1. Consider a gaine where the row player moves first, choosing between T and B. The...
Q.2 Consider the following normal-form game: Player 2 Player 1 3,2 1,1 -1,3 R. 0,0 Q.2.a Identify the pure-strategy Nash equilibria. Q.2.b Identify the mixed-strategy Nash equilibria Q.2.c Calculate each player's expected equilibrium payoff.
3. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, z. The game is presented in the following matrix: W Z X y a 3,3 2,1 0,2 2,1 b 1,1 1,2 1,0 1,4 0,0 1,0 3,2 1,1 d 0,0 0,5 0,2 3,1 с Find all the Nash equilibria in the game in pure strategies.
1. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, 2. The game is presented in the following matrix: a b c d w 3,3 1,1 0,0 0,0 x 2,1 1,2 1,0 0,5 y 0,2 1,0 3, 2 0,2 z 2,1 1,4 1,1 3,1 (a) Find the set of rationalizable strategies. (b) Find the set of Nash...
Consider the following two person static game where Player 1 is the row player and Player 2 is the column player C D A 1, 0,2 2,0 B 0,0 1,3 O a. There is an equilibrium where Player 1 plays A with probability 3/4 O b. There is no mixed strategy Nash equilibrium O c. There is an equilibrium where Player 1 plays A with probability 2/3. O d. There is an equilibrium where Player 1 plays A with probability...
1. (60 marks) Consider a two-person game, in which every player has two pure strategies to play. The payoff matrix of the game is as follows Strategy 2 Player One Player Two Strategy I Strategy II Strategy 1 0,0 1,3 1,1 Find all the Nash equilibria of the game.
3. Player 1 and Player 2 are going to play the following stage game twice: Player 2 Left Middle Right Player 1 Top 4, 3 0, 0 1, 4 Bottom 0, 0 2, 1 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...
onsider the following two person static game where Player 1 is the row player and Player 2 is the column player C D E A 1,1 0,2 2,0 B 0,0 1,-1 -1,3 a. There is an equilibrium where Player 1 plays A with probability 3/4. b. There is an equilibrium where Player 1 plays A with probability 2/3. c. There is an equilibrium where Player 1 plays A with probability 1/2. d. There is no mixed strategy Nash equilibrium.
2. (25 pts) Consider a two player game with a payoff matrix (1)/(2) L U D R (2,1) (1,0) (0,0) (3,-4) where e E{-1,1} is a parameter known by player 2 only. Player 1 believes that 0 = 1 with probability 1/2 and 0 = -1 with probability 1/2. Everything above is common knowledge. (a) Write down the strategy space of each player. (b) Find the set of pure strategy Bayesian Nash equilibria.
1. Consider the coupon game. But suppose that instead of decisions being made simultaneously, they are made sequentially, with Firm 1 choosing first, and its choice observed by Firm 2 before Firm 2 makes its choice. a. Draw a game tree representing this game. b. Use backward induction to find the solution. (Remember that your solution should include both firms’ strategies, and that Firm 2’s strategy should be complete!) 2. Two duopolists produce a homogeneous product, and each has a...
2) True or false: The strategy profile where player 1 plays B and player 2 plays C is a Nash equilibrium 3) True or false: The strategy profile where player 1 plays B and player 2 plays B is a Nash equilibrium? True or false: The strategy profile where player 1 plays B and player 2 plays C is a Nash equilibrium? Player 2 A 4,4 1,1 Player 1 B 1,1 1,1 C 5,0 0,0