoff for player 1 is 1 and for player 2 it's 5. If A and Y are played, the payoff for player 1 is 6...