What would you do? What would be considered ‘rational’ from the perspective of utility maximization? What would you do if this is a continued game and the same scenario will happen multiple times not just once? Do you think others will react the same way you would?
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So imagine you are playing this game as the second player and you are both given a 10 dollars and the dictator decides to offer you 25 cents and that she/he will keep $9.25. Your only choice is to accept the 25 cents or reject the offer and get no money at all.
What would you do? What would be considered ‘rational’ from the perspective of utility maximization? What would you do if this is a continued game and the same scenario will happen multiple times not just once? Do you think others will react the same way you would?
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- In 'the dictator' game, one player (the dictator) chooses how to divide a pot of $10 between herself and another player (the recipient). The recipient does not have an opportunity to reject the proposed distribution. As such, if the dictator only cares about how much money she makes, she should keep all $10 for herself and give the recipient nothing. However, when economists conduct experiments with the dictator game, they find that dictators often offer strictly positive amounts to the recipients. Are dictators behaving irrationally in these experiments? Whether you think they are or not, your response should try to provide an explanation for the behavior.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…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.
- 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.Suppose you are playing a game in which you and one other person each picks a number between 1 and 100, with the person closest to some randomly selected number between 1 and 100 winning the jackpot. (Ask your instructor to fund the jackpot.) Your opponent picks first. What number do you expect her to choose? Why? What number would you then pick? Why are the two numbers so close? How might this example relate to why Home Depot and Lowes, Walgreens and Rite-Aid, McDonald’s and Burger King, and other major pairs of rivals locate so close to each other in many well-defined geographical markets that are large enough for both firms to be profitable?Consider the following game. You will roll a fair, 6-sided die either once or twice. You decide whether to do the second roll after you see how the first one lands. The payoff is $n, where n is the outcome of the last roll. For example, if the first roll lands 4 and the second lands 2, you win $2. If you only do one roll and it lands 4, you win $4. Suppose you make your decision about whether to go for a second roll based on expected monetary value. Then you will go for a second roll if (and only if) the first roll lands x or lower. What is x?
- Consider a game where player A moves first, choosing between Left and Right. Then, after observing player A’s choice, player B moves next choosing between Up and Down. Which of the following is true? This is a game where players A and B have the same number of strategies. Player A will get a higher payoff than player B as A moves first. This is game will only have one Nash equilibrium. This is a game of perfect information.In 2003, Saudi Arabia and Venezuela produced an average of 8 million and 3 million barrels of oil a day, respectively. Production costs were about $10 a barrel and the price of oil averaged $28 per barrel. Each country had the capacity to produce an additional 1 million barrels per day. At that time, it was estimated that each country 1-million-barrel increase in supply would depress the average price of oil by $3. A. Draw a normal form representation of a game where Saudi Arabia has 2 possible actions to produce 8 million or 9 million barrels of oil and Venezuela has 2 possible actions: to produce 3 or 4 million barrels of oil. Fill in the payoffs for each player and action. Draw a table. B. What action should each country take and why? C. Does the asymmetry in the countries' sizes cause them to take different attitudes towards expanding out? Explain why or why not.. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that
- Describe the game and find all Nash equilibria in the following situation: Each of two players chooses a non-negative number. In the choice (a1, a2), the payoff of the first player is equal to a1(a2 - a1), and the payoff of the second player is equal to a2(1 – a1 – a2).Suppose that two bears play a Hawk-Dove game as discussed in class. The payoff to each bear is -6 if both play Hawk. If both play Dove, the payoff to each bear is 3, and if one plays Hawk and the other plays Dove, the one that plays Hawk gets a payoff of 8 and the one that plays Dove gets 0. Describe the pure strategy and mixed strategy Nash equilibria in this game? What are the utilities to each bear in the mixed strategy Nash equilibria?Consider a sequential game where there are two players, Jake and Sydney. Jake really likes Sydney and is hoping to run in to her at a party this weekend. Sydney can't stand Jake. There are two parties going on this weekend and each player's payoffs are a function of whether they see one another at the party. The payoff matrix is as follows: Sydney Party 1 Party 2 Party 1 6, 18 18, 6 Jake Party 2 24,8 0,24 a) Does this game have a pure strategy Nash Equilibrium? b) What is the mixed strategy Nash Equilibrium? c) Now suppose Sydney decides what party she is going to first. Her roommate is friends with Jake and will call him to tell him which party they go to. Write the extensive form of this game (game tree). d) What is the subgame perfect Nash equilibrium from part c?