Consider the prisoners’ dilemma we discussed in class, with the following twist. If both prisoners choose...
Consider the prisoners’ dilemma we discussed in class, with the following twist. If both prisoners choose the same strategy (defect or cooperate) the payoffs are as in the original prisoners’ dilemma: when both cooperate each gets a payoff of 2 and if both defect each gets 1. However, if one of them defects and the other cooperates, the one cooperating is given the opportunity to revise his decision. If he does not revise then the payoffs are 3 for the one defecting and 0 for the one cooperating. If he switches to defect then he gets 1.5 and the other prisoner gets 1. what is the extensive form and normal form?
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Consider the prisoners’ dilemma we discussed in class, with the
following twist. If both prisoners choose...
1. Let's make a deal. Now suppose the two firms could agree to share technology secrets...
1. Let's make a deal. Now suppose the two firms could agree to share technology secrets and split the monopoly profits. If they both cooperate, they each earn 2, and if they both defect, they each earn 1 (payoffs are in billions of dollars). However, if one firm cooperates, the other can defect and earn 3, while the other earns 0. (a) Write down this prisoner's dilemma with a payoff matrix. (b) If the firms interact just once (1.e. the...
Exercise 2 - A variation ofthe Prisoner's Dilemma game. Consider the following Prisoner's Dilemma game. The...
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...
5. [20 points] Bruster's and Rita's both sell equally delicious ice cream and compete for the...
5. [20 points] Bruster's and Rita's both sell equally delicious ice cream and compete for the same customers. Each can offer customers a rewards card (offering free ice cream after a certain number of purchases) or not. Profits at each firm are greater if neither firm offers a rewards card than the case in which both do offer rewards cards. If one firm offers a rewards card and the other doesn't, the one offering the rewards card earns higher profits...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2....
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
3. (Level A) Suppose the following Prisoner's Dilemma is repeated infinitely: 112 C D C 2,...
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...
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...
Declining Industry: Consider two competing firms in a declining industry that cannot support both firms profitably....
Declining Industry: Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible choices, as it must decide whether or not to exit the industry immediately, at the end of this quarter, or at the end of the next quarter. If a firm chooses to exit then its payoff is 0 from that point onward. Each quarter that both firms operate yields each a loss equal to -1, and each quarter that...
2. (Level A) Suppose the following Prisoner's Dilemma is repeated infinitely 112 C D Dlx 011...
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...
3. (Level A) Suppose the following Prisoner's Dilemma is repeated infinitely 112 C D C 2,...
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...
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...
1. Let's make a deal. Now suppose the two firms could agree to share technology secrets and split the monopoly profits. If they both cooperate, they each earn 2, and if they both defect, they each earn 1 (payoffs are in billions of dollars). However, if one firm cooperates, the other can defect and earn 3, while the other earns 0. (a) Write down this prisoner's dilemma with a payoff matrix. (b) If the firms interact just once (1.e. the...
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...
5. [20 points] Bruster's and Rita's both sell equally delicious ice cream and compete for the same customers. Each can offer customers a rewards card (offering free ice cream after a certain number of purchases) or not. Profits at each firm are greater if neither firm offers a rewards card than the case in which both do offer rewards cards. If one firm offers a rewards card and the other doesn't, the one offering the rewards card earns higher profits...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
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...
Declining Industry: Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible choices, as it must decide whether or not to exit the industry immediately, at the end of this quarter, or at the end of the next quarter. If a firm chooses to exit then its payoff is 0 from that point onward. Each quarter that both firms operate yields each a loss equal to -1, and each quarter that...
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...
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...
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