Q3. Imagine that two partners are trying to divide up $66. Imagine that this game is played only once and that player 1 gets to decide how to divide the $66. Upload a picture of the game tree. You only need to include a minimum of 5 branches.
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- You and your friend will divide $4. You have agreed to use the following procedure.Each of you will name a number of dollars, either $0, $1, $2, $3, or $4. You will chooseyour numbers simultaneously. If the sum of the amounts is less than or equal to $4, theneach of you receives the amount you named and the rest of the money is thrown away.If the sum of the amounts is greater than $4 and the amounts named are different, thenthe person who named the smaller amount receives that amount and the other personreceives the remaining money. If the sum of the amounts is greater than $4 and theamounts named are the same, then each receives $2. (a)Draw the payoff matrix of this game. Let “you” be the row player and “yourfriend” be the column player.(b) Derive the best reply functions of all players.(c) Find the Nash equilibrium (or all of the equilibria) of this game using thebest reply functions you found in part (a).Jill and Jack both have two pails that can be used to carry water down from a hill. Each makes only one trip down the hill, and each pail of water can be sold for $4. Carrying the pails of water down requires considerable effort. Both Jill and Jack would be willing to pay $2 each to avoid carrying one pail down the hill, and an additional $3 to avoid carrying a second pail down the hill.a. If Jack and Jill each must decide whether to carry one or two pails of water down from the top of the hill, how many pails will each child choose to carry? ___ pail(s)b. Jill and Jack’s parents are worried that the two children don’t cooperate enough with one another. Suppose they make Jill and Jack share equally their revenues from selling the water. Given that both are self-interested, construct the payoff matrix for the decisions Jill and Jack face regarding the number of pails of water each should carry. Carry 1 pail Jack Carry 2 pails…V4. Assume there are only two oil producing countries in the world, C1 and C2. Each can export either 2 million or 4 million barrels of oil. If a total of 4 million barrels of oil are exported (both countries combined) then each barrel sells at $25. If there are 6 million barrels exported between them, each barrel sells at $15 and if there are 8 million barrels exported between them, then each barrel sells at $10. a) Write the “pay-off” matrix/table (i.e., the table or matrix indicating the strategies for each country, i.e., the amount of barrels they export and the revenue they make). b) Determine the Nash equilibrium for the game. c) Is there a strategy that results in larger revenue for both the countries? If so, which is that? d) For what wegitage for future payoff, δ, will both countries agree to use the strategy that benefits both of them, better?
- You play a game by drawing a card from a standard deck then replacing the drawn card. If you draw a king or a queen, you win Php 500. If you draw an ace, you win Php 800. However, you lose Php 650 for anything else. • If you continue to play the game, how much do you expect to win or lose in the game? • Is this a fair game? Why or why not?Question 4: (Answer in 200-400 words in total PLEASE ANSWER THIS HOMEWORK QUESTION The purpose of the Paris agreement was to set a coordination mechanism between countries and limit carbon emissions at a global level. In this period of climate emergency, high carbon emissions and the non respect of Paris agreement by numerous countries, have been criticized in the newspapers and described as dangerous for future generations. From a game theory perspective, respecting or not the Paris agreement can be modeled as a strategic game. Let’s assume that we have two countries who can choose between option 1: not respecting and exiting the Paris agreement (increase their carbon emission); and option 2: respecting the Paris agreement (limit their carbon emission). The following matrix gives the payoffs of each choice, where in each cell, the first number is the payoff of country A and the second number is the payoff of country B. Country B Repect the agreement Exiting the…Three players (Allen, Mark, Alice) must divide a cake among them. The cake is divided into three slices.The table below shows the value of each slice in the eyes of each of the players. S1 S2 S3 Allen $7.00 $6.00 $5.00 Mark $4.00 $4.00 $4.00 Alice $5.00 $4.00 $6.00 Which of the slices does Allen deem fair? Group of answer choices S1 and S2 S1 and S3 S2 and S3 S1, S2, and S3 S1 only
- Consider the following game played by four individuals, players 1, 2, 3, and 4. Each individual has $10,000. Each player can donate between $0 and $10,000 to build a public park that costs $20,000. If they collect enough money, they construct the park, which is worth $9,000 to each of them. However, if they collect less than $20,000, they cannot build a park. Furthermore, regardless of whether the park is built or not, individuals lose any donations that they make. a) Describe the Nash equilibria for a simultaneous game. What makes them equilibria? Hint: There are many equilibria, so you may want to use a mathematical expression! b) Suppose that players 1, 2, and 3, each donate $4,000 for the park. How much will player 4 donate and why. What are the resulting payoffs for the players? c) Suppose instead that player 1 donated first, player 2 second, player 3 third, and player 4 last. Furthermore, players could only donate in intervals of 1,000 (0, $1,000, $2,000, etc.). How much will…Please see below. Note that these pictures go together.Q23. At what time is the game expected to stop? 1 2 3 4 5 6 after time 6 (when there are no more moves)
- Cameron and Luke are playing a game called ”Race to 10”. Cameron goes first, and the players take turns choosing either 1 or 2. In each turn, they add the new number to a running total. The player who brings the total to exactly 10 wins the game. a) If both Cameron and Luke play optimally, who will win the game? Does the game have a first-mover advantage or a second-mover advantage? b) Suppose the game is modified to ”Race to 11” (i.e, the player who reaches 11 first wins). Who will win the game if both players play their optimal strategies? What if the game is ”Race to 12”? Does the result change? c) Consider the general version of the game called ”Race to n,” where n is a positive integer greater than 0. What are the conditions on n such that the game has a first mover advantage? What are the conditions on n such that the game has a second mover advantage?Splitting Pizza: You and a friend are in an Italian restaurant, and the owner offers both of you a free eight-slice pizza under the following condition. Each of you must simultaneously announce how many slices you would like; that is, each player i ∈ 1, 2 names his desired amount of pizza, 0 ≤ si ≤ 8. If s1 + s2 ≤ 8 then the players get their demands (and the owner eats any leftover slices). If s1 + s2 > 8, then the players get nothing. Assume that you each care only about how much pizza you individually consume, and the more the better.What outcomes can be supported as pure-strategy Nash equilibria?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?)