QUESTION 3 Let c(w1; w2; y) be a cost function, and let A > 1. We have: Oa.q A w; Aw2; y) = o(w1; w2; y) O b.q A w1; Aw2; y) = Ac(w1; w2; y) Oc. d A w1; Aw2: y) > Ao(w1; w2; y) Od.( A w1; Aw2: y) < Ao(w1; w2; y)
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- Question I am in possession of two coins. One is fair so that it lands heads (H) and tails (T) with equal probability while the other coin is weighted so that it always lands H. Both coins are magical: if either is flipped and lands H then a $1 bill appears in your wallet, but when it lands T nothing happens. You may only flip a coin once per period. The interest rate is i per period. You are risk-neutral and thus only concern yourself with expected values (and not variance). For simplicity, in the questions below assume you will live forever. 1. How much are you willing to pay for such a coin that you know is fair? 2. How much are you willing to pay for such a coin that you know is weighted? 3. I currently own the coins and know which is fair and which is weighted, but you cannot tell which is which. You may make an offer to purchase a coin of your choosing, which I am free to accept or reject. What is the most you are willing to offer? Explain how you arrived at this answer. 4.…Let's say we have a game called "guess 2/3 of the average," where players can choose any number x ∈ [0, 100]. 5% of players are at level N0, 40% at level N1, 35% at level N2, 15% at level N3, and 5% at level N4. Players at level N0 choose a number randomly, while players at higher levels choose a number according to their beliefs, which are as follows: players at higher levels believe that all other players are one level lower than themselves. (a) What will be the winning number and which level players will be the winners? (b) Under the assumptions of classical game theory, the mentioned version of the game "guess 2/3 of the average" has exactly one equilibrium, in which everyone chooses the number 0. Prove that this outcome is indeed a Nash equilibrium of the game.Once your producers understand the “I WANT $3” game, you will present the “I WANT TO BE A MILLIONAIRE” game. Its rules are: There are two contestants/opponents (who do not know each other and cannot communicate with each other during the game). Each player is given $1 million at the start of the game. Independently and simultaneously, each player must choose to add to their award $0, $1, $2, $3, $4, ……$999,999, or $1,000,000. Doing so decreases the other player’s award by twice that amount. Each player ends the game with a payoff based on their initial one million, the additional amount that they announced, and the reduction due to the opponent’s announcement. The game matrix for this expanded game has 1,000,001 rows, 1,000,001 columns, and 1,000,002,000,001 pairs of payoffs. I STRONGLY RECOMMEND THAT YOU DO NOT DRAW IT! But building on what you learned in part (a), answer the following two questions: i) What is the Nash equilibrium of this game? ii) What are the Nash…
- You and your roomate are deciding whether to go to a party or not on Friday. Going to the party is fun and gives a benefit of 4. If you go to the party, there is a 50% chance you will get covid. If you do not attend the party but your roommate does and gets covid, there is 80% chance that you will get covid. The impact of getting covid is -10. If both of you stay home, you will not be exposed to covid and will not have fun, leading to a payoff of 0 for both of you. 3. Construct a game matrix based on the description above and find any (c) Nash equilibria. How would your answer change if one roomate was less social and enjoyed (d) partying less than the other? Change the payoff matrix in a way that is both consistent with one roommate being less social than the other and changes the prediction you found in (a). (Note: if you found multiple possible equilibria in (a), changing the outcome could mean either making one of your prior Nash equilbria the only Nash equilibrium or making an…Jack and Diane work at a bakery. Jack can make either five batches of cookies or two cakes per hour, while Diane can make either four batches of cookies or three cakes per hour. At 9:00 a.m. they receive an order for 24 batches of cookies and nine cakes. What time is the soonest they can have the order ready?Matthew is playing snooker (more difficult variant of pool) with his friend. He is not sure which strategy to choose for his next shot. He can try and pot a relatively difficult red ball (strategy R1), which he will pot with probability 0.4. If he pots it, he will have to play the black ball, which he will pot with probability 0.3. His second option (strategy R2) is to try and pot a relatively easy red, which he will pot with probability 0.7. If he pots it, he will have to play the blue ball, which he will pot with probability 0.6. His third option, (strategy R3) is to play safe, meaning not trying to pot any ball and give a difficult shot for his opponent to then make a foul, which will give Matthew 4 points with probability 0.5. If potted, the red balls are worth 1 point each, while the blue ball is worth 5 points, and the black ball 7 points. If he does not pot any ball, he gets 0 point. By using the EMV rule, which strategy should Matthew choose? And what is his expected…
