Jagtar and Ravi both grow mangoes, which they sell in the same local market. They are deciding whether to pick 5 baskets worth of mangoes or 10 baskets, and have the following profit matrix: Jagtar 5 1 17 5 22 16 1 14 Ravi 1 24 14 a. What is the Nash equilibrium if both individuals make their decisions simultaneously? b. Does your analysis change if the local market charges a lump-sum fee of 12 to set up a stall and sell the mangoes in the space it provides? c. What would happen if the local market were instead to charge a lump-sum fee of 18?

Jagtar and Ravi both grow mangoes, which they sell in the same local market. They are deciding whether to pick 5 baskets worth of mangoes or 10 baskets, and have the following profit matrix: Jagtar 5 1 17 5 22 16 1 14 Ravi 1 24 14 a. What is the Nash equilibrium if both individuals make their decisions simultaneously? b. Does your analysis change if the local market charges a lump-sum fee of 12 to set up a stall and sell the mangoes in the space it provides? c. What would happen if the local market were instead to charge a lump-sum fee of 18?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

See similar textbooks

Similar questions

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…
Ten commuters must decide simultaneously in the morning to use route A or route B to go from home (same place for all) to work (ditto). If a of them use route A, each of them will travel for 10a + 40 minutes; if b of them use route B, each of them will travel for 10b minutes. Everyone wishes to minimize his/her commuting time. Your tasks: Describe the pure Nash equilibrium (or Nash equilibria) of this ten-person game. Compute the corresponding profile of commuting times. Explicitly list all equilibrium conditions that are satisfied. à. b. What is the traffic pattern (strategies) minimizing the total travel time of all commuters (the sum of their travel times)? Describe the corresponding profile of commuting times (individual payoffs/cost). What does this mean about the Price of Anarchy of this game (assuming that the objective function is the total travel time)? с.
Use the following payoff matrix for a one-shot game to answer the accompanying questions. A 5,5 0, -200 B -200, 0 20, 20 Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication. Which of these outcomes would you consider most likely? Explain. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter, and what outcome do you think would occur as a result?
Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land. Farmer 2 Farmer1 1 cow 2+ cows 1 cow 8,8 2,10 2+cows 10,2 4,4 What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off) The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:…
Team 2 plays A Team 2 plays B Team 1 plays A 2, 1 0,0 Team 1 plays B 0,0 1, 2 Consider the game above. Which of the following is a Nash Equilibrium of the game? O Team 1 plays A two thirds of the time and plays the rest of the time, while team 2 plays A two thirds of the time and plays B the rest of the time. Team 1 plays A one quarter of the time and plays B the rest of the time, while team 2 plays A one quarter of the time and plays B the rest of the time. Team 1 plays A one quarter of the time and plays B the rest of the time, while team 2 plays A three quarters of the time and plays B the rest of the time. O None of the other answers are correct. Team 1 plays A two thirds of the time and plays B the rest of the time, while team 2 plays A one third of the time and plays B the rest of the time.
Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 1, -1 -1, 1 Right -1, 1 1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays up
Write the game below in normal form and find all Nash equilibria. C 2. Write the game below in normal form and find all Nash equilibria. जल P = 1/1535 Nature ताल P = 1/3 P1 A (3,6) P1 B P2 B C2 P2 Pz Pz (0,3) ✓ (9,0) (3,3) ✓ (0, 6) (-3,3) ✓ (9,6) Х (3,0) (-3, 12)
Consider a beauty-contest game in which n players simultaneously pick a number between zero and 100 inclusive; the person whose number is closer to half of the average number wins a prize. What is the unique Nash equilibrium of this game? What number will a level-3 thinker pick?
The bimatrix represents a simultaneous move game between Rowena and Colin. Rowena's payoff is the left number in each cell. ROWENA O O 2 Calculate Rowena 's expected payoff in the mixed strategy Nash equilibrium. 3.5 2.5 Up Down 3 Left 1,16 2,20 COLIN Right 4,6 3,40
1. Ten commuters must decide simultaneously in the morning to use route A or route B to go from home (same place for all) to work (ditto). If a of them use route A, each of them will travel for 10a + 40 minutes; if b of them use route B, each of them will travel for 10b minutes. Everyone wishes to minimize his/her commuting time. a) Describe the pure Nash equilibrium (or Nash equilibria) of this ten-person game. Compute the corresponding profile of commuting times. Explicitly list all equilibrium conditions that are satisfied.
Q3 Consider the following three-player normal form game (Player 3 is the page player): Player 3 A в Player 2 Player 2 A в A B 1,2, 3 в 2,3,1 Player 1 A Player 1 A 2, 1, 3 3, 2, 1 3, 2, 1 1,2, 3 в 1,3, 2 3, 1,2 For each player, strategies are A and B. a) Find the pure strategy Nash equilibrium of the above game. Assume now that the above game is played sequentially, with Player 3 moving first, Player 1 moving second, and Player 2 moving third. b) Write down the game tree. c) For each player, list all the available pure strategies. d) Find the subgame perfect equilibrium outcome and compare it with the equilibrium outcome you found in subquestion a). Comment.
Suppose Antonio and Trinity are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Antonio chooses Up and Trinity chooses Down, Antonio will receive a payoff of 7 and Trinity will receive a payoff of 5. Trinity Up Down Up 4,8 7,5 Antonio Down 3,2 5,6 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses, and Trinity chooses Grade It Now Save & Continue Continue without saving @ 2 F2 #3 80 Q F3 MacBook Air 44 F7 Dll F8 44 F10 74 $ 4 05 Λ & % 5 6 7 8 * 0 Q W E R T Y U 1 A N S X 9 0 -O O D F G H J K L on را H command C > B N M Λ - - P [ H Λ command opti