12. An important characteristic of a dominant strategy is that: Select one: a. it is the best strategy to dominate your opponents b. it always leads to a Nash equilibrium where all players equally well off c. it can prevent the game reaching a Nash equilibrium d. it is the best strategy for a player, regardless of whatever strategy the opponent chooses
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- Sometimes oligopolies in the same industry are very different in size. Suppose we have a duopoly where one firm (Film A) is large and the other film (Film B) is small, as the prisoners dilemma box in Table 10.4 shows. Assuming that both films know the payoffs, what is the likely outcome in this case?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 moveConsider this as a simultaneous-move (static) game: Player A Top Bottom Player B Left Right ETEL UU 1.b) Does any player have a dominant strategy in this game? Explain. 1.a) Write down the Best Response Correspondence for each of the two players. Molimonsbestich Quinit 1.c) Find all Nash Equilibria in pure strategies of this game. 1.d) Is there any Nash Equilibria in mixed strategies? If so, find it. Elekt
- 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 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)?Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?
- 12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?4. This problem is based on after chapter question 11. If you are not familiar with the rule of baseball game, just use the figure below. a. Find the subgame perfect Nash equilibrium. Note: like many sports games we discussed, the equilibrium is often about mixed-strategies. b. What are the equilibrium payoffs of two players? FIGURE PR9.11 The Suicide Squeeze Game Torre Suicide squeeze Torre 10 LaRussa 0 Pitchout No suicide squeeze 2 ∞0 N LaRussa 8 Suicide squeeze No pitchout Suicide squeeze 9 Pitchout No suicide squeeze 4 6 No suicide squeeze Torre LaRussa No pitchout Suicide squeeze 37 No suicide squeeze 5 55 5Consider the extensive form game portrayed below. The top number at aterminal node is player 1’s payoff, the middle number is player 2’s payoff,and the bottom number is player 3’s payoff.a. Derive the strategy set for each player. (Note: If you do not want to listall of the strategies, you can provide a general description of a player’sstrategy, give an example, and state how many strategies are in thestrategy set.)b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it isnot a SPNE.
- a. The president of a Japanese electronics company, Takashi Hashiyama, famously chose the auction housefor his company’s art collection by having representatives from two auction houses, Christie’s and Sotheby’s,play a round of rock-paper-scissors. At stake were millions of dollars in commissions. Show the payoff matrixfor a game where the payoff is 1 if you win, 0 if you tie, and -1 if you lose. I’m sure you know this already, butjust in case: rock breaks scissors, scissors cut paper, and paper smothers rock. Here’s an article about the actualgame if you’re interested. b. If you were in a high stakes game…1. For the following game Player B Player A Left 7,17 10,5 4,4 Middle Right 14,11 4,3 10,25 21,21 Тop Middle 14,4 Bottom 7,3 a) Determine the Nash equilibrium is any? b) Represent the game sequentially starting with player 1 and determine the sub-game perfect equilibrium c) Represent the game sequentially starting with player 2 and determine the sub-game perfect equilibrium d) Find the mixed strategy Nash equilibrium of the following game e) Firm 1 Firm 2 High price Low price High price 4,3 2,4 Low price 2,4 3,31. Consider a two-period repeated game in which the stage game shown below is played twice and the repeated-game payoffs are simply the sum of the payoffs in cach of the two periods. Show that there exists a unique subgame perfect Nash equilibrium in which the Nash equilibrium of the stage game is played in every period. Player 2 W Y A 3,2 3, 1 2,0 4, -4 B 1, 3 4,2 3, 1 2, 3 Player 1 0, 2 1,3 9, 8 0,9 D -4, 4 3, 2 10, 1 0,0 Consider a two-period repeated game in which the stage game shown below is played twice and the repeated-game payoffs are simply the sum of the payoffs in each of the two period. Find a subgame perfect reputational equilibrium in which players choose a non- stage-Nash-equilibrium strategy in the first period? SHOW YOUR WORK. 2. Player 2 Y A 3, 2 3, 1 2,0 4, -4 B. 1,3 4, 5 3, 1 2, 3 Player I 1, 3 3, 2 0, 2 9,8 0, 9 -4,4 10, 1 0,0 NOTE: A reputational Nash equilibrium should be written in a form shown below: LJin Stage 1 - the better equilibrium of the stage game in…