Using the credible threat approach to find SPNE in the finitely repeated games ,where multiple pure strategy NE exist in the one stage of game
1. Consider the following normal form game 112 L CR T|10 1012 1210 13 M 12...
1. Consider the following normal form game: 112 L CR T 10 102 12 0 13 M 12 25 5 0 0 B|13 010 011 a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? (b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two...
1. Consider the following normal form game: 112 LC R T10 102 12 0 13 M 12 25 5 0 0 В|13 010 0111 (a) (Level A) First suppose this game is played only once. What are the pure strategy Nash equilibria? b) (Level B) Now suppose this game is played twice. Players observe the actions chosen in the first period prior to the second period. Each player's total payoff is the sum of his/her payoff in the two periods....
3. (Level A) Suppose the following Prisoner's Dilemma is repeated infinitely: 112 C D C 2, 2 0, 3 D 3,0 1, 1 Let uj be the payoff to player i in period t. Player i (i-1,2) maximizes her average discounted sum of payoffs, given by ( where o is the common discount factor of both players Suppose the players try to sustain (C, C) in each period by the Grim Trigger strategy. That is, each player plays the following...
3. (Level A) Suppose the following Prisoner's Dilemma is repeated infinitely 112 C D C 2, 2 0, 3 D 3, 0|1, 1 Let uļ be the payoff to player i in period t. Player i (i = 1, 2) maximizes her. average discounted sum of payoffs, given by ( where δ is the common discount factor of both players Suppose the players try to sustain (C, C) in each period by the Grim Trigger strategy. That is, each player...
Consider the infinitely repeated version of the symmetric two-player stage game in figure PR 13.2. The first number in a cell is player 1's single-period payoff. Assume that past actions are common knowledge. Each player's payoff is the present value of the stream of single-period payoffs where the discount factor is d. (a) Derive the conditions whereby the following strategy profile is a subgame perfect Nash Equilibrium: 2 Consider the infinitely repeated version of the symmetric two-player stage game in...
Exercise 6 (Difficult),. Consider the following modification of the prisoner's dilemma game. A-1,-1-9,0-6,-2 B | 0,-9 |-6-61-5-10 C1-2,-6 |-10,-51-4,-4 You should recognise the payoff's from (A, L), (A, R). (B, L). (B, R) as those in the prisoner's dilemma game studied in class. We added two strategies, one for each player. Also note that strategies A and L are still (when compared to the original prisoner's dilemma game) strictly dominated . What is the set of Nash equilibria of this...
3. (Level A) Suppose the following Prisoner's Dilemma is repeated infinitely: C 2, 2 0, 3 D 3,0 1, Let uj be the payoff to player i in period t. Player i (i 1,2) maximizes her average discounted sum of payoffs, given by ( o0 (1-6 X6u where o is the common discount factor of both players Suppose the players try to sustain (C, C) in each period by the Grim Trigger strategy. That is, each player plays the following...
Consider the following normal form game: U D LR 7,7 4,8 8,4 5,5 a. Are there dominant actions for any of the players? b. Find all Nash equilibria of this game. c. Suppose we repeat this game 10 times, specify a subgame perfect equi- librium of this finitely repeated game. d. Suppose this game is repeated infinitely: Identify a subgame perfect equilibrium of this game which gives an average (normalized) dis- counted payoff of 7 to both players. Clearly identify...
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash equilibria of the game. [8 Marks] b). Find the pure-strategy subgame-perfect equilibria of the game. [6 Marks] c). Derive the mixed strategy Nash equilibrium of the subgame. If players play this mixed Nash equilibrium in the subgame, would 1 player In or Out at the initial mode? [6 Marks] [Hint: Write down the normal-form of the subgame and derive the mixed Nash equilibrium of...
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...