Three roommates are trying to renovate their kitchen. They decided to vote on whether or not it is worth renovating. If at least 2 people vote for the renovation, then it will happen and everyone would split the costs of renovation equally. Their utility functions are U1= (1+ R)y1; U2 = (2 + R)y2 and U3 = (3 + R)y3, where R=1 if the kitchen is renovated and 0 otherwise, and y; is the amount of money i spends on |3| private consumption. Agent 1 has $900; Agent 2 has $2100 and Agent 3 has $1500; renovation project costs $1500 total. 1. Will the house be renovated if no bribes are allowed? 2. Can they reach an agreement so that the house ends up being renovated?
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- You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…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…In the final round of a TV game show, contestantshave a chance to increase their current winnings of$1 million to $2 million. If they are wrong, theirprize is decreased to $500,000. A contestant thinkshis guess will be right 50% of the time. Should heplay? What is the lowest probability of a correctguess that would make playing profitable?
- Cost-Benefit Analysis Suppose you can take one of two summer jobs. In the first job as a flight attendant, with a salary of $5,000, you estimate the probability you will die is 1 in 40,000. Alternatively, you could drive a truck transporting hazardous materials, which pays $12,000 and for which the probability of death is 1 in 10,000. Suppose that you're indifferent between the two jobs except for the pay and the chance of death. If you choose the job as a flight attendant, what does this say about the value you place on your life?N=2 video broadcasting websites, You and Twi, must decide the number of minutes of ads to be displayed for every video that the user elects to watch. Let tY be the number of ad-minutes per video set by You, and tT the number of ad-minutes per video set by Twi. Streaming one video costs You cY=0.02, while it costs Twi cT=0.03. There are 100 million potential users, and each watches videos according to the following demand curves: qY((tY,tT) =10-2tY+tT=10-2tT+tY a- What is the cross-price elasticity between You and Twi? b- Suppose, for now, that You and Twi enter an (illegal) agreement by which they set tY=tT=t Derive the total number of users in the market as a function of t. Derive the profits for each website as a function of t. c- Now let the two platforms compete by each setting their number of ad-minutes: i. What is the best reply of You? What is the best reply of Twi? ii. Find the Nash Equilibrium of the game. iii. How many total users choose You and how many total users choose…Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.
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- 1. Mr. Smith can cause an accident, which entails a monetary loss of $1000 to Ms. Adams. The likelihood of the accident depends on the precaution decisions by both individuals. Specifically, each individual can choose either "low" or "high" precaution, with the low precaution requiring no cost and the high precaution requiring the effort cost of $200 to the individual who chooses the high precaution. The following table describes the probability of an accident for each combination of the precaution choices by the two individuals. Adams chooses low precaution Adams chooses high precaution Smith chooses low precaution Smith chooses high precaution 0.8 0.5 0.7 0.1 1) What is the socially efficient outcome? For each of the following tort rules, (i) construct a table describing the individuals' payoffs under different precaution pairs and (ii) find the equilibrium precaution choices by the individuals. 2) a) No liability b) Strict liability (with full compensation) c) Negligence rule (with…To go from Location 1 to Location 2, you can either take a car or take transit. Your utility function is: U= -1Xminutes -5Xdollars +0.13Xcar (i.e. 0.13 is the car constant) Car= 15 minutes and $8 Transit= 40 minutes and $4 What is your probability of taking transit given the conditions above? What is your probability of taking transit if the number of buses on the route were doubled, meaning the headways are halved? Remember to include units.2. Consider the following Bayesian game with two players. Both players move simultaneously and player 1 can choose either H or L, while player 2's options are G, M, and D. With probability 1/2 the payoffs are given by "Game 1" : GMD H 1,2 1,0 1,3 L 2,4 0,0 0,5 and with probability 1/2 the payoffs are according to "Game 2" : G |M|D H 1,2 1,3 1,0 L 2,4 0,5 0,0 (a) Find the Nash Equilibria when neither player knows which game is actually played. (b) Assume now that player 2 knows which one among the two games is actually being played. Check that the game has a unique Bayesian Nash Equilibrium.