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.
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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.
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- Samiyah and DeAndre decide to play the following game. They take turns choosing either 1, 2, or 3. As each number is chosen, it is added to the previously chosen numbers. The winner is the player who chooses a number that brings the cumulative number to 10. For example, if Samiyah chooses and DeAndre chooses 2 (so the cumulative number is 5) and Samiyah chooses 2 and DeAndre chooses 3 then DeAndre wins as his choice of 3 results in the sum equaling 10. Using SPNE, who wins?two players, a and b are playing an asymmetrical game. there are n points on the game board. each turn player a targets a pair of points and player b says whether those two points are connected or unconnected. a can target each pair only once and the game ends when all pairs have been targeted. player b wins if a point is connected with all other points on the very last turn, while player a wins if any point is connected with all other points on any turn but the very last one or if no point is connected to all other points after the last turn. for what values of n does either player have a winning strategy?Two players bargain over 1 unit of a divisible object. Bargaining starts with an offer of player 1, which player 2 either accepts or rejects. If player 2 rejects, then player 1 makes another offer; if player 2 rejects once more, then player 2 makes an offer. If player 1 rejects the offer of player 2, then once more it is the turn of player 1 where he makes two consecutive offers. As long as an agreement has not been reached this procedure continues. For example, suppose that agreement is reached at period 5, it follows that player 1 makes offers in period 1,2 then player 2 makes an o er in period 3, then player 1 makes offers in 4,5. Negotiations can continue indefinitely, agreement in period 't' with a division (x, 1- x) leads to payoffs ( , (1-x)).(The difference from Rubinstein's alternating offer bargaining is that player one makes two consecutive offers, whereas player 2 makes a single offer in her turn.) a. Show that there is a subgame perfect equilibrium in which player 2's…
- Player 1 and Player 2 are trying to agree on how to split a pie of size 1 in a two-stage bargaining game. If no agreement is reached after the two stages are complete, the pie is split for them according to a pre-arranged agreement that gives Player 1 and Player 2 one-quarter and three quarters of the pie, respectively. In the first stage, Player 1 makes an offer (x1, x2), where x1 + x2 = 1. Player 2 can either accept this offer (at which point the game ends and the pie is split according to Player 1’s offer), or can make a counter-offer. When Player 2 makes a counter offer, Player 1 can either accept (in which case the pie is split according to Player 2’s offer) or can reject, in which case the pie is split according to the pre-arranged agreement. Both players have a discount factor d – getting dx in the first stage (after Player 1’s proposal) is as good as getting x in the second stage (after Player 2’s proposal). a) In the last stage of the game, Player 1 will accept any offer…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?)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 Jerry have any strictly dominant strategy? Does Elaine?
- Two individuals each receive fifty dollars to play the following game. Independently of each other, they decide how much money to put in a common pot. They keep the rest for themselves. As for the money in the pot, it is increased by 80% and then distributed equally among the two individuals. For instance, suppose that the first individual puts $10 in the pot while the second individual puts $20. Increasing the total pot of $30 by 80% gives $54 to share equally between the two individuals. So the first individual’s payoff in this case is $(40 + 27) = $67, while the second individual’s payoff is $(30 + 27) = $57. (a) Compute the Nash equilibrium. (b) Is the Nash equilibrium Pareto efficient? ExplainExercise 7: The facility location game. Our example is a game in which two firms compete through their choice of locations. Suppose that two firms A and B are each planning to open a store in one of six towns located along six consecutive exits on a highway. We can represent the arrangement of these towns using a six-node graph as in Figure 1 Now, based on leasing agreements, Firm 1 has the option of opening its store in any of towns 1, 3, or 5, while Firm 2 has the option of opening its store in any of towns 2, 4, or 6. These decisions will be executed simultaneously. Once the two stores are opened, customers from the towns will go to the store that is closer to them. So for example, if Firm A open its store in town 3 and Firm B opens its store in town 2, then the store in town 2 will attract customers from 1 and 2, while the store in town 3 will attract customers from 3, 4, 5, and 6. If we assume that the towns contain an equal number of customers, and that payoffs are directly…You and a classmate are assigned a project on which you will receive one combined grade. You each want to receive a good grade, but you also want to avoid hard work. In particular, here is the situation: • If both of you work hard, you both get an A, which gives each of you 40 units of happiness. • If only one of you works hard, you both get a B, which gives each of you 30 units of happiness. • If neither of you works hard, you both get a D, which gives each of you 10 units of happiness. • Working hard costs 25 units of happiness. Complete the following payoff matrix given the previous information. In each cell, your classmate's payoff is on the left and yours is on the right. Your Decision Work Shirk Classmate's Decision Work , , Shirk , , The likely outcome is that your classmate and you . If you get this classmate as your partner on a series of projects throughout the year, rather than only once, you are…
- You and a classmate are assigned a project on which you will receive one combined grade. (You each want to receive a good grade, but you also want to avoid hard work. In particular, here is the situation:• If both of you work hard, you both get an A, which gives each of you 40 units of happiness.• If only one of you works hard, you both get a B, which gives each of you 30 units of happiness.• If neither of you works hard, you both get a D, which gives each of you 10 units of happiness.• Working hard costs 25 units of happiness. a. Fill in the payoffs in the following decision box: REFER IMAGE b. What is the likely outcome? Explain your answer.c. If you get this classmate as your partner on a series of projects throughout the year, rather than only once, how might that change the outcome you predicted in part (b)?d. Another classmate cares more about good grades: She gets 50 units of happiness for a B and 80 units of happiness for an A. If this classmate were your partner (but your…You and a classmate are assigned a project on which you will receive one combined grade. (You each want to receive a good grade, but you also want to avoid hard work. In particular, here is the situation:• If both of you work hard, you both get an A, which gives each of you 40 units of happiness.• If only one of you works hard, you both get a B, which gives each of you 30 units of happiness.• If neither of you works hard, you both get a D, which gives each of you 10 units of happiness.• Working hard costs 25 units of happiness.a. Fill in the payoffs in the following decision box: b. What is the likely outcome? Explain your answer.c. If you get this classmate as your partner on a series of projects throughout the year, rather than only once, how might that change the outcome you predicted in part (b)?d. Another classmate cares more about good grades: She gets 50 units of happiness for a B and 80 units of happiness for an A. If this classmate were your partner (but your preferences…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. If the apartment owner decides to fine both the roommates if the apartment is dirty, such that now if neither of them clean they each get a 5 utility loss, what would the new equilibrium be now? a. John cleans, Joe doesn’t b. Joe cleans, John doesn’t c. Neither of them clean the apartment d. Both A&B