Illustration 26.2. Company A has three strategies available to it, while its competitor B also has three available strategies. The pay-offs (from the point of view of A are given in Table 26.7 below: TABLE 26.7. PAY-OFF MATRIX FOR ILLUSTRATION 26.2 B’s strategies b, b3 10 -7 -2 A's strategies a 3 dz -10 - 6 3
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- . The table below states the payoffs in political points (measured in billions of rubles) to two nations that are rivals in world politics, Russia and Ukraine. Each country can take one of two courses: peace; or war. In each cell, the first payoff is for Russia, and the second payoff is for Ukraine. (a) Assume that neither country observes the military strategy of its rival, and solve the game (if it can be solved). Explain your solution step-by-step. Does this outcome maximize total political points? (b) In general, what is a Nash equilibrium? Is the solution to this game a Nash equilibrium? (c) Suppose that each country deposits a fund of two billion rubles with the United Nations. Either country would forfeit this fund if it wages war. What is the solution now to the game? Is this a Nash equilibrium? Russia, Ukraine Peace War Peace 4,4 1, 5 War 5, 1 2,2Q. 3 (a) Consider complete pivoting strategy to discuss the following system of 1 equation. 4x, - 4x, - 3x, +7x, 1.3 8x, - 3x, - 8x, +17x, 6.6 12x, - 12x, - 16.x, + 29x, -2.1 - 8x, + 33 x, - 25x, +36x, = 10.4 %3D (b) Discuss the real roots of polynomial equation x*-5x' + 5x + 5x-7 = 0, correct to 4 dp, given that the equation has roots near 3 and -1.For the situation, identify the two players and their possible choices, and construct a payoff matrix for their conflict. In an attempt to gain more viewers, Channel 86 and Channel 7 are each trying to decide whether to schedule a quiz show or a reality series in their 8:00 prime time slot. Market research indicates that if Channel 86 chooses a quiz show, it will gain 5% of the market if Channel 7 runs a quiz show and lose 8% if Channel 7 runs a reality series, while if Channel 86 chooses a reality series, it will gain 9% if Channel 7 runs a quiz show and lose 9% if Channel 7 runs a reality series. [Hint: Use Q and R for quiz show and reality series.] Channel 7 Q R Channel 86 Q R % % % %
- Reduce the payoff matrix by dominance.For the situation, identify the two players and their possible choices, and construct a payoff matrix for their conflict. Andersonville has two gas stations, Ralph's Qwik-Serv and Charlie's Gas-n-Go. Both Ralph and Charlie are considering raising prices by 1¢, staying with their current prices, or lowering prices by 1¢. If they both make the same choice, there will be no change in their market shares, but if they make different choices, the one with the lower price will gain 6% of the market for each penny difference in their prices. Charlie R R % -4 X % -8 X % Ralph {s 4 X % % -4 X % 8 X % 4 X % What does R represent?Given the following payoff matrix: C C₁ C₂ C3 6 -3 1 0 10 -5 -6 1 0 R 1 2 r3 (a) What is the payoff when strategies and 1 C₂ are selected? The row player pays the column player 3. The row player pays the column player 10. The row player receives 3 from the column player. The row player receives 10 from the column player. (b) What is the largest gain possible for the row player? (c) What is the greatest loss possible for the column player? (d) What is the largest gain possible for the column player?
- For the situation, identify the two players and their possible choices, and construct a payoff matrix for their conflict. Andersonville has two gas stations, Ralph's Qwik-Serv and Charlie's Gas-n-Go. Both Ralph and Charlie are considering raising prices by 1¢, staying with their current prices, or lowering prices by 1¢. If they both make the same choice, there will be no change in their market shares, but if they make different choices, the one with the lower price will gain 4% of the market for each penny difference in their prices. Charlie R S L Ralph R S L % % % % % % % % %The following question is based on the following information about the stocks of KT Corporation, International Flavors & Fragrances, and Quality Systems. Price Dividend Yield KT (KT Corporation) $16 7% IFF (InternationalFlavors & Fragrances) $56 2% QSII (Quality Systems) $80 2% You invested a total of $11,600 in shares of the three stocks at the given prices, and expected to earn $272 in annual dividends. If you purchased a total of 200 shares, how many shares of each stock did you purchase? KT IFF QSIIFor the situation, identify the two players and their possible choices, and construct a payoff matrix for their conflict. Andersonville has two gas stations, Ralph's Qwik-Serv and Charlie's Gas-n-Go. Both Ralph and Charlie are considering raising prices by 1¢, staying with their current prices, or lowering prices by 1¢. If they both make the same choice, there will be no change in their market shares, but if they make different choices, the one with the lower price will gain 3% of the market for each penny difference in their prices. Charlie R R % % % Ralph { s % % % % % %.
- Your broker has suggested that you diversify your investments by splitting your portfolio among mutual funds, municipal bond funds, stocks, and precious metals. She suggests six good mutual funds, six municipal bond funds, seven stocks, and three precious metals (gold, silver, and platinum). (a) Assuming your portfolio is to contain one of each type of investment, how many different portfolios are possible?4. The payoff matrix for a game is -3 37 A = -4 1 -5 2 (a). Find the expected payoff to the row player if the row player R uses the maximin pure strategy and the column player C uses the minimax pure strategy. (b) Find the expected payoff to the row player if R uses the maximin strategy 40% of the time and chooses each of the other two rows 30% of the time, while C uses the minimax strategy 50% of the time and chooses each of the other columns 25% of the time. (c) Which of these pairs of strategies is more advantageous to the row player? ie olk DroYour broker has suggested that you diversify your investments by splitting your portfolio among mutual funds, municipal bond funds, stocks, and precious metals. She suggests three good mutual funds, four municipal bond funds, seven stocks, and three precious metals (gold, silver, and platinum). (a) Assuming your portfolio is to contain one of each type of investment, how many different portfolios are possible?choices (b) Assuming your portfolio is to contain two mutual funds, three municipal bond funds, one stock, and two precious metals, how many different portfolios are possible?choices