Question

If Star Ltd. adopts strategy A, which strategy should Sun Ltd. adopt for maximum gain?

• A. A
• B. B
• C. C
• D. A or C
• A. 10000
• B. 0
• C. 12000
• D. None of these
• A. A
• B. B
• C. C
• D. A or C
• A. If Sun Ltd. adopts strategy A, adopt strategy B.
• B. If Sun Ltd. adopts strategy B, adopt strategy B.
• C. If Sun Ltd. adopts strategy C, adopt strategy B.
• D. If Sun Ltd. adopts strategy C, adopt strategy A.
• A. I only
• B. I & III
• C. II only
• D. III only

Answer 1

The Correct Option is B

Step 1: Read off Sun Ltd.'s payoff when Star Ltd. plays A.
Star Ltd. has fixed its strategy at A, so we look at the "Star Ltd. plays A" column of the payoff table.
Sun Ltd. plays A: payoff = 8000.
Sun Ltd. plays B: payoff = 6000.
Sun Ltd. plays C: payoff = 8000.

Step 2: Subtract Sun Ltd.'s own running expense.
Sun Ltd.'s real gain is not the raw payoff alone. It also has to pay for whichever strategy it runs, and that expense comes from the Sun Ltd. row of the expenses table.
The expense for Sun Ltd. playing A is 8000, for B is 2000, and for C is 8000.
Net gain = payoff minus this expense.

Step 3: Work out the net gain for each choice.
Sun Ltd. plays A: net gain = \(8000 - 8000 = 0\).
Sun Ltd. plays B: net gain = \(6000 - 2000 = 4000\).
Sun Ltd. plays C: net gain = \(8000 - 8000 = 0\).

Step 4: Check why the other options fail.
Strategy A gives Sun Ltd. a net gain of only 0, since the 8000 payoff is fully eaten up by the 8000 expense of running strategy A.
Strategy C gives the same result of 0, for the same reason: payoff and expense are both 8000.
Option (4), "A or C", is wrong because both A and C leave Sun Ltd. with a smaller net gain (0) than B (4000).

Final Answer:
Strategy B gives Sun Ltd. the highest net gain of 4000, so Sun Ltd. should adopt strategy B. \[ \boxed{\text{Strategy B}} \]

Answer 2

Step 1: Read off Sun Ltd.'s payoff when Star Ltd. plays B.
Star Ltd. has fixed its strategy at B, so we look at the "Star Ltd. plays B" column of the payoff table.
Sun Ltd. plays A: payoff = 12000.
Sun Ltd. plays B: payoff = -2000.
Sun Ltd. plays C: payoff = 16000.

Step 2: Subtract Sun Ltd.'s own running expense.
The expense for Sun Ltd. playing A is 8000, for B is 2000, and for C is 8000. Net gain equals payoff minus this expense.

Step 3: Work out the net gain for each choice.
Sun Ltd. plays A: net gain = \(12000 - 8000 = 4000\).
Sun Ltd. plays B: net gain = \(-2000 - 2000 = -4000\).
Sun Ltd. plays C: net gain = \(16000 - 8000 = 8000\).

Step 4: Compare with the given options.
The best Sun Ltd. can do here is a net gain of 8000, by playing strategy C.
Option (3), 12000, is just the raw payoff of playing A; it ignores that A also costs 8000 to run, and in any case it is not even the biggest raw payoff on offer.
Option (2), 0, does not match any of the three computed net gains (4000, -4000, 8000).
Option (1), 10000, does not appear anywhere in this table at all.

Final Answer:
Since the true maximum net gain, 8000, is not listed among options (1), (2) or (3), the correct choice is "None of these". \[ \boxed{\text{None of these}} \]

Answer 3

Step 1: Read off Sun Ltd.'s payoff when Sun Ltd. plays B.
Sun Ltd. has fixed its own strategy at B, so we read the "B" row of the payoff table across all three of Star Ltd.'s choices.
Star Ltd. plays A: payoff to Sun Ltd. = 6000.
Star Ltd. plays B: payoff to Sun Ltd. = -2000.
Star Ltd. plays C: payoff to Sun Ltd. = 0.

Step 2: Subtract Sun Ltd.'s own expense, which stays fixed here.
Since Sun Ltd. is playing B in every case, its own running expense is always 2000 (the B entry in the Sun Ltd. expenses row), no matter what Star Ltd. does. Net gain = payoff minus 2000.

