Suppose the only place to buy a PlayStation game console is from either Target or Wal-Mart. • If both stores charge $400, each store makes 10k each. • If both stores charge $300, the each store make $7.5k. • If one store charges $400, and the other store charges $300, the store charging $300 makes $15k, while the other store only makes $5k. Suppose each store, independently, decide to establish a matching price policy. They promise buyers to match the price of the competitor. The result of this policy would be that the Nash equilibrium of the game would be for: Target charges $400 and Walmart charges $300 both companies charge $300 for the game both companies charge $400 for the game Target charges $300 and Walmart charges $400
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- Two oil companies are deciding how much oil to extract from their properties, which lie above the same underground reservoir. The faster that oil is extracted, the less total oil is extracted. Letting x denote the extraction rate for company X and y denote the extraction rate for company Y, we assume that the total amount of oil extracted is 1/(x + y) million gallons of oil. Of the total amount that is extracted, the share going to company X is x/(x + y), and the share to company Y is y/(x + y); that is, a company’s share depends on how fast it extracts compared with the other company. The price of oil is $100 per gallon. Each company chooses its extraction rate from the interval [1,10] in order to maximize the monetary value of the oil that it extracts. Find the Nash equilibrium extraction rates. (Note: You can assume that the payoff function is hill shaped.)We have a group of three friends: Kramer, Jerry and Elaine. Kramer has a $10 banknote that he will auction off, and Jerry and Elaine will be bidding for it. Jerry and Elaine have to submit their bids to Kramer privately, both at the same time. We assume that both Jerry and Elaine only have $2 that day, and the available strategies to each one of them are to bid either$0, $1 or $2. Whoever places the highest bid, wins the $10 banknote. In case of a tie (that is, if Jerry and Elaine submit the same bid), each one of them gets $5. Regardless of who wins the auction, each bidder has to pay to Kramer whatever he or she bid. Does this game have a Nash Equilibrium? (If not, why not? If yes, what is the Nash Equilibrium?)Suppose that player 1 (row) and player 2 (column) play a simultaneous game. Player 1 can choose to go out (Go) or stay at home (Stay). Player 2 can then choose whether to buy tickets to the movies (Movie), to the basketball game (Game) or not buy tickets (None). This game is shown below. Player 1(row) Player 2 (column) Movie Game None Go (6, 4) (4, 6) (0, 0) Stay (2, - 2) (2, - 4) (3, 3) What is the Maxi-Min strategy for player 1 and for player 2? Explain why. What are the Nash equilibrium or equilibria for this game? Explain why. What kind of game is this? Argue what is the most likely outcome.
- Consider two students, Hana and Avan at AUIS. Both students are taking their final exam in their economic class today and they are both, independently, trying to decide whether they will conceal or reveal their answers while working on the exam. It takes time and effort to conceal answers so both students realize that revealing their answers will allow them to concentrate more fully on the exam. In addition, they both realize that if the other student reveals his answers they may potentially improve their scores. Avan believes she will make an 85 on the exam if both students conceal their answers, an 80 on the exam if she conceals her answers while Hana reveals her answers, an 87 on the exam if she reveals her answers while Hana does not reveal her answers, and an 85 on the exam if both students do not conceal their answers. Hana knows that if she conceals her answers she will get a 60 on the exam and if she does not conceal her answers she will get a 65 provided that Avan conceals her…Suppose there is a remote stretch of highway along which two restaurants, Last Chance Café and Desolate Diner, operate in a duopoly. Neither restaurant invests in keeping up with health code regulations, but regardless they both have customers as they are the only dining options along a 79-mile portion of the road. Both restaurants know that if they clean up and comply with health codes they will attract more customers, but this also means that they will have to pay workers to do the cleaning. If neither restaurant cleans, each will earn $10,000; alternatively, if they both hire workers to clean, each will earn only $7,000. However, if one cleans and the other doesn't, more customers will choose the cleaner restaurant; the cleaner restaurant will make $15,000, and the other restaurant will make only $3,000. Complete the following payoff matrix using the information just given. (Note: Last Chance Café and