Two people have $4 to divide between themselves. They use the following process to divide the money. Each person names a number of dollars (a nonnegative integer), at most equal to 4. If the sum of the mounts that the people name is at most 4, then each person receives the amount of money she names (and the remainder is destroyed). If the sum of the amounts that the people name exceeds 4 and the amounts named are different, then the person who names the smaller amount receives that amount and the other person receives the remaining money. If the sum of the amounts that the people name exceeds 4 and the amounts named are the same, then each person receives $2. (a) Write a payoff matrix to represents the game. (b) Find all strictly dominated strategies for each player. (c) Find all weakly dominated strategies for each player. (d) Find all the Nash equilibria of the game in pure strategies.

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…

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 apartment

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…

Consider the following simultaneous move game: Player 1 Strategy Yes No Player 2 Yes 400, 400 600, 500 No 200, 375 300, 525 a. What is the maximum amount Player 1 should be willing to pay for the opportunity to move first instead of moving at the same time as Player 2? b. What is the maximum amount Player 2 should be willing to spend to keep Player 1 from getting to move first?

Consider the following story: Charlie finds two fifty-pence pieces on the floor. His friend Dylan is standing next to him when he finds them. Chris can offer Dylan nothing at all, one of the fifty-pence pieces, or both. Dylan observes the offer made by Charlie, and can either accept the offer (in which case they each receive the split specified by Charlie) or reject the offer.If he rejects the offer, each player gets nothing at all (because Charlie is embarassed and throws the moneyaway).(a) Formulate this interaction as an extensive-form game. To keep things simple, players’ payoff is equal to their monetary gain.(b) List all histories of the game. Split these into terminal and non-terminal histories.(c) What are the strategies available to Charlie? What are the strategies available to Dylan? Draw the strategic-form game.(d) Find the pure-strategy Nash equilibria of this game.(e) What do you think will happen?

Tom and Jerry are room mates. They spend a total of 80 hours a week together in their room. Tom likes loud music, even when he sleeps. His utility function is UT(CT, M) = CT + M, where CT is the number of cookies he eats per week and M is the number of hours of loud music per week that is played while he is in their room. Jerry hates all kinds of music. His utility function is M² 12 UJ = CJ Every week, Tom and Jerry each get 12 chocolate chip cookies sent from home. They have no other source of cookies. We can describe this situation with a box that looks like an Edgeworth box. The box has cookies on the horizontal axis and hours of music on the vertical axis. Let the bottom-left corner be the origin for Tom, and the bottom-right corner be the origin for Jerry. Suppose the dorm's policy is "rock-n-roll is good for the soul." Thus, M=80 in the initial endowment. Consider a trade between Tom and Jerry: Jerry gives Tom one cookie for reducing one hour of music. Then the change in Jerry's…

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…

Kip is trying to decide whether to take a one-day martial arts class at Rex Kwan Do. The fee for the class is $400. Kip will also have to pay his brother Napoleon $150 for that day in return for giving him a ride into town. Instead of taking the class, Kip could spend all day on the computer chatting with his girl, LaFawnduh. This gives him a value of $300. On the other hand, he could spend all day working with his Uncle Rico and making sweet moolah. Uncle Rico has promised to pay him $350 on that day if he works with him. What is Kip’s marginal cost of joining Rex Kwan Do?   Correct answer: $900  why don't you include 300 also? explanation

suppose that the world is comprised of two countries: X and Y.  Because of the absence of centralized world governance, the control of global externalities is particularly challenging, which is the case with greenhouse gases linked to climate change.  The entries in the following Payoff Table describe each country's well-being under different abatement patterns:    X\Y  No Abate Abate   No Abate  12,12  24,8  Abate  8,24  20,20  Now suppose that the game is repeated indefinitely. Define the concepts of Trigger Strategies and also the concept of Business as Usual Strategies for the repeated game. Verify that trigger strategies supporting cooperative payoffs (20,20) constitute a non-cooperative equilibrium of the repeated game when δ=0.8. Are trigger strategies still an equilibrium when δ=0.30? Explain intuitively why and verify that Business as Usual still is an equilibrium in this case.