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- Consider the following situation. Maipo and Pisco need to decide how to divide a cake between the two of them. Both like cake and want to get as much cake as they can. They decide to let Maipo cut the cake first and then Pisco gets to pick which piece he wants. For simplicity, assume that Maipo can only cut the cake in two ways: He can either divide it into two pieces that are equal size (i.e., both will get half the cake) or he can divide the cake into two pieces where one piece is twice the size of the other (i.e., one will get a piece that is two-thirds of the cake and the other will get a piece that is one-third of the cake). Set up this game as a sequential game and draw the game tree that represents it Note: You can either draw the game tree by hand and then photograph/scan the tree and paste it into the assignment or use the drawing tool in Word to draw the tree. Find the sub-game perfect Nash Equilibria to this game. Underline the strategies or highlight the…Suppose that 2 roommates, Andy and Bob, are trying to pick an apartment in Chicago. Locations can be chosen from set of alternatives A={ x: x exists [0,1]}. Andy and Bob both want to minimize their daily commute but they work at different locations: Andy at xA=0.3, while Bob at xB=0.6. Specifically, their utility functions are: ui(x)= -(x-xi)2. Question: What is the set of all Pareto Efficient outcomes in A, assuming no money can be exchanged.Two friends are deciding where to go for dinner. There are three choices, which we label A, B, and C. Max prefers A to B to C. Sally prefers B to A to C. To decide which restaurant to go to, the friends adopt the following procedure: First, Max eliminates one of three choices. Then, Sally decides among the two remaining choices. Thus, Max has three strategies (eliminate A, eliminate B, and eliminate C). For each of those strategies, Sally has two choices (choose among the two remaining). a.Write down the extensive form (game tree) to represent this game. b.If Max acts non-strategically, and makes a decision in the first period to eliminate his least desirable choice, what will the final decision be? c.What is the subgame-perfect equilibrium of the above game? d. Does your answer in b. differ from your answer in c.? Explain why or why not. Only typed Answer
- Theo and Addy are deciding what toys to pick out at the toy store. Depending on what toys they pick, they can play different games together, but they can’t coordinate their choices. They can’t talk to one another at all until after that make their choice. Below is their payout matrix which shows their utility for each choice. All the bold figures are for Theo and all the non bold figures are for Addy. Addy Strategies Theo Strategies Toy Gas Pump Jump Rope Toy food 20 10 10 3 Ball 7 3 9 4 a) If Theo chooses Toy Food, what would be the possible outcomes for Addy? What would be best for Addy? b) If Addy chose a Toy Gas Pump, what are the possible outcomes for Theo? What would be best for Theo? c) Does Addy have a dominant strategy? If yes, what is her strategy? If not how can you tell? d) Does Theo have a dominant strategy? If yes, what is her strategy? If not how…7 my brother and I go out to dinner. There are two items on the menu – hamburgers ($7.5) and steak ($25). My brother and I each get $10 of enjoyment from hamburgers and $20 of enjoyment from steak. · What are the Nash equilibrium strategies/orders if we each pay for our own meal? · What are the Nash equilibrium strategies/orders if we split the final bill?Define the Various Mathematical Implications of Homoskedasticity?
- u work for a marketing firm that has just landed a contract with Run-of-the-Mills to help them promote three of their products: splishy splashies, flopsicles, and mookies. All of these products have been on the market for some time, but, to entice better sales, Run-of-the-Mills wants to try a new advertisement that will market two of the products that consumers will likely consume together. As a former economics student, you know that complements are typically consumed together while substitutes can take the place of other goods. Run-of-the-Mills provides your marketing firm with the following data: When the price of splishy splashies increases by 4%, the quantity of flopsicles sold increases by 1% and the quantity of mookies sold decreases by 5%. Your job is to use the cross-price elasticity between splishy splashies and the other goods to determine which goods your marketing firm should advertise together. Complete the first column of the following table by computing the…In the economy, is there only one efficient combination of goods?Andy, Brad, and Carly are playing a new online video game: Zombie Civil War. Each has an army of 100 zombies and must decide how to allocate them to battle each of the other two players’ armies. Three simultaneous battles are occurring: one between Andy and Brad, one between Andy and Carly, and one between Brad and Carly. Let Ab denote how many zombie soldiers Andy allocates to his battle with Brad, with the remaining 100 - Ab soldiers in Andy’s zombie army assigned to the battle with Carly. Bc denotes the number of zombie soldiers that Brad allocates to his battle with Carly, and 100 - Bc zombies go to his battle with Andy. Ca is the the number of zombie soldiers that Carly allocates to the battle with Andy, and 100 - Ca in her battle with Brad. To see how payoffs are determined, consider Andy. If Ab > 100 - Bc, so that Andy has more zombies than Brad in the Andy-Brad battle, then Andy wins the battle and receives w points where w > 2. If Ab = 100 - Bc, so that Andy and Brad…
- Rachel, Monica, and Phoebe are roommates; each has 10 hours of free time you could spend cleaning your apartment. You all dislike cleaning, but you all like having a clean apartment: each person’s payoff is the total hours spent (by everyone) cleaning, minus a number 1/2 times the hours spent (individually) cleaning.That is, ui(s1, s2, s3) = s1 + s2 + s3 -1/2si Assume everyone chooses simultaneously how much time to spend cleaning. a. Find the Nash equilibrium. b. Find the Nash if the payoff for each player is: ui(s1, s2, s3) = s1 + s2 + s3 − 3si Is the Nash equilibrium Pareto efficient? If not, can you find an outcome in which everyone is better off than in the Nash equilibrium outcome?Suppose China and the US are deciding whether to join an international agreement to mitigate climate change. The matrix below contains payoffs that represent each country’s net benefit from their decisions. Use this information to answer Question 24. CHINA USA Join Agreement Do Not Join Agreement Join Agreement (100,100) (0,125) Do Not Join Agreement (125,0) (25,25) [24] What does each country decide to do in a Nash equilibrium? AND What is the efficient outcome? Nash: Efficient:A Gain from Trade occurs when a unit is sold for a price greater than the unit of the good is worth to a seller and, simultaneously, bought for a price less than the good is worth to a buyer. Consider the first 2 units of the good that would be sold in this market (the vertical red line on the graph). Which answer choices are correct? If Kai and Mint sold one unit each to Gob and Yam at a price of $6, the trade would be mutually beneficial. At a price of $6, Gob would benefit by $3 because she is paying $6 for a unit of the good which is worth $9 to her. At a price of $6, Kai would benefit by $4 because she is getting $6 for a unit of the good which is worth $2 to her. For the first 2 units of the good there is potential gain from trade of $7 for each of the 2 units. For the first 2 units of the good sold the difference between the value to buyer and seller is $9 each. This means there is a potential gain from trade of $9 per unit. If the first 2 units of the…