2. Consider the following game table: Colin Rowena North East Top 4, 3, 1 Middle 3,5 2, 2,3 Bottom 3 3,4 4,2 a. Complete the payoffs of the game table above so that Colin has a dominant strategy. State which strategy is dominant and explain why. (Note: There are many equally correct answers.) Complete the payoffs of the game table above so that neither player has a dominant strategy, but also so that each player does have a dominated strategy. State which strategies are dominated and explain why. (Again, there are many equally correct answers.) b. South ,2

2. Consider the following game table: Colin Rowena North East Top 4, 3, 1 Middle 3,5 2, 2,3 Bottom 3 3,4 4,2 a. Complete the payoffs of the game table above so that Colin has a dominant strategy. State which strategy is dominant and explain why. (Note: There are many equally correct answers.) Complete the payoffs of the game table above so that neither player has a dominant strategy, but also so that each player does have a dominated strategy. State which strategies are dominated and explain why. (Again, there are many equally correct answers.) b. South ,2

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 3MC

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You are playing a game with a friend. It’s yourmove but you don’t have a dominant strategy.Your payoff depends on what your friend doesafter your move. You consider flipping a coin todecide what to do. You are about to reach for acoin, but then you realize that your friend has adominant strategy. Explain how using backwardinduction (rather than a coin toss) will now determine your next move
Consider the following simultaneous game: Player 1 U D Player 2 L 30,10 -10, 20 R 10, 20 5,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.
The following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff of
ITERATIVE DOMINANCE Consider the following game in strategic form. a₁ 22 a3 bi 35,52 30,30 28,9 (9,11) (45,47) (47,28) (52,16) (28,9) (30,30) (16,45) (11,35) (35,52) b2 11,35 9,11 16,45 b3 52,16 45,47 47,28 Which of the following payoff profiles survive iterative deletion of strictly dominated strategies? (Mark all profiles that survive.)
Two farmers, Ali and Hasan, graze their animals on a common land. They canchoose to use the common resource lightly or heavily and the resulting strategic interactionmay be described as a strategic form game. The payoff matrix is the following: (The table is attached on iamges part) Suppose that the game is repeated infinitely. If both players play a Grim-Trigger strategy, findthe discount factor δ such that (Light,Light) be a Nash equilibrium
INFINITE REPETITION Consider the infinitely repeated game constructed from the following stage game. bị b2 a1 8,8 3,13 a2 13,3 0,0 Suppose that both players use the discount factor d to evaluate future payoff streams. What is the smallest value of d such that there exists a subgame perfect Nash equilibrium in which the action profile is played in all periods? (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.)
GAME UUU B1 Player B B2 A1 7,13 5, 10 A2 3,8 9,16 Player A A3 5,8 4,7 In Game UUU (see table above), assuming players move simultaneously, Player A choosing A1 and Player B choosing B3 is a Nash equilibrium. Player A choosing A3 and Player B choosing B2 is a Nash equilibrium. Both Player A choosing A1 and Player B choosing B1 and Player A choosing A2 and player B choosing B2 are Nash equilibria in pure strategies Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.
11. The following payoff table involves two players each of whom has three possible moves. L M N L 30,15 45,35 55,25 M 25,35 20,20 30,50 N 15,35 35,40 15,15 a. Is there any dominant strategy equilibrium?
QUESTION 4. Consider the following game. Player 1's payoffs are listed first, in bold: P2 W X Y Z 200, A 100, 500 300, 300 500, 3 1 B 0, 300 400 3 0, 0 P1 500 0 " C 20, 300 10, 300 50 2 310 400 a. Does either player have any weakly dominant strategies? List it/them or explain why not. b. Does either player have any strictly dominated strategies? If yes, list it/them. C. If the game were played sequentially with Player 1 going first, what is the subgame perfect Nash equilibrium?
Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.
Consider the following simultaneous game: Player 1 U D Player 2 L 30,20 -10, -10 R -10, -10 20,30 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has two Nash equilibria in pure strategies. Player 1's payoff in each of the Nash equilibria is 30.
1) Put together an example of a 2x2 game (two players with each having two options) that has NO pure-strategyNash equilibria. (Hint: just try some values and then change them as you need to; as an example think aboutthe Rock, Scissors paper which has no pure strategy NE).2) Using your own words, explain how the concept of elimination of dominated strategies differs from theconcept of Nash equilibrium.3) Indicate whether the following statement is TRUE or FALSE and explain your answer: If one player is theleader in a game it means that s/he has the first move in the game. The key thing is that this move can beobserved by the follower before making his/her own decision, otherwise it would be a simultaneous movegame that cannot be solved by backwards induction.4) MULTIPLE CHOICE (identify the one best answer below and explain your reasoning for each option): Recallthe Game of chicken from the previous problem set. If James is the leader in the game then: (hint: you candraw the game tree…