Rock-paper-scissors is a game in which players typically use mixed strategies. Can you think of other examples? What are some of the characteristics of games that usually involve playing mixed strategies?
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Rock-paper-scissors is a game in which players typically use mixed strategies. Can you think of other examples? What are some of the characteristics of games that usually involve playing mixed strategies?
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- Answer all the questions, show all the working. Consider the following game in normal form. Not cooperate Cooperate Not cooperate 20,20 50,0 Cooperate 0,50 40,40 What is Nash equilibrium? Is it efficient? Why? What needs to be complied with so that the players would like to cooperate? What happens when one of the players does not cooperate? Why? Define trigger strategy. Calculate the discount factor (δ) that would make both players decide to cooperate.Use the following normal-form game to answer the questions below. Player 1 (B.C) (B.D) (A.C) (A.D) Strategy A B a. Identify the one shot Nash equilibrium. 60, 60 30, 130 Yes Player Z D 130, 30 80, b. Suppose the players know this game will be repeated exactly three times, Can they achieve payoffs that are b shot Nash equilibrium?Use the following normal-form game to answer the following questions. a. For what values of x is strategy D (strictly) dominant for player 2? b. For what values of x is strategy B (strictly) dominant for player 1? c. For what values of x is (B, D) the only Nash equilibrium of the game?
- 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…Use the following one-shot, normal-form game to answer the following questions a. Find each player’s dominant strategy, if it exists. b. Find each player’s secure strategy. c. Find the Nash equilibrium.The order of play tends to matter in sequential games where rivals must predict best reply-responses and counter-responses in order to achieve a desired payoff. Discuss an instance in which you or your firm used game theory and explain why the relationship between the players was a strategic one. Did the use of a credible threat or commitment affect the outcome? Were there any first-mover of fast-second strategies used?
- In game theory, what are some conflicts (history/fiction) in which there is a nash equilibrium between 2 actors?Explain the nature of game theory. What current issue could this be applied to?Can you explain the "altruism and reciprocity" game theory, and provide an example? Is this the same as the "trust game?"
- In a small town there are two pizza restaurants . If neither restaurant advertises, its revenue will not change. If only one firm advertises, the firm that advertises will double its revenue and the firm that doesn't advertise will see a decrease in its revenue, but if both firms advertise, their revenue will not change. What outcome would be predicted by game theory in this market? Both restaurants will advertise. Game theory would predict chat sometimes one restaurant would advertise, and the rest of the time both will advertise. Neither restaurant will advertise Game theory is only a theory and cannot predict real-world events. One restaurant will advertise.QUESTION 18 Imagine the following game: The players: Emirates Airlines and Etihad Airlines The choice: cut fares by 50% or leave fares alone If both airlines cut fares, Each airline's profit = 400 million If neither airline cuts fares, Each airline's profit = 600 million If only one airline cuts its fares, Its profit = 800 million The other airline's profits = 200 million How many million each company will make in the Nash equilibrium of the game?Consider the following game where two players have to decide if they want to buy a movie ticket or a baseball ticket. They have the highest payoffs when they both buy tickets to the same activity, but must decide simultaneously what to buy without knowing what the other person will do. a. Does either player have a dominant strategy? b. How many equilibria does this game have? c. Is this an example of a prisoner’s dilemma? Explain. d. What will be the outcome if your friend buys their ticket first and you can observe their choice?
