Problem 10 Find all pure-strategy Nash Equilibria of the three-player game below. Notice that player 3...
a.) Find all pure-strategy Nash equilibria. b.) *Find all mixed-strategy Nash equilibria. c.) Explain why, in any mixed-strategy equilibrium, each player must be indifferent between the pure strategies that she randomizes over. Consider the following game: - 2 LR 2
Game Theory: Put the given game in strategic form, Find all pure strategy Nash equilibriam, Change a single outcome so that B weakly dominates A for player I. Please Explain what the lines mean and explain each step in how to do this problem! 1,1,4 II 2,2,2 -2,-2,-2 3,2,0 5,-1,4 0,0,0 a) Put the given game in strategic form. b) Find all pure strategy Nash equilibria. c) Change a single outcome so that B weakly dominates A for player I
4. Find all pure-strategy and mixed-strategy Nash equilibria of the following two-player simultaneous-move games. Player B LeftRight 6,5 2,1 Up 0,1 Player A 6,11 Down Player B LeftRight 1,4 0,16 2,13 4,3 Up Player A Down 4. Find all pure-strategy and mixed-strategy Nash equilibria of the following two-player simultaneous-move games. Player B LeftRight 6,5 2,1 Up 0,1 Player A 6,11 Down Player B LeftRight 1,4 0,16 2,13 4,3 Up Player A Down
Determine ALL of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following 3 games: Player 1 H T Player 2 HT (1, -1) (-1,1) | (-1,1) (1, -1) | Н Player 1 H D Player 2 D (2, 2) (3,1) | (3,1) |(2,2) | Player 2 A (2, 2) (0,0) Player 1 A B B (0,0) | (3,4)
Find all the Nash equilibria in the following game and indicate which are strict. Player 2 d b a -1,4 1,-3 2,7 W 2,7 Player 1 2.1 0,4 1, 3 1, 2 Y -1,6 6,2 3.2 1,1 Z 7,1 5.2 0.2 3,1 O (Wa) and (W,c). Neither are strict. O (W,c) and (Z,b). Both are strict O (Wc) and (Z,b). Neither are strict. O There are no Nash equilibria in this game.
6. Consider the following game: a. Identify all Nash Equilibria (Pure Strategy and Mixed) of this simultaneous game. b. Draw the two extensive form games that arise from each firm moving first. What are the Subgame Perfect Equilibria of these games? c. Identify a trigger strategy for each player that sustains (B,B) as an equilibrium. For what interest (discount) rates will this outcome be sustainable?
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.
Consider the following game: a) Identify all Nash Equilibria (Pure Strategy and Mixed) of this simultaneous game. b) Identify a trigger strategy for each player that sustains (B,B) as an equilibrium in an infinitely repeated game. For what interest(discount) rates will this outcome be sustainable? Firm 2 А B A -5,-5 195,-50 Firm 1 -50,215 45,75
Q3 Three-Player Game Consider a 3-player matrix game. The correct interpretation is as follows: the row indicates which strategy was chosen by player I; the column indicates which strategy was chosen by player II. If player III chooses strategy X, then the three players' payoffs are given by the first matrix; if player III chooses strategy Y , then the three players' payoffs are given by the second matrix. II II LR 4, 7, 5 8, 1, 3 1, 1,8...
GAME MATRIX Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria. Consider two players (Rose as player...