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?
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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?
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- 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…10. Player A and Player B are playing a game . First , Player A chooses to either " Keep " or " Pass " . Second , Player B observes A's choice and Player B then chooses to either Keep or Pass . This process continues which creates the sequential game below . Please mark decisions that rational and selfish players will choose at every decision node ( 3 decisions by player A and 3 decisions by player B ) - mark them on the Figure . What is the equilibrium of this game ?Tom and Jerry have two tasks to do all day: Set traps and build bombs. If Tom spends all day setting traps, he will have set 16 traps. If he instead devotes his days to building bombs, Tom will build four bombs. If Jerry spends his day setting traps, he will set 14 traps; if he spends the day building bombs, he will build 7 bombs. After looking at the production possibilities for Both Tom and Jerry, we can conclude that: -Jerry has the comparative advantage in trap production -Tom has the comparative advantage in trap production -Tom has the comparative advantage in bomb production -No comparative advantage exist
- 2 Consider Anna and Joe, who value a certain good by the same amount v and can choose to either contribute (C) e to get the good or not (N) where v > e> 0. Obtaining the good only requires c from one person. The game is summarized in the payoff table below: Joe V-c,V-c V-c,V v,V-c 0,0 Find a pure strategy equilibrium and a mixed strategy equilibrium. Anna O ZSophia is a contestant on a game show and has selected the prize that lies behind door number 3.The show’s host tells her that there is a 50% chance that there is a $15,000 diamond ring behindthe door and a 50% chance that there is a goat behind the door (which is worth nothing to Sophia,who is allergic to goats). Before the door is opened, someone in the audience shouts, “I will giveyou the option of selling me what is behind the door for $8,000 if you will pay me $4,500 for thisoption.” [Assume that the game show allows this offer.]a. If Sophia cares only about the expected dollar values of various outcomes, will she buythis option?b. Explain why Sophia’s degree of risk aversion might affect her willingness to buy thisoptionned... ESS... 15 PPF2 Review Consider the diagram depicting the tradeoff faced by the Mars colony in production of spaceships or habitats. Suppose that the colony is currently producing nothing but spaceships. It is decided, however, that spaceship production should be reduced by one unit so that some habitats may be produced. How many habitats can then be produced if one spaceshift is foregone? 14 13 12 11 8 10 PPE 9 7 6 5 4 3 Review 2 1 0 Habitats 1 2 3 (3, 8) 4 (4, 6) 5 6 Close 7 Spacecraft 8 9
- **Practice*** Amy and Bob are playing the following board game:(I) Amy starts. She has three possible actions: Pass, Attack, or Defend.(II) Bob observes what Amy chose, and then chooses between three actions with the same names: Pass, Attack, or Defend.(III) If either player passes, or one attacks and the other defends, then the game ends. But if either both players attack, or if both players defend, then Amy has to choose between two actions: Respond or Not Respond. The payoffs are as follows:- If both players pass, both players get a payoff of 0.- If a player attacks and the other player defends, the player that attacks gets a payoff of 1, while the player that defended gets a payoff of 2.- If a player passes but the other player attacks or defends, the player who passes gets a payoff of -1, and the player who attacked or defended gets a payoff of 3.- If both players attack or both players defend:– If Amy responds, she gets a payoff of 4, and Bob gets a payoff of 0.– If Amy does…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…Exercise 4.1 Amy and Bill simultaneously write a bid on a piece of paper. The bid can only be either 2 or 3. A referee then looks at the bids, announces the amount of the lowest bid (without revealing who submitted it) and invites Amy to either pass or double her initial bid. - The outcome is determined by comparing Amy's final bid to Bill's bid: if one is greater than the other then the higher bidder gets the object and pays his/her own bid; if they are equal then Bill gets the object and pays his bid. Represent this situation by means of two alternative extensive frames. Note: (1) when there are simultaneous moves we have a choice as to which player we select as moving first: the important thing is that the second player does not know what the first player did; (2) when representing, by means of information sets, what a player is uncertain about, we typically assume that a player is smart enough to deduce relevant information, even if that information is not explicitly given to…
- 1. We can use game theory to model everyday interactions. Consider a game that you're well familiar with: The choice of which side of a hallway to select if someone is coming from the other direction and has not yet made their own selection clear. How many Nash equilibria are in this game? Remember, an outcome is a Nash equilibrium if nobody has a profitable unilateral deviation; if no one has reason to be the only one to change what they're doing. 2. Consider following scenario which we can think of as a game played between two oligopoly firms, Timmer's snow removal & Jack's snow removal services. It costs Timmer $200 per customer per year. It costs Jack's $225 per customer per year. If the firms compete by strategically setting prices, what Nash equilibrium price do we expect? Explain. Remember, an outcome is a Nash equilibrium if nobody has a profitable unilateral deviation; if no one has reason to be the only one to change what they're doing.Two roommates John and Joe are playing a simultaneous game of cleaning the apartment. If neither of them clean, the apartment gets filthy and both get a utility of 2. If John cleans and Joe doesn’t, John gets a utility of 1 and Joe gets a utility of 4. If Joe cleans and John doesn’t, Joe gets a utility of 1 and John gets a utility of 4 and if both clean up the apartment, they each get a utility of 3.What is the Nash equilibrium of this game? Group of answer choices Joe cleans, John doesn’t John cleans, Joe doesn’t Both of them clean the apartment Neither of them clean the apartmentTwo fishermen (Andy and Bob) are fishing in the same lake. Each can either fish for 5 or 6 hours. Their payoffs depend on how much time each of them fishes: - If they both fish for 6 hours each, their payoff is 2 fish for Andy and 2 fish for Bob; - if they both fish for 5 hours each, their payoff is 3 fish for Andy and 3 fish for Bob; - if one fishes for 5 hours and the other for 6, then the payoff of the former is 1 fish and of the latter is 4 fish. What are the payoffs at the Nash Equilibrium if they play sequentially, and Bob plays first? (Hint: Before you choose the correct answer, write the game in a tree form and find the Nash Equilibrium) Select one: a. Andy gets 2 and Bob gets 2 b. Andy gets 3 and Bob gets 3 c. Andy gets 1 and Bob gets 4 d. Andy gets 4 and Bob gets 1