Three friends i = 1, 2, 3 get together for a few drinks and decide to share the total bill equally. Friend i's preferences are represented by the utility function u₁(x₁, y₁) = 2√x-y₁. where x; is the number of drinks that i consumes and y; is the amount of money that i pays. Each drink costs $1. (a) Describe the strategic game generated by this situation.
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- A principal can choose to make the allocation of tasks broad (B) or narrrow (N). At the same time an agent can choose to work put in high effort (H) or low effort (L). The payoffs are 20 to the principal and 30 to the agent is the actions chosen are B and L. For all other combinations of actions the payoffs are 0 to both players. Which of the following statements are true? DA Nash equilibrium of the game is (B, H) A Nash equilibrium is (N, L) There is no Nash equilibrium in pure strategies in this game. A Nash equilibrium is (N, H) A Nash equilibrium is (B, L)4. David plays in a game where his strategy (set of possible choices) is denoted by x, which can be any integer between 1 and 7, against Goliath, whose strategy is denoted by y, which can be any integer between 1 and 7. David's and Goliath's utility functions are the same and given by: U(x, y) = (x-2)(y-2). Based on this information, determine whether each of the following statements are true or false. (a) The combination (x, y) = (2, 2) is a Nash equilibrium. (b) This game has no dominant strategy (a choice of integer that gives the highest payoff regardless of what the opponent chooses). (c) This game has only one dominated strategy (a choice of integer that would never be a best response to the opponent's choice of integer).Suppose that Romeo in Problem 8 has the utility function U= S° RS2, and Juliet has the utility function U= S2RS5, where SRis Romeo's spaghetti consumption and Sj is Juliet's. They have 42 units of spaghetti to divide between them. Juliet would want to give Romeo some spaghetti if she has more than 28 a) units. Romeo would want to give Juliet some spaghetti if he has more than 26 units of spaghetti. C) Romeo and Juliet would never disagree about how to divide the spaghetti. d) Romeo would want to give Juliet some spaghetti if he had more than 21 units of spaghetti. Juliet would want to give Romeo some spaghetti if she has more than 30 units e) of spaghetti.
- (4) Resource Allocation. Consider a combinatorial auction with three items {a,b,c} and three players (I, II, III. The valuations each player has for each subset of a b с ab bс ас abc I 1 2 1 6 4 11 II 3 5 3 3 5 III| 4 5 0 7 5 7 the items is shown below. What is the allocation produced under the VCG (Vickrey-Clarke-Groves) mechanism and what are the VCG payments of the players?Consider the following game - one card is dealt to player 1 ( the sender) from a standard deck of playing cards. The card may either be red (heart or diamond) or black (spades or clubs). Player 1 observes her card, but player 2 (the receiver) does not - Player 1 decides to Play (P) or Not Play (N). If player 1 chooses not to play, then the game ends and the player receives -1 and player 2 receives 1. - If player 1 chooses to play, then player 2 observes this decision (but not the card) and chooses to Continue (C) or Quit (Q). If player 2 chooses Q, player 1 earns a payoff of 1 and player 2 a payoff of -1 regardless of player 1's card - If player 2 chooses continue, player 1 reveals her card. If the card is red, player 1 receives a payoff of 3 and player 2 a payoff of -3. If the card is black, player 1 receives a payoff of 2 and player 2 a payoff of -1 a. Draw the extensive form game b. Draw the Bayesian form gameOwen and Simon both like playing with balls and cars. Suppose B represents the number of balls, and C represents the number of cars. If Owen's utility function can be given by U(B, C) = 10B + 5C, and Simon's utility function can be given by U(B, C) = 6B + 6C, which of the following trades would be mutually beneficial? Ⓒa. Owen gives Simon 2 balls in exchange for 3 cars b. Owen gives Simon 2 cars in exchange for 3 balls ⒸC. Owen gives Simon 3 cars in exchange for 2 balls Ⓒd. Owen gives Simon 3 balls in exchange for 2 cars
- You suspect that you are a price leader in the market. Moreover, you are considering expanding your operations. H.R. Shovenstuff will observe your moves and then follow, but he is more secretive so you will not know whether to price high or low after his pricing decision has been made. Using the following game tree, solve for the Nash equilibrium. High Price Shovenstuff High Price Low Price You High Price (2,1) (6,2) Invest Low Price Invest, High Price, High Price O Invest, Low Price, High Price Invest, Low Price, Low Price O Don't Invest, High Price, High Price Don't Invest, Low Price, High Price LOW Price (2,4) You High Price (4,4) Don't Invest High Price Low Price Shovenstuff Low Price You High Price (8,1) (2.6) Low Price (2,1)Suppose players A and B play a discrete ultimatum game where A proposes to split a $5 surplus and B responds by either accepting the offer or rejecting it. The offer can only be made in $1 increments. If the offer is accepted, the players' payoffs resemble the terms of the offer while if the offer is rejected, both players get zero. Also assume that players always use the strategy that all strictly positive offers are accepted, but an offer of $0 is rejected. A. What is the solution to the game in terms of player strategies and payoffs? Explain or demonstrate your answer. B. Suppose the ultimatum game is played twice if player B rejects A's initial offer. If so, then B is allowed to make a counter offer to split the $5, and if A rejects, both players get zero dollars at the end of the second round. What is the solution to this bargaining game in terms of player strategies and payoffs? Explain/demonstrate your answer. C. Suppose the ultimatum game is played twice as in (B) but now there…Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.
- This figure below shows the payoffs involved when Sarah and Joe work on a school project together for a single grade. They both will enjoy a higher grade when more effort is put into the project, but they also get pleasure from goofing off and not working on the project. The payoffs can be thought of as the utility each would get from the effort they individually put forth and the grade they jointly receive. Serah Lew Effen High Eet Low Effert Joe 15 High Effon The outcome of the game in the figure shown will be: Multiple Choice Joe puts forth high effort and Sarah puts forth low effort. Joe puts forth low effort and Sarah puts forth high effort. Joe and Sarah both put forth low effort. Joe and Sarah both put forth high effort.Game Theory Question A non-profit firm is on a local community online donation platform for a community event it wants to hold (only community members can donate via the website). The event will be held only if the non-profit firm collects $20,000 total from members of the community. Each member values the event at $500. Suppose that there are 100 community members. Community members can only donate by purchasing a lottery ticket from the firm. Each ticket costs $200 and only one ticket can be purchased per member. The proceeds will be collected by the firm. The lottery winner gets a premier meal at a local restaurant that's worth $100. Remember, the firm keeps all the donated money. If the amount of donations is less than $20,000, then the firm returns the donated money to the community members (since there'll be no event held but the lottery winner still gets to eat that fancy meal). If the donations sum up to $20,000, the community event will take place. What are the Nash…Consider the following simplified bargaining game. Players 1 and 2 have preferences over two goods, x and y. Player 1 is endowed with one unit of good x and none of good y, while Player 2 is endowed with one unit of y and none of good x. Player i has utility function: min{xi, yi} where xi is i's consumption of x and yi his consumption of y. The "bargaining" works as follows. Each player simultaneously hands any (nonnegative) quantity of the good he possesses (up to his entire endowment) to the other player. (a) Write this as a game in normal form. (b) Find all pure strategy equilibria of this game. (c) Does this game have a dominant strategy equilibrium? If so, what is it? If not, why not? Please show all work. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.