What is the difference between 'grim trigger' and 'tit-for-tat' in the context of the repeated prisoner's dilemma? Tit-for-tat requires players to consider the entire history of past play when making their choice. O Grim trigger is able to achieve cooperation in some cases where Tit-for-Tat cannot. Grim trigger allows players to achieve the cooperative payoff. Grim trigger is more forgiving and allows for occasional defection. Tit-for-tat only defects after the opponent defects. O No Answer

What is the difference between 'grim trigger' and 'tit-for-tat' in the context of the repeated prisoner's dilemma? Tit-for-tat requires players to consider the entire history of past play when making their choice. O Grim trigger is able to achieve cooperation in some cases where Tit-for-Tat cannot. Grim trigger allows players to achieve the cooperative payoff. Grim trigger is more forgiving and allows for occasional defection. Tit-for-tat only defects after the opponent defects. O No Answer

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 15.1IP

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Two players, Player 1 and Player 2, are playing a repeated prisoner’s dilemma. Payoffs are described in the following matrix. Answer which statement is correct: Select one: a. A trigger strategy will never support (A,A) as an equilibrium b. A tit-for-tat strategy will never support (A,A) as an equilibrium c. A tit-for-tat strategy will support (A,A) as an equilibrium if δ > 0.7 d. A trigger strategy will support (A,A) as an equilibrium if δ > 0.7
Consider a modification of driving conventions, shown in the figure below, in which each player has a third strategy: to zigzag on the road. Suppose that if a player chooses zigzag, the chances of an accident are the same whether the other player drives on the left, drives on the right, or zigzags as well. Let that payoff be 0, so that it lies between –1, the payoff when a collision occurs for sure, and 1, the payoff when a collision does not occur. Find all Nash equilibria.
What is a prisoners' dilemma? a game that involves no dominant strategies a game in which prisoners are stumped because they cannot communicate with each other a game in which players act in rational, self-interested ways that leave everyone worse off a game in which players collude to outfox authorities
A strategy that a player will pursue regardless of any other player's decision is called _________. Question 10 options: game theory. collusion. prisoner's dilemma. dominant strategy.
Consider the following sequential strategic situation, called the centipede game. The game has 100 stages. Two players take turns making decisions, starting with player 1. At stage t = 1,...,99, player 1 (if the stage is odd) or player 2 (if the stage if even) chooses whether to "Terminate the game" or to "Continue the game." If the game is terminated instage t = 1,...,99, the player terminating the game receives a payoff of t, while the other player receives a payoff of zero. Finally, at stage t = 100, player 2 chooses between action A with a payoff of 99 for each player, or action B with a payoff of zero for player 1 and a payoff of 100 for player 2. Draw the game tree for this situation. What is the SPNE?
In the collusion game, collusion was only sustainable in the infinite horizon repeated game. One Nash Equilibrium of that game can be found when all players play a “grim trigger” strategy, where they collude until an opponent chooses to compete, and then compete for all future rounds as a punishment. In such a game, if the one period bonus that comes from competing is low enough, firms always collude and the punishment is never triggered. Is the punishment (vowing to compete forever after one deviates) realistic, especially if firms can communicate freely? Why or why not? (Hint: Is a grim trigger Nash Equilibrium a Subgame Perfect Nash Equilibrium? What kinds of Nash Equilibria does Subgame erfection rule out in sequential games?)
Which of the following is FALSE for the grim trigger strategy and the infinite horizon repeated Prisoner's Dilemma game illustrated above? A. In the grim trigger strategy profile, if a player chooses D in a period, then both players chooses D forever after that period B. The threshold discount factor for sustaining cooperation under grim trigger strategy depends on the utility numbers in the stage game C. If all utility numbers remain the same but 3 is replaced by 5 in the stage game, then cooperation CANNOT be sustained in this game for all possible values of the discount factor.
Two firms are playing an infinitely-repeated prisoner's dilemma pricing game of the following form: Firm 1 Firm 2 Low price High Price Low price 4, 4 20, 0 High price 0, 20 12,12 Consider the decision to cheat ONLY ONCE for a firm in this game against the opponent that is a Tit-for-Tat player. Cheating firm gets an extra in payoffs for the first round, but has to face $0 payoffs for the second round in order to be able to bring the opponent to the collusive outcome again in the third round. What is the minimum rate of return (r) that would make defecting only once? Show your calculations.
Microsoft and a smaller rival often have to select from one of two competing technologies, A and B. The rival always prefers to select the same technology as Microsoft (because compatibility is important), while Microsoft always wants to select a different technology from its rival. If the two companies select different technologies, Microsoft's payoff is 3 units of utility, while the small rival suffers a loss of utility of 1. If the two companies select the same technology, Microsoft suffers a loss of utility of 1 while the rival gains 1 units of utility.
Games to Pass the Time Set up the payoff matrix. You and your friend have come up with the following simple game to pass the time: at each round, you simultaneously call "heads" (H) or "tails" (T). If you have both called the same thing, your friend wins 1 point; if your calls differ, you win 1 point. Bored with the game described above, you decide to use the following variation instead: If you both call "heads," you win 3 points; if you both call "tails," you win 2 points; if your calls differ, then your friend wins 3 points if you called "heads" and 2 points if you called "tails." Friend H T You H T
The London Metro Bus is crowded for travel during peak hours. During such travel hours two daily passengers ‘James’ and ‘Robert’ enter the Metro. Luckily, two adjacent seats are free in the bus. Each of them must decide whether to sit or stand. For both, sitting alone is more comfortable than sitting next to the other person, which in turn is more comfortable than standing. consider James as ‘row player’ and Robert as ‘column player). a) Model the situation as a strategic game, assuming both ‘James’ and ‘Robert’ care only about their own comfort. Find the Nash equilibrium (equilibria) if it exists. Also, does a dominant strategy exist for either ‘James’ or ‘Robert’? show ALL steps and working in support to the answer
How many strategies does a player have in the repeated Prisoner's Dilemma Game with horizion 2 ? How many strategies does a player have in the repeated Prisoner's Dilemma Game with horizion 3 ?