This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide l output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A, Pr Firm B). Refer to Table. The dominant strategy For Firm A is to produce 5 units and the dominant strategy for Firm B is to produce 6 units. 5 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 6 units.
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- A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (36 + J )C - 2C 2 and the profits of the jeweler will be (30 + C )J - 2J 2. The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend. The amount spent by the clothing store will be Group of answer choices $17. $34. $51. $8.50. $25.50.Q56 A Nash equilibrium is an outcome... a. Achieved by cooperation between players in the game. b. That is achieved by collusion where no party has an incentive to change their behaviour. c. Where each player's strategy depends on the behaviour of its opponents. d. That is achieved when players in the game have jointly maximized profits and divided those profits according to market share of each player. e. Where each player's best strategy is to maintain its present behaviour given the present behaviour of the other players.The mixed stratergy nash equalibrium consists of : the probability of firm A selecting October is 0.692 and probability of firm A selecting December is 0.309. The probability of firm B selecting October is 0.5 and probability of firm selecting December is 0.5. In the equilibrium you calculated above, what is the probability that both consoles are released in October? In December? What are the expected payoffs of firm A and of firm B in equilibrium?
- When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .Look again at Figure 21.12. It appears that the investor in panel b can't lose and the investor in panel a can' t win. Is that correct? Note: The solution should not be hand written.You and your partner are choosing how much effort to put towards a group project for a course . You both care about the quality of the project , which increases in both of your effort choices . But you both also pay a cost of effort . You are enjoying the course much more than your partner , so your cost of effort is lower . Where y and p denote the amount of effort put by you and your partner , respectively , • Your payoff is 60yp - y³ . • Your partner's payoff is 60yp - 8p³ . Decisions about effort provision are made simultaneously . Answer the following questions about the set of pure strategy Nash equilibria of this game . Please round to 3 decimal places where rounding is needed . a ) In one pure strategy Nash equilibrium , you put more effort towards the project than your partner . In this Nash equilibrium , what is your effort level ? b ) In one pure strategy Nash equilibrium , you put the same level of effort towards the project as your partner . In this Nash equilibrium ,…
- Mohamed and Kate each pick an integer number between 1 and 3 (inclusive). They make their choices sequentially.Mohamed is the first player and Kate the second player. If they pick the same number each receives a payoff equal to the number they named. If they pick a different number, they get nothing. What is the SPE of the game? a. Mohamed chooses 3 and Kate is indifferent between 1, 2 and 3. b. Mohamed chooses 3 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2, and 3 if Mohamed chooses 3. c. Mohamed chooses 1 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2 and 3 if Mohamed chooses 3. d. Mohamed chooses 3 and Kate chooses 3.You and a rival are engaged in a game in which there are three possible outcomes: you win, your rival wins (you lose), or the two of you tie. You get a payoff of 50 if you win, a payoff of 20 if you tie, and a payoff of 0 if you lose. What is your expected payoff in each of the following situations? (a) There is a 50% chance that the game ends in a tie, but only a 10% chance that you win. (There is thus a 40% chance that you lose.) (b) There is a 50–50 chance that you win or lose. There are no ties. (c) There is an 80% chance that you lose, a 10% chance that you win, and a 10% chance that you tie.For questions 32 - 35 consider the following "research and development" game. Firms A and B are contemplating whether or not to invest in R8D. Each has two options: "Invest" and "Abstain." A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn't invent X. it makes 50 in revenue. If a firm invests and is the only one to invent X. it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other's investment decisions. Find the Nash Equilibrium (or Equilibria) of the "research and development" game. A. There are no Nash Equilibria B. Invest/Invest C. Invest/Abstain, and…
- For questions 32 - 35 consider the following "research and development" game. Firms A and B are contemplating whether or not to invest in R8D. Each has two options: "Invest" and "Abstain." A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn't invent X. it makes 50 in revenue. If a firm invests and is the only one to invent X. it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other's investment decisions. Find the Nash Equilibrium (or Equilibria) of the "research and development" game. There are no Nash Equilibria Invest/Invest Invest/Abstain, and Abstain/Invests…Two partners start a business. Each has two possible strategies, spend full time or secretly take a second job and spend only part time on the business. Any profits that the business makes will be split equally between the two partners, regardless of whether they work full time or part time for the business. If a partner takes a second job, he will earn $20,000 from this job plus his share of profits from the business. If he spends full time on the business, his only source of income is his share of profits from this business. If both partners spend full time on the business, total profits will be $200,000. If one partner spends full time on the business and the other takes a second job, the business profits will be $80,000. If both partners take second job, the total business profits are $20,000. a) This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium. b) This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in…A strategy for player 1 is a value for x1 from the set X. Similarly, a strategyfor player 2 is a value for x2 from the set X. Player 1’s payoff is V1(x1, x2) =5 + x1 - 2x2 and player 2’s payoff is V2(x1, x2) = 5 + x2 - 2x1.a. Assume that X is the interval of real numbers from 1 to 4 (including 1and 4). (Note that this is much more than integers and includes such numbers as 2.648 and 1.00037). Derive all Nash equilibria.b. Now assume that the game is played infinitely often and a player’s payoff is the present value of his stream of single-period payoffs, where dis the discount factor.(i) Assume that X is composed of only two values: 2 and 3; thus, aplayer can choose 2 or 3, but no other value. Consider the followingsymmetric strategy profile: In period 1, a player chooses the value 2. In period t(≥2), a player chooses the value 2. In period a player chooses the value 2 if both players chose 2 in all previous periods; otherwise, she chooses the value 3. Derive conditions which ensure…