Two rival soap companies want to sell off their old winter products of clothing to make room in their stores for their spring soaps. They both are thinking of having a sale of the winter soaps (where they sell their winter soaps at a reduced price). The following table shows the payoff matrix, in terms of profits, that represents the strategic interaction between the two soap companies in a one-shot, simultaneous game. Select one correct answer.
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- 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.The next three questions pertain to the following normal-form game played by Pepsi and Coke: Coke Pepsi → | Advertise Don't 3.3 0,5 Advertise 5.0 Don't 4,4 7. Write in the blank Coke's best response to Pepsi, if Pepsi Advertises, 8. If the firms could collude, what pair of actions would they try and agre0 on (write "Advertise" or "Dont" on the line)? Pepsi: Coke: 9. What are the Nash equilibrium strategies of the firms? Coke: Pepsi: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
- Consider 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. ElektThe following payoff matrix depicts the profits for the only two firms in this oligopolistic industry. In each cell, the 1st number is Firm A’s profit and the 2ndnumber is Firm B’s Profit. (Scenario: Payoff Matrix for Firms A and B) In the scenario Payoff Matrix for Firms A and B. If they play the game for 10 times, what will be firm A's pay off if both A and B will choose "always choosing High price strategy", i.e the firm will always choose High price each time? 60 Need more information to tell. 100 6Consider a sequential-move game in which an entrant is considering entering an industry in competition with an incumbent firm. If the entrant does not enter ("Out"), the incumbent firm earms a payoff of 10, while the entrant earns a payoff of 0. If the entrant enters ("In"), then the incumbent can either accommodate or fight. If the incumbent accommodates, both eamn a payoff of 5. If the incumbent fights, then the entrant can either leave the industry ("Withdraw") or remain in it ("Stay"). If the entrant stays, both earn a payoff of -5. If the entrant withdraws, the entrant earns a payoff of - 1, and the incumbent earms a payoff of 8. The extensive form of the game is depicted in the following figure, where the payoffs are of the form (Entrant Payoff, Incumbent Payoff). Entrant In Out Incumbent Accommodate Fight O Entrant (5,5) (0,10) Stay Withdraw (-5,-5) (-1,8)
- Suppose only two airlines, United and Delta, provide flights between Atlanta and Winston - Salem. Both firms must choose whether to advertise or not advertise. The advertising strategies with corresponding profits are depicted in the payoff matrix to the right. United Airline's profits are in blue and Delta Airline's are in red United Airline's dominant strategy is to and Delta Arline's dominant strategy is to What is the Nash equilibrium for this game? O A. United and Delta will both choose not to advertise. O B. United will choose to advertise and Delta will choose not to advertise. < Previous KalturaCapture....dmg tf00002104_wac.docx WConsider 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.Please look at the payoff matrix below which shows the benefits that would accrue to each player in a 2-player.non-sequential, non-repeated game. a) Identify the collusive (cooperative) equilibrium. b) Identify the secure strategy (maximin) equilibrium c) Identify the maximax equilibrium d) Identify the Nash equilibrium Apple Inc. Strategy 1 Strategy 2 Strategy 3 20 40 60 60 1000 200 Strategy A 70 50 90 Banana Inc. 400 70 300 Strategy B 40 80 100 90 150 80 Strategy C
- Barnes and Nobel and Amazon are the two largest online book retailers in the U.S.. The two companies compete in the online market for‘Harry Potter and the Sorcerer’s Stone’, a famous book by the English author J. K. Rawling. Both companies can buy copies of the bookfrom Scholastic at $8 per copy and have an additional average cost $1 per copy.Use game theoretical concepts to explain why, even if the two companies have significant market power, on most days they both sell the bookat $9 per copy.2: Provide a definition for a Nash equilibrium and then find all pure-strategy Nash equilibria of the following game: Left Center Right Up Middle 1,3 2,7 6,3 2,9 4,4 7,10 Down 3,8 2,5 3,41) 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…