Desolate Diner are both profit-maximizing firms.) Desolate Diner…12.3 Armed Conflict: Consider the following strategic situation: Two rival armies plan to seize a disputed territory. Each army's general can choose either to attack (A) or to not attack (N). In addition, each army is either strong (S) or weak (W) with equal probability, and the realizations for each army are independent. Furthermore the type of each army is known only to that army's general. An army can capture the territory if either (i) it attacks and its rival does not or (ii) it and its rival attack, but it is strong and the rival is weak. If both attack and are of equal strength then neither captures the territory. As for payoffs, the territory is worth m if captured and each army has a cost of fighting equal to s if it is strong and w if it is weak, where s <w. If an army attacks but its rival does not, no costs are borne by either side. Identify all 12.7 Exercises • 267 the pure-strategy Bayesian Nash equilibria of this game for the following two cases, and briefly describe…
- 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…Albena and Elena are two close friends who run a very popular restaurant where portions of either gozlemes ( a bread with spinach and feta cheese) or kebab are served. As shown on the table, Albena can make 20 portions of gozleme per hour but only 10 portions of kebab per hour. assume that Elena can make 8 portions of gozleme or 5 portions of kebab per hour. Suppose now that after a quarrel on this date, Albena and Elena decide not to coordinate their production and agree to divide the total orders of 80 portions of gozleme and 80 portions of kebab into two. Assume that a portion of both gozleme and kebab is sold at $3. To maximize her revenue, how should Elena allocate her time to the production of gozleme and kebab? For the preceding part, assume now that a portion of gozleme is sold at $3, whereas a portion of kebab is sold at $5. To maximize her revenue, how should now Elena allocate her time to the production of gozleme and kebab?Assume two moms live next to each other and both have one preschooler. They meet each other for the first time and discover that both of them work part-time twice a week. It turns out that both of them have their children attend a child care facility close to home. Furthermore, they each learn that when one mom is working the other is at home and vice versa. One of the moms has an idea and proposes to the other mom that each take care of the other's child while they work. That way they can save money on child care. If they do this, what will happen to the official GDP reported by the government and why? Is society necessarily worse off as a result of this arrangement?
- Q14. Do players have perfect information in the above game? Yes, all of them have perfect information No, player 2 has imperfect information No, player 3 has imperfect information No, no player has perfect information Q15. If we want to describe the above game with a strategic form representation, what would the strategy sets for the three players be? Player 1={a, b, c} ; Player 2={x, y}; Player 3={r, s} Player 1={a, b, c} ; Player 2={xx, xy, yx, yy}; Player 3={r, s}Daniel and Kevin are two hardworking builders for solo, independently-owned companies. They can produce Chairs and Tables. As a result, they each have PPFs (Possibilities Production Frontiers) that illustrate their production. Daniel's PPF is shown by the equation: Qc = 12 - 3Qt. Likewise, Kevin's PPF is shown by the equation: Qt = 12 - 3Qc. Since they trust each other and are honest in their terms, Daniel and Kevin trade with each other and only each other; they do not take their goods to markets, and they do not interact with outside sellers/buyers. Since they want to make sure that they provide for their families in the most fair way possible, they set up and agree upon a few terms of trade. The terms are as follows: FIRST, the terms of trade are 1 Chair in exchange for 1 Table. SECOND, each of them specializes according to their own comparative advantage. THIRD, since Kevin needs a few extra things, he CONSUMES 3 units of the goods that he produces. With that said, I have a few…Suppose Toyota and Honda must decide whether to make a new kind of side-impact airbags standard equipment on all models. Side impact-airbags raise the price of each automobile by $1000. If both firms make side-impact airbags standard equipment, each company will earn profits of $2.5 billion. If neither company adopts the side-impact airbag technology, each company will earn $1 billion (due to lost sales to other automakers). If one company adopts the technology as standard equipment and the other does not, the adopting company will earn a profit of $3 billion and the other company will lose $1.5 billion. If you were a decision maker at Honda, would you make side-impact airbags standard equipment?