Player 2 C R T 8, ? 46, 2 Player 1 M 6, 12 5,? 4, 6 B ? ,6 6,8 8,3 Consider the following two-player, simultaneous- move game: a)Complete the payoffs of the game table above so that Column has a dominant strategy. State which strategy is dominant and explain why. (Note: there are many correct answers; pick one that works) b)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
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- 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?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)?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…
- ALBUS MINERVA N S Z MINERVA لی a C a b 3,3 ALBUS b 0,4 2,2 4 N S 15,2 1,3 13,1 For the above sequential game, both Albus and Minerva make moves in two possible situations. A number in purple indicates which node of the two for each of Albus and Minerva. Albus' strategy NS indicates a strategy of taking action N at node 1 and action 5 at node 4. Minerva's strategy ab indicates a strategy of taking action a at node 2 and action b at node 3. Adopt this format of writing strategies, find the subgame perfect Nash equilibrium. Fill in the blanks: The subgame perfect Nash equilibrium of this game is "Albus" Minvera"Hi this is from a textbook. Thank you. Consider the following game in which Sally can play T or B and John chooses between L or R. Each player makes their choice simultaneously. If Sally chooses T and John chooses L, Sally gets a payoff of 5 and John has a payoff of 4. If Sally plays T and John R, Sally’s payoff is 8 and John gets 3. If Sally Chooses B and John L, the payoffs are 3 to Sally and 2 to John. Finally, if Sally chooses B and John R, the payoffs are 7 to Sally and 0 to John. Which statement is true? a) The Nash equilibrium is (B,R); this is a prisoners’ dilemma b) The Nash equilibrium is (T,R); this is a prisoners’ dilemma c) The Nash equilibrium is (T,R); this is not dominant strategy equilibrium d) The Nash equilibrium is (T,L); this is a dominant strategy equilibrium e) None of the abovees Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. C 23, 5 27, 5 a. What is player 1's optimal strategy? Player 1 Strategy O Strategy B O Player 1 does not have an optimal strategy. Strategy A b. Determine player T's equilibrium payoff. 21 D 10, 16 4,9 Player 2 E 18, 18
- Player 2 E F H A 6, 5 6, 7 9, 6 7,6 В Player 1 C 6, 7 6, 9 8, 5 9, 7 5, 8 5, 6 7,5 7,5 7,9 8, 7 11, 6 5, 6 (1) In the Unique Nash equilibrium of this game, which strategy does Player1 play? And why? (2) In the Unique Nash equilibrium of this game, which strategy does Player2 play? And why? (3) Is this game dominance solvable? And Why? (4) Does this game have at least one inadmissible Nash equilibrium? And Why?Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. Player 2 E Strategy C 6, 14 12, 5 Player 1 a. What is player 1's optimal strategy? B D 7, 11 18, 20 15, 1 7, 25 O Player 1 does not have an optimal strategy. O Strategy B Strategy A b. Determine player 1's equilibrium payoff. F 10, 19 16, 17Solve 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.
- K In a game, there are two players: Player 1 and Player 2. They have two strategies to select from, A and B. Where the first payoff and the second payoff in every cell is for Player 1 and Player 2 respectively. Which of the following is an example of a game without a dominant strategy? (Check all that apply.) A. C. Player 1 Player 1 A B A B A 3,-3 1, 1 A 2,1 0,0 Player 2 Player 2 B 3, -3 5, -5 B 0,0 1,2 B. D. Player 1 Player 1 A B A B A 1,-1 -1, 1 Player 2 Player 2 A 3.5, -1.5 2.7, -1 B -1, 1 1,-1 B -5, 3 0,0 If the dominant strategy for Player 1 is selecting strategy A and the dominant strategy for Player 2 is strategy B, then A B is an example of a c From ame C Murat Çok Di id Kushn y My Hand1. 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 3,3Consider the following simultaneous move game: Player 1 \ Player 2 Top Bottom Select one: Left Right 5,3 4,1 2,0 0,2 Player 2 has a dominant strategy in this game. Player 1 has a dominant strategy in this game. O This game has a Nash equilibrium in dominant strategies. This game does not have a Nash equilibrium in pure strategies. None of the statements is correct. O