1) Bargaining Adam has a car in good condition that he uses daily and that he values at 4000$. Blair values the same car at 4300$. Blair has 5000$ to spend. Adam has received an offer for 3500$ from a third party. a) What are the threat points for Adam and Blair? What is the surplus they could get from cooperating? What is the range of prices for the sale of the car that can support that cooperative outcome? b) Now suppose that the offer from the third party is 4200$. What are the new threat points? What is the new surplus of cooperation between Adam and Blair? c) Finally, suppose that the seller of a car has to pay a tax of 200$ and the buyer of a car has to pay registration fee of 150$. There is no offer from a third party. What are the threat points? What is the new surplus from cooperation? What is the range of prices that

See the extensive form game in the image attached (the payoffs of player 1 are written on top and the payoffs of player 2 are on the bottom).  a) Write this game in normal form (a player's strategy is a complete contingent plan that tells them what to play at each of their information sets) (b) Find all the Nash equilibria of the normal form game from part (a)

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(The Beckhams' dilemma) Victoria and David are husband and wife. They both prefer ciean to dirty house but neither likes to clean the house. Their payoffs are given in the table below. Victoria Clean Don't clean 0,8 Clean 5,5 David Don't clean 8,0 1,1 a) Let say they play the clean house game only once, what is the Nash equilibrium? b) Let say Victoria and David has to decide whether to clean or not every day for indefinite number of days. How grim-trigger strategy will be our subgame perfect Nash equilibrium? In other words, what is the patience rate that ensure Victoria and David maintain the cleanliness of the house?

Suppose that Jason and Chad each are thinking of opening up a diet coke stand on the fourth floor of this building. Suppose that potential customers are evenly spaced on a distance that is normalized to 1. Customers will buy a diet coke from whichever stand requires the least walking. If they are the same distance the customer will flip a coin. This is depicted below. 1/4 1/2 3/4 Suppose that Jason and Chad are simultaneously choosing the location of their stands, what is the Nash Equilibrium location? a. One of them puts a stand at 3/4 and the other puts a stand at 1/4 b. Chad and Jason put their stands right next to each other at 1/2 c. One of them puts a stand at 0 and the other puts a stand at 1 d. There is no Nash Equilibrium