1. Represent each of the following strategies for an infinitely repeated Prisoner’s Dilemma game in a diagram.
(a) Choose C in period 1 and after any history in which the other player chose C except, possibly, the previous period; choose D after any other history. (That is, punishment is grim, but its initiation is delayed by one period.)
(b) Choose C in period 1 and after any history in which the other player chose D in at most one period; choose D after any other history. (That is, punishment is grim, but a single lapse is forgiven.)
(c) Tit-For-Two-Tat: Choose C in period 1 and after any history in which the other player did not choose D in the previous two periods; choose D after any history in which the other player chose D in the previous two periods.
1. Represent each of the following strategies for an infinitely repeated Prisoner’s Dilemma game in a...
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: 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...
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...
2. (Level A) Suppose the following Prisoner's Dilemma is repeated infinitely: 12 C D D 01 1 Let ul 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 2-Period Limited Retaliation Strategy (2-LRS). That is, each player plays the following strategy: Play...
2. (Level A) Suppose the following Prisoner's Dilemma is repeated infinitely 112 C D Dlx 011 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 t=1 where δ-1 is the common discount factor of both players Suppose the players try to sustain (C, C) in each period by the 2-Period Limited Retaliation Strategy (2-LRS). That is, each player plays the following strategy . Play C in...
Exercise 2 - A variation ofthe Prisoner's Dilemma game. Consider the following Prisoner's Dilemma game. The game coincides with that we discussed in class, except for the fact that every player sees his payoff decrease by m>0 when he chooses to confess. For instance, prisoner 1's payoff decreases by m in the top row (where he confesses) but is unaffected when he is at the bottom row (where he does not confess). A similar argument applies to prisoner 2, who...
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...
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...
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 L CR T|10 1012 1210 13 M 12 25 5 0 (0 B113 0100 (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. Consider the...