- please answer within 30 minutes.Two travelers own an identical suitcase that contains identical antiques. The airline is liable for a maximum of $100 per suitcase. To determine how much to reimburse each traveler, the airline puts them in different rooms (so that they cannot communicate), and ask them to write down an amount (an integer number) between $2 and $100. If both write down the same number, the airline will reimburse both travelers that amount. However, if the two amounts are different, both travelers will be paid the lowest of the two numbers along with a bonus/malus: $2 extra will be paid to the traveler who wrote down the lower value and a $2 deduction will be taken from the person who wrote down the higher amount. What are the travelers’ best response functions? What are the Nash equilbria of the game? Are they Pareto efficient? Explain the intuition why.**Practice** In order to alleviate their risks, they are considering a risk-sharing agreement. Carol would buy one CC and David would buy one DD. Six months from now, they would sell their coins, add up the total amount of money, and split it equally between them. Thus, if only one of the coins is successful, they would both still have some positive amount of money at the end. Assume that they can verify whether the other really made the investment. They know whether the investment is successful, since the price of the coin is public information, and they trust that the other will pay them as promised. Which of the following statements is accurate?A. They will not make that risk-sharing agreement.B. Carol is willing to take the risk-sharing agreement, but David is not.C. They may be willing to make that risk-sharing agreement, but it depends on information not given in the question.D. They will surely make the risk-sharing agreement.E. None of the statements above is correct.
- Question 5 You negotiate with a retailer over a contract according to which the retailer would buy a large fraction of your current production for next year. The retailer is perfectly informed about consumer demand, but you do not know whether demand is high or low. You only know that the probability for high demand is 80%. If demand is high, the retailer's profit is £5 million minus what he pays to you according to your contract. If demand is low, the retailer's profit is £3 million minus what he pays to you. Your costs of producing the output specified in the contract are £1 million. You can make sequential offers for the retailer's total payment for you to deliver a fixed quantity of your production. As you know that your competitor is also seeking a similar contract with this retailer, and the retailer can only supply one firm due to limited shelf space, you know that you can only make at most two offers. If your first offer is rejected, the retailer will strike the deal with your…A computer reseller needs to decide how many laptops to order next month. The lowest end laptop costs $220 and the retailer can sell these for $300. However, the laptop manufacturer already announced that they are coming out with a new model in a couple of months. Any laptops that will not be sold by the end of next month will have to be heavily discounted at half-price. The reseller also needs to consider that every time he fails to fulfill a laptop order, he stands to lose $25 for every unit. Based on the past months’ sales, the reseller estimates the demand probabilities for sales (S) as follows: P(0 units) = 0.3; P(1 units) = 0.4; P(2 units) = 0.2; P(3 units) =0.1. The reseller thinks it’s a good idea to conduct a survey on whether or not his customers are going to buy laptops and how many. The survey results will either be Yes (Y), No (N) or Don’t Know (DK). The probability estimates of the results based on the demand for number of units are: P(Y|S = 0 units) = 0.1 P(Y|S = 1…Mete is Esra's boyfriend. Esra is expecting a marriage proposal from Mete. Today is Sunday. Mete says Esra that: (1) he is going to propose Esra on Monday or Tuesday or Wednesday or Thursday or Friday, at 10:00 pm. (2) he knows right now the day when he will propose (3) but the day of proposal will be a surprise to Esra: On the day of the proposal, she would not be expecting the proposal that day. Esra says Mete that what he says is impossible. Explain why Esra is right in a few sentences.
