Suppose Aldi and Woolworth are involved in a price war. Which of the following is correct? Select one: O a. This is a static game by its nature O b. This is a repeated prisoners' dilemma game O c. The process cannot be formulated as a game O d. None of the listed options
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- Describe the payoffs for an R&D game of chicken and contrast them with the payoffs in a prisoners' dilemma game. The outcome is that In the prisoners' dilemma R&D game, a firm can use the R&D O A. if either it or its competitor conducts the R&D; one firm conducts R&D; B. only if it conducts the R&D; one firm conducts R&D; OC. If either it or its competitor conducts the R&D; neither firm undertakes R&D; D. only if it conducts the R&D; both firms undertake R&D; In an R&D game of chicken, a firm can use the R&D The outcome is that A. only if it conducts the R&D; one firm conducts R&D B. only if it conducts the R&D; both firms undertake R&D C. if either it or its competitor conducts the R&D; one firm conducts R&D D. If either it or its competitor conducts the R&D; both firms undertake R&Dage Which of the following statements is the best description of a Nash equilibrium? Select one: O a. An equilibrium outcome achieved by cooperation between players in the game b. An outcome that is achieved when players in the game have jointly maximized profits and divided those profits according to market share of each player O c. An outcome where each player's strategy depends on the behaviour of its opponents d. An outcome where each player's best strategy is to maintain its present behaviour given the present behaviour of the other players Next pageConsider the following game, which is played simultaneously: B 1 1 -1 A 2 1 What type of game this is? O Battle of the Sexes O Chicken O None of the other choices is correct O Prisoner's Dilemma O Stag Hunt -1 3 32 2 1 2
- 1) What are the Nash equilibria? Which one is unreasonable/non-credible threat? 2) What are the subgame perfect Nash equilibria? Does SPNE concept eliminate the unreasonable Nash equilibrium?Consider the following price game: Firm 1 Firm 2 High Low High 20, 20 12, 24 Low 24, 12 14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?1. Suppose the following prisoner's dilemma is played twice with the payoff for the entire game being the sum of the payoffs from the two stages. Assume there is no discounting. Player 1 B Player 2 B 2,6 3,3 A 5,5 6,2 a. What is the Nash equilibrium for stage two? b. Show what the game in stage 1 amounts to when the players anticipate the Nash equilibrium for stage 2. c. Provide the subgame-perfect outcome for this game.
- rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.1. Static and Dynamic Game. Consider the following 2-by-2 game: C D 1A (1,10) (1,1) B (2, a) (0,1) (a) erwise, find the pure-strategy Nash equilibria, if any of this game. (There is no need to look for equilibria in mixed strategies) Assume for now that a = 2. Using dominant strategies or oth- (b) Now, consider the dynamic game in which player 1 moves before player 2, and the payoffs remain unchanged. i.: possible strategies for each player? Recall that a strategy profile for a player not at the initial node of the game tree must specify an action for the player at every node. Draw the game tree for this dynamic game. What are the ii "Find the backward-induction solution(s) to this game. Calculate the equilibrium payoffs for each player. Com- pared to the simultaneous game, is there a first-mover advantage or a ii. second-mover advantage? (c) Now, assume that a = 0 in the original static game. i. Find all the Nash equilibria in pure and mixed strategies. Denoting p the probability…D A popular way of sharing a cake between two people is to have one of the two cut the cake and the other chooses the who gets what piece. A. Write down the extensive form representation of this game. B. Solve for the Nash equilibrium strategy equilibrium. 4
- es What are the necessary features of a prisoner's dilemma-type game? Check All That Apply Two prisoners must be locked in separate jail cells. There must be a unique Nash equilibrium. The Nash equilibrium outcome must be inefficient. The game must have exactly three players. The game must have a dominant strategy.Which of the following is FLASE for an extensive form game with perfect information? A. All Nash equilibria has the property of non-credible threat B. Subgame perfect equilibrium eliminates non-credible threats O C. In a Nash equlibrium strategy, each agent's strategy is a contingent planConsider the following classic game, called Hawk and Dove. Player 2 Hawk Dove Hewk 0,0 4,1 Player 1 Dove 1,4 33 Select all pure strategy Nash equilibria and check the corresponding option if you think there exists a mixed strategy Nash equilibrium too. O There exists also a mixed strategy Nash equilibrium O Hawk, Dove O Dove, Hawk O Hawk, Hawk O Hawk, Hawk