Step 3: Work out Sun Ltd.'s net gain for each of Star Ltd.'s choices.
Star Ltd. plays A: net gain to Sun Ltd. = \(6000 - 2000 = 4000\).
Star Ltd. plays B: net gain to Sun Ltd. = \(-2000 - 2000 = -4000\).
Star Ltd. plays C: net gain to Sun Ltd. = \(0 - 2000 = -2000\).

Step 4: Choose the strategy that hurts Sun Ltd. the most.
Star Ltd. wants Sun Ltd.'s net gain to be as small as possible, ignoring its own outcome. Comparing 4000, -4000 and -2000, the smallest value is -4000, which happens when Star Ltd. plays B.
Star Ltd. playing A actually leaves Sun Ltd. with its biggest gain (4000), the opposite of what Star Ltd. wants, so option (1) is wrong.
Star Ltd. playing C leaves Sun Ltd. with -2000, which is better for Sun Ltd. than -4000, so C does not minimise Sun Ltd.'s gain either, ruling out options (3) and (4).

Final Answer:
Star Ltd. should adopt strategy B to cut Sun Ltd.'s net gain down to its lowest possible value. \[ \boxed{\text{Strategy B}} \]

Answer 4

Step 1: Work out Star Ltd.'s own net position.
Whatever Sun Ltd. gains as a raw payoff, Star Ltd. loses the same amount, since the table swings the money between the two rivals. On top of that, Star Ltd. also pays its own running expense, which is 7000 for A, 8000 for B, and 8000 for C.
So Star Ltd.'s net position = -(Sun Ltd.'s raw payoff) - (Star Ltd.'s own expense). A more negative number means a bigger loss for Star Ltd.

Step 2: Compute Star Ltd.'s net position if Sun Ltd. plays A.
The payoff row for Sun Ltd. playing A is 8000, 12000, 8000 (against Star A, B, C).
Star A: \(-8000 - 7000 = -15000\). Star B: \(-12000 - 8000 = -20000\). Star C: \(-8000 - 8000 = -16000\).
The best (least negative) choice here is Star A, at -15000, not Star B. This already rules out option (1).

Step 3: Compute Star Ltd.'s net position if Sun Ltd. plays B.
The payoff row for Sun Ltd. playing B is 6000, -2000, 0.
Star A: \(-6000 - 7000 = -13000\). Star B: \(2000 - 8000 = -6000\). Star C: \(0 - 8000 = -8000\).
The best choice here is Star B, at -6000, which is Star Ltd.'s smallest loss among the three. This matches option (2) exactly.

Step 4: Compute Star Ltd.'s net position if Sun Ltd. plays C, and finish checking.
The payoff row for Sun Ltd. playing C is 8000, 16000, 4000.
Star A: \(-8000 - 7000 = -15000\). Star B: \(-16000 - 8000 = -24000\). Star C: \(-4000 - 8000 = -12000\).
The best choice here is Star C, at -12000, not B and not A, so both option (3) and option (4) give worse advice than the true best response.

Final Answer:
Only option (2) tells Star Ltd. to do what actually minimises its own loss (playing B when Sun Ltd. plays B, cutting the loss to 6000). That is the genuinely intelligent move. \[ \boxed{\text{Option (2)}} \]

Answer 5

Step 1: Read off the raw payoff when both play C.
From the payoff table, the entry for Sun Ltd. playing C against Star Ltd. playing C is 4000. This is the raw amount that would pass from Star Ltd. to Sun Ltd. before either company's own expense is counted.

Step 2: Bring in each company's own expense for running strategy C.
From the expenses table, running strategy C costs Sun Ltd. 8000 and costs Star Ltd. 8000 as well.

Step 3: Work out Sun Ltd.'s net position.
Sun Ltd.'s net = raw payoff minus Sun Ltd.'s own expense = \(4000 - 8000 = -4000\).
A negative net means Sun Ltd. actually ends up with a loss of 4000, not a gain. So statement III, "Sun Ltd.'s loss is 4000", is true, and statement II, "Sun Ltd.'s gain is 4000", is false, since the true result is a loss, not a gain.

Step 4: Work out Star Ltd.'s net position.
Star Ltd. loses whatever raw payoff Sun Ltd. gains, and also pays its own expense: net for Star Ltd. = \(-4000 - 8000 = -12000\).
So Star Ltd. ends up with a net loss of 12000, which makes statement I, "Star Ltd.'s net loss is 12000", true.

Final Answer:
Statements I and III are both true, while statement II is false, so the correct choice is "I & III". \[ \boxed{\text{I \& III}} \]