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parameter x = 5
List all pure strategies for either player that are weakly dominated.
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- Which one is the best strategy for Player 1? Player 1 (10, 20) Leave Leave Cooperate Stay Cooperate Player2 Not cooperate Stay (15, 14) Not cooperate Leave Player 2 (17, 11) Stay (16, 12)Assume that two collectors, X and Y are in a first prize sealed bid auction for a batch of vintage comic books. X and Y have different valuations (V) for this batch of comic books e.g. VX And VB are between $2000 and $4000. Both collectors know their own V but does not know the V of the other collector. All they know is that the other collector’s V is a uniformly distributed number between $2000 and $4000. Assume risk neutrality for X and Y e.g. expected payoff for X is: (VX – bX)Pr(bX) and expected payoff for Y is (VY – bY)Pr(bY). These collectors will make their bids strategically. Show how X’s bidding strategy is bX = ½ Vx + 1 and Y’s is bY = ½ Vy +1 in a Nash equilibrium.Suppose there are two bidders for a single object. Each bidder has a value for the object, v1 and v2, which is randomly drawn uniformly from 0 to 80. (Note that this means the probability that a value is 25 or lower is 25/80, and more generally, the probability that a value is k or lower is k/80). Bidders see their own values but not the values of their rival bidders. Consider a first price sealed bid auction where the winner of the object is the bidder who submits the highest bid and pays the price that he bid. Suppose that you are bidder 1 and you believe that your rival always bids a constant fraction α of his value. (For example, if bidder 2’ value is 15, he will bid 15α.). 1. What is your expected winning probability of the auction from any given bid b1? (Hint, you win the auction when your bid amount b1 is greater than your opponent’s bid). 2. What is your expected payoff from any given bid, b1? (You need to write your answer as a function of v1, b1, and α). 3. Compute your best…
- fast i will 10 upvotesA total of 10 players are each choosing a number from {0,1,2,3,4,5,6,7,8}. If a player's number equals exactly half of the average of the numbers submitted by the other nine players, then she is paid $100; otherwise, she is paid 0. Solve for the strategies that survive the IDSDS.Channels 7 and 10 are the only television networks. They want to capture as much of the market as possible because it helps them earn more advertising revenue. Each channel can choose to show a cooking or a reality show on Sunday night. If they both airing cooking shows or both airing reality shows, Channel 10 gets 60% of the market. If Channel 10 is showing a cooking show and Channel 7 is showing a reality show, Channel 10 gets 70% of the market. If Channel 10 is showing a reality show and Channel 7 is showing a cooking show, Channel 7 gets 45% of the market. In a sequential game, Channel 7 moves first. What is true? Group of answer choices Channel 7 will choose reality. Channel 7 has a second mover advantage. Channel 10 will choose cooking. Channel 10 will choose reality. Channel 7 will choose cooking.
- Faris Co. and Fahad Co. are rivalry in Bahrain's market. Suppose the payoff to each of four strategic interactions are as follows: Faris Co. Response Action Reduce Price Don't Reduce Price Gain = BD 30,000 Reduce Price Loss = BD 1,000 Don't Reduce Price Loss = BD 5,000 No loss or gain The probability of Faris Co. to reduce price is 95 % (otherwise, probability of Faris Co. for not reducing price is 5 %), assume that Fahad Co. choose "reduce price" strategy a. What is size of loss from "reduce price" for Fahad Co.? b. What is size of gain from "don't reduce price" for Fahad Co? c. What is the expected payoff of a "reduce price" for Fahad Co.? and give an example (application) of d. Explain the concept of 'game theory' game theory Fahad Co. ResponseThelma and Louise are competitors in a local beer market and each is trying to decide if it is worthwhile to advertise. If both of them advertise, each will earn a profit of $2000. If neither of them advertises, each will earn a profit of $5000. If one advertises and the other doesn't, then the one who advertises will earn a profit of $7500 and the other will earn a profit of $1000. To make the most money, what should Thelma do and how much profit will she earn? Select one: a. she should advertise, and she will earn $7500 b. she should do whatever Louise does, and will earn either $2000 or $5000 C. she should not advertise, and she will earn $5000 d. she should advertise, and she will earn $2000 Next pageThe Government of Malaca has decided to sell pollution permits that will allow people to discharge pollutants into its largest freshwater lake. Each permit represents the right to discharge one tonne of pollutants. Malaca has determined that the lake will tolerate a maximum of 10 tonnes of pollutants per year and has decided to sell the permits using a Dutch auction. This means that the auction starts at a very high price, which is reduced in steps until the price reaches a level that will result in all 10 tonnes of pollution permits being sold at the same price. The results of the bidding are shown in table below. Price per Pollution Bidder Bidder Bidder Bidder Bidder Permit A. B D $5, 500 1 5,000 4,500 4,000 1. 1. 1 2 2. 3 2 1 2 3,500 3,000 2,500 2,000 4 3 2 4 4 4 3 4 4 1,500 7 a. What will be the price of pollution permits as a result of this auction? Price: $ b. Suppose that Bidder E happened to be an environmental protection group. If this group had not participated in the…
- In this game, (80, 50) 52% a) (R, N) b) (R, R) c) (S, N) d) (R, P) S is a Nash equilibrium First Player (20,68) 12% R P Second Player N (90,70) 36%There are N>=2 collectors who engage in the auction of an antique. The collectorshave a common valuation of the antique, denoted by v, which is known to all. Thecollectors make a simultaneous bid. Let pn denote the bid by collector n = 1,....,N. The one with the highest bid wins the antique. The winner receives payoff v-pi.The other(s) receive zero payoff. If more than one collectors make the same highestbid, then they have an equal chance of winning the item. Prove that: A) It is not a Nash Equilibrium (NE) if the highest bid is v and onlyone collector bids this price.(b) It is not a NE if the highest bid is less than v.(c) It is a NE that the highest bid is v and more than one collector bidsthis priceIn a mixed strategy equilibrium of the game below, what is the probability with which Player 2 chooses r (if there are multiple equilibria with different probabilities of a, choose any one)? Player 2 y a 3, 3 4, 2 Player 1 b 6,3 2, 6 5. 3 3, 2 Numerical answer