Two fishermen (Andy and Bob) are fishing in the same lake. Each can either fish for 5 or 6 hours. Their payoffs depend on how much time each of them fishes: - If they both fish for 6 hours each, their payoff is 2 fish for Andy and 2 fish for Bob; - if they both fish for 5 hours each, their payoff is 3 fish for Andy and 3 fish for Bob; - if one fishes for 5 hours and the other for 6, then the payoff of the former is 1 fish and of the latter is 4 fish. What are the payoffs at the Nash Equilibrium if they play sequentially, and Bob plays first? (Hint: Before you choose the correct answer, write the game in a tree form and find the Nash Equilibrium) Select one: a. Andy gets 2 and Bob gets 2 b. Andy gets 3 and Bob gets 3 c. Andy gets 1 and Bob gets 4 d. Andy gets 4 and Bob gets 1

Two fishermen (Andy and Bob) are fishing in the same lake. Each can either fish for 5 or 6 hours. Their payoffs depend on how much time each of them fishes: - If they both fish for 6 hours each, their payoff is 2 fish for Andy and 2 fish for Bob; - if they both fish for 5 hours each, their payoff is 3 fish for Andy and 3 fish for Bob; - if one fishes for 5 hours and the other for 6, then the payoff of the former is 1 fish and of the latter is 4 fish. What are the payoffs at the Nash Equilibrium if they play sequentially, and Bob plays first? (Hint: Before you choose the correct answer, write the game in a tree form and find the Nash Equilibrium) Select one: a. Andy gets 2 and Bob gets 2 b. Andy gets 3 and Bob gets 3 c. Andy gets 1 and Bob gets 4 d. Andy gets 4 and Bob gets 1

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q14. Do players have perfect information in the above game? Yes, all of them have perfect information No, player 2 has imperfect information No, player 3 has imperfect information No, no player has perfect information Q15. If we want to describe the above game with a strategic form representation, what would the strategy sets for the three players be? Player 1={a, b, c} ; Player 2={x, y}; Player 3={r, s} Player 1={a, b, c} ; Player 2={xx, xy, yx, yy}; Player 3={r, s}
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
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Consider the following situation. Maipo and Pisco need to decide how to divide a cake between the two of them. Both like cake and want to get as much cake as they can. They decide to let Maipo cut the cake first and then Pisco gets to pick which piece he wants. For simplicity, assume that Maipo can only cut the cake in two ways: He can either divide it into two pieces that are equal size (i.e., both will get half the cake) or he can divide the cake into two pieces where one piece is twice the size of the other (i.e., one will get a piece that is two-thirds of the cake and the other will get a piece that is one-third of the cake). Set up this game as a sequential game and draw the game tree that represents it Note: You can either draw the game tree by hand and then photograph/scan the tree and paste it into the assignment or use the drawing tool in Word to draw the tree. Find the sub-game perfect Nash Equilibria to this game. Underline the strategies or highlight the…
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Alice and Betsy are playing a game in which each can play either of two strategies, leave or stay. If both play the strategy leave, then each gets a payoff of $400. If both play the strategy stay, then each gets a payoff of $800. If one plays stay and the other plays leave, then the one who plays stay gets a payoff of $C and the one who plays leave gets a payoff of $D. When is the outcome where both play leave a Nash equilibrium? a) never, since 800 > 400 b) when 400 > C and D > 800 but not when 800 > D c) whenever 400 > C d) when D > C and C > 400 e) whenever d < 800
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…
Rosencrantz and Guildenstern play a game in which they simultaneously put down some number of coins with either a head or a tail showing on each coin. Rosencrantz puts down one coin and Guildenstern puts down two coins. Rosencrantz pays Guildenstern one dollar for each coin that shows the side that Rosencrantz played; for example, if Rosencrantz played a head and Guildenstern played a head and a tail, Rosencrantz would pay Guildenstern two dollars, since two heads were displayed among the three coins. a. Formulate a strategic game that represents this situation. b. Find all Nash equilibria of this game (including any mixed strategy equilibria). c. For each of the Nash equilibria in (b), give Guildenstern’s expected payoff.
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