3 Theater 1 and Theater 2 are the only movie theaters in town. They each choose one ofthree prices for movie tickets: Low, Medium, or High. If they select the same price, theywill split the market. If one of the movie theaters chooses a lower price, it will get moreclients. Their interaction is described as a game.Theater 2High($6,000, $0)|($2,000, $5,000) | ($4,000, $4,000) | ($7,000, $2,000)($2,000, $7,000) ($5,000, $5,000)Medium($3,000, $3,000) ($5,000, $2,000)LowLowMediumHigh($0, $6,000)a) Do these players have a maxi-min or dominant strategies? If so, what are they?b) What are the Nash equilibrium or equilibria for this game? Explainc) What kind of games is this? What is the profit-maximizing (the highest total profit)outcome and how can the theaters reach it?Theater 1

Game Theory is a part of economics that studies the different ways the various choices of economic…

Theater 1 and Theater 2 are the only movie theaters in town. They each choose one of three prices for movie tickets: Low, Medium, or High. If they select the same price, they will split the market. If one of the movie theaters chooses a lower price, it will get more clients. Their interaction is described as a game. Theater 2 High ($6,000, $0) |($2,000, $5,000) ($4,000, $4,000)| ($7,000, $2,000) ($5,000, $5,000) Low Medium Low |($3,000, $3,000) ($5,000, $2,000) Medium High ($0, $6,000) ($2,000, $7,000) a) Do these players have a maxi-min or dominant strategies? If so, what are they? b) What are the Nash equilibrium or equilibria for this game? Explain c) What kind of games is this? What is the profit-maximizing (the highest total profit) outcome and how can the theaters reach it? Theater 1

Theater 1 and Theater 2 are the only movie theaters in town. They each choose one of three prices for movie tickets: Low, Medium, or High. If they select the same price, they will split the market. If one of the movie theaters chooses a lower price, it will get more clients. Their interaction is described as a game. Theater 2 High ($6,000, $0) |($2,000, $5,000) ($4,000, $4,000)| ($7,000, $2,000) ($5,000, $5,000) Low Medium Low |($3,000, $3,000) ($5,000, $2,000) Medium High ($0, $6,000) ($2,000, $7,000) a) Do these players have a maxi-min or dominant strategies? If so, what are they? b) What are the Nash equilibrium or equilibria for this game? Explain c) What kind of games is this? What is the profit-maximizing (the highest total profit) outcome and how can the theaters reach it? Theater 1

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

See similar textbooks

Similar questions

In the following game, find the dominated strategies for each player and the reduced game and solve the pure equilibrium strategy. Also solve the mixed equilibrium strategy, if it doesn't exist, explain Y1 Y2 Y3 |(10,-10) (2,-2) X1 |(4,-4) (5,-5) X2 (3,-3) (4,-4) X3 (8,-8) (6,-6) (9,-9)
Consider the following game. Firm 1 can implement one of two actions, A or B. Firm 2 observes the action chosen by Firm 1 and then decides whether to fight it or not. (-10, 20) F2 Fight A Don't fight -(30, 10) Firm 1 (-10, 0) Fight B Don't fight -(20, 15) (a) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses fight if A, and fight if B. • this strategy profile is [Select] (b) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses fight if A, and don't fight if B. • this strategy profile is [Select] O (c) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses don't fight if A and don't fight if B. • this strategy profile is [Select] 00 F2 ()
Two workers are on a production line. They each have two actions: exert effort, E, or shirk, S. Effort costs a worker e > 0 and shirking costs them nothing. If two workers do action E a lot of output is produced and the workers earn £3 each. If only one worker chooses action E less output is produced and they both earn £1. The workers earn nothing if they both shirk. (i) Describe this situation as a strategic form game (assuming the workers do not observe each other's effort choice when making their own decision). (ii) For what values of e does this game have strictly dominant strategies? (iii) Describe the Nash equilibria of this game for e = 0,1, 2, 3. (iv) The workers now are re-arranged into a production line. First worker 1 moves and then worker 2 moves. Worker 2 can now see worker l's effort level before they choose their effort. Draw this extensive form game. (v) Find the subgame perfect equilibria of the production-line game for c = 1/2 and c = 3/2.
Two network TV channels compete in the same market. They can broadcast a sitcom or a game show in prime time. Their objective is to maximize viewership in their local market. The outcomes corresponding to each of their strategies is shown below. Use your mouse to point and click on the Nash equilibrium outcome(s). [There may be more than one so make sure you work out all the best response strategies]. Network 1 Sitcom O Game show O Sitcom Network 2 55%,45% 50%,50% Game show 52%,48% O 45%,55% O
In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Is there a pure strategy? Why or why not? Determine the optimal strategies and the value of this game. Does the game favor one player over the other? Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A’s winnings? Comment on why it is important to follow an optimal game theory strategy.
Suppose there are two players playing a game with east or west and south and nerth ways. Find the expected Nash equilibrium by using the concept of probabilities. Player X Left[L) Right|R) Player Y Up(U) (5,6) (0,8) (4,6) Down[D) (0,9)
Keep Prices Advertise Lower Prices (4.6) Firm 1 Advertise; lower prices Not advertise; lower prices Advertise; keep prices Not advertise; keep prices Firm 2 Not Advertise Keep Prices (15,5) Consider the above extensive form game. The subgame perfect Nash-equilibrium is Lower Prices (6,10) (5,11)
In a gambling game, Player A and Player B both have a $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A.
Which of the following conditions correctly describes a Nash equilibrium when two firms are in the market? Multiple Choice n91s1. $2)2 (51. $2) for all s1 and 12(51, $2)212(51. 52) for all s2. aqls1, s2)22(s1, s2) for all s1 and a2(s1, 52) 2 n1ls1.52) for all s2. Rylsi. s2)2 als1. 52) for all s as1. 52)22(1. s2) for all sy and a2(s. s2)2 a1(s1, s2) for all s2
$11. Anne and Bruce would like to rent a movie, but they can't decide what kind of movie to get: Anne wants to rent a comedy, and Bruce wants to watch a drama. They decide to choose randomly by playing "Evens or Odds." On the count of three, each of them shows one or two fingers. If the sum is even, Anne wins and they rent the comedy; if the sum is odd, Bruce wins and they rent the drama. Each of them earns a payoff of 1 for winning and 0 for losing "Evens or Odds." (a) Draw the game table for "Evens or Odds." (b) Demonstrate that this game has no Nash equilibrium in pure strategies.
Suppose that player 1 (row) and player 2 (column) play a simultaneous game. Player 1 can choose to go out (Go) or stay at home (Stay). Player 2 can then choose whether to buy tickets to the movies (Movie), to the basketball game (Game) or not buy tickets (None). This game is shown below. Player 1(row) Player 2 (column) Movie Game None Go (6, 4) (4, 6) (0, 0) Stay (2, - 2) (2, - 4) (3, 3) What is the Maxi-Min strategy for player 1 and for player 2? Explain why. What are the Nash equilibrium or equilibria for this game? Explain why. What kind of game is this? Argue what is the most likely outcome.
For the friend-foe game, recall that there were 3 Nash equilibria possible, but the equilibria set didn't include the cooperative outcome, for which both players would win. Friend Foe Friend 500,500 0,1000 Foe 1000,0 0.0 a) If the game is played répeatedly. propose a play strategy that will enforce cooperation. For what valucs of o (discount factor) the equilibrium will be (Friend. Friend)?