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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Two street racers are playing a simultaneous game of chicken. They have to race towards each other and whoever swerves first is chicken and faces shame, a loss of 8. while the winner enjoys a gain of 3. If neither stop, they would crash into each other, a loss of 10. If both of them swerve at the same time, they are both chicken and face a loss of 5 each If player B destroys his own brakes before the race, and player A sees that, what would the new Nash equilibrium be in this case? a. Player A stops, Player B does not b. Player B stops, Player A does not c. Both players stop d. Neither players stop
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2. Consider the two-player strategic form game represented in the following payoff table: t 1 m b 7,2 1,2 3,7 2 M 2,4 3,4 1,6 R 1,3 7,1 4,2 Player 1 chooses between rows, S₁ = {t, m, b), and receives the first listed payoff in each cell. Player 2 chooses between columns, S₂ = {L, M, R), and receives the second listed payoff in each cell. a. Does either player have a strictly dominant strategy? Explain. b. Explaining your steps carefully, identify the set of rationalizable strategies in this game. c. Making sure to explain your solution method, solve for all pure strategy Nash equilibria in this game.
3.Students A and B decide whether to clean the dormitory. Regardless of whether the other party participates, the cleaning cost for each student to clean the dormitory is $ 8; and the benefit for each student from cleaning is $5 times the number of participants. (hint: if both of them clean the dormitory together, A and B benefit. If one cleans while the other does not, A and B benefit too) (a) Please use a game theory to briefly describe the above scenario, (that is to calculate the revenue for different strategies) (b) Draw the payoff matrix, find the Nash equilibrium.
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the Consider a simultaneous-move integer game between two players: Marilyn and Noah. Each of player is required to announce a positive integer between 1 to 4. In other words, a player can announce 1, 2, 3, or 4. Two players announce their integers simultaneously. Notice that this game is different from the games we learned in class in that each player has four actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both O. What is Marilyn's maximin strategy? 01 02 03 O
Consider the following two player game. In each cell the first number refers to the payoff to Player 1 while the second number refers to the payoff to Player 2. Suppose the two players move simultaneously (at the same time). Which one of the following statements is CORRECT? Player #1 Player #2 Top Bottom Left 7.7 4.0 Right 0,4 4,4 O There are three equilibria in this game: two pure strategy equilibria at [Top, Left] and [Bottom, Right) and al third equilibrium in mixed strategies. In the mixed strategy equilibrium of this game. Player 1 should play Top with probability 2/5 and Bottom with probability 3/5; Player 2 should play Left with probability 2/5 and Right with probability 3/5. O There are three equilibria in this game; two pure strategy equilibria at (Top. Left) and (Bottom, Right) and a third equilibrium in mixed strategies. In the mixed strategy equilibrium of this game, both players should randomize over the strategies with probability and %. O There is a unique dominant…
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