Consider a game between 2 payers (Ann and Bill) where each chooses between 3 actions (Up, Middle and Down). 1) Create a payoff matrix that reflects this. 2) Fill in payoff numbers that makes this game a Prisoner's Dilemma. 3) Explain why your game is a Prisoner's Dilemma.
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Consider a game between 2 payers (Ann and Bill) where each chooses between 3 actions (Up, Middle and Down).
1) Create a payoff matrix that reflects this.
2) Fill in payoff numbers that makes this game a Prisoner's Dilemma.
3) Explain why your game is a Prisoner's Dilemma.
Step by step
Solved in 2 steps
- Is the solution to the prisoner’s dilemma game a Nash equilibrium? Why? The solution to the prisoner’s dilemma game is a Nash equilibrium because no player can improve his or her payoff by changing strategy unilaterally. The solution to the prisoner’s dilemma game is not a Nash equilibrium because players do not end up in the best combination for both. The solution to the prisoner’s dilemma game is not a Nash equilibrium because both players can improve their payoffs by cooperating. The solution to the prisoner’s dilemma game is a Nash equilibrium because it is a noncooperative game in which both players have to expect that the other is purely selfish.Table 15.4, Prisoner Dilemma. Suppose the game starts with both Jesse and Frank planning to “Stay Mum” in the lower right cell. Discuss how each player would evaluate the situation and decide whether to change decisions. If each player makes decisions to minimize the penalty, in which cell will this game end? Is there a Nash equilibrium?Three married couples in the state of Maryland—Bob and Carol, Ted and Alice, and Ross and Mike (remember, same-sex marriage is legal in the state of Maryland)—are thinking about renting a boat to go sailing on the Chesapeake Bay. The cost of a boat rental is $600. Each of the three couples puts some amount of money in an envelope. Thus, each player in this game is a couple. If the total amount collected is at least $600, then the boat is rented. If the amount collected is more than $600, then the money left over after renting the boat is spent on wine. If the total amount collected is less than $600, then they do not rent the boat, and the money is spent on a dinner. Assume the benefit to a couple from the boat trip is 400, the benefit from each dollar spent on wine is 50 cents, the benefit from each dollar spent on dinner is 40 cents, and the personal cost of the contribution to a couple equals the amount of contribution. For example, if the boat is rented, $50 of wine is purchased…
- Suppose that you and a friend play a matching pennies game in which each of you uncovers a penny. If both pennies show heads or both show tails, you keep both. If one shows heads and the other shows tails, your friend keeps them. Show the pay- off matrix. What, if any, is the pure-strategy Nash equilibrium to this game? Is there a mixed-strategy Nash equilibrium? If so, what is it?Can you explain the "altruism and reciprocity" game theory, and provide an example? Is this the same as the "trust game?"a.) Suppose you manage a large company’s marketing department and are responsible for deciding whether or not to advertise in the Super Bowl. Your team of analysts estimate that for each advertisement, your firm would generate $6 million in additional revenue for the company. It cost $7 million to run a 30-second advertisement. Therefore, your company would expect to lose $1 million in profit for each advertisement. b.) Depict this situation with a game theory payoff matrix. Your company (A) and a major competitor (B) have two potential strategies: to advertise or to not advertise during the Super Bowl. The payoffs in each cell represent the change in firm profits from advertising. Create payoffs in each cell such that the Nash equilibrium is that both firms advertise despite having a higher profit if neither firm advertised
- Imagine a game where individuals can be either cooperative (like splitting a resource) or selfish (like grabbing the entire resource). Depending on the relative costs and benefits of interacting and the resource, there might be a variety of possible payoff matrices for such an interaction. Of the following matrices, which one illustrates the largest “temptation to cheat?”Economics Game theory: Consider a collective action game with thirty individuals (N = 30). When the number of participants in the joint project is n, each individual, including shirkers, receives a benefit of B(n) = 18n and each participant incurs a cost of C(n) = 32 – 2n. Please answer the questions I am asking! 1. Find all of the Nash equilibria, both stable and unstable ones. 2. Find the socially optimal outcome. 3. Check if any of the Nash equilibria is socially optimal. Explain your answer.Two firms are competing on price. If they have the same price, they share the market - otherwise the one with the lowest price captures all demand Market demand follows Q(P)=100-3P Cost is C(Q)=10Q Firms can only choose between the following prices: 9, 10, 11, 12. In the Nash equilibrium of this game, what prices are charged? Suggestion: calculate the profits they obtain for each of the price combinations, write down the game in its normal form (payoff matrix), and then use the underlining method to match best responses. 12 11 9 10
- Game theory can capture strategic situations where your outcome depends not only upon your own choice but also upon the choice of another. Present a coordination game of your choice where you and another player each have two choices or strategies. Explain in words the Nash Equilibrium concept, and identify the Nash equilibrium or Nash equilibria for your game. Explain why the outcomes that are not Nash equilibria are not.Use the following payoff matrix to answer the questions below. Cooperate Defect 1 Cooperate 100, 100 40, 125 Defect 125, 40 50, 50 Which player (if any) has a Dominant Strategy? [ Select ] What is the Nash Equilibrium of this game? [ Select ] Does this game satisfy the definition of a prisoner's dilemma? [ Select ]Here is a payoff matrix that is interesting. I am not in an imaginative mood, so I won't try to tell a story about why the payoffs come out this way. Find all the pure-strategy Nash equilibria. Is this a game where you expect that players would end up in a Nash equilibrium? What would you expect to happen and why? Row Top Row Bottom Column Left 4, -3000 12,8 Column Right 10,6 5, 4
