aash18
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#1
Report Thread starter 11 years ago
#1
just going through a few papers and markschemes and confused abt a few things...

1. if for example row1 dominates row2 can the entries in row1 be greater than or equal to the corresponding entries in row2 or do they have to be just greater than to apply the dominance rule

2. if you are asked for the north-west corner solution and it turns out to be degenrate, is it wrong to give the answer without the zero put in

3. does the minimum cut have to go through only saturated arcs or can there be unsaturated arcs in there as well

4. in linear programming when you are using the simplex algorithm what do you do if you end up with two negative values in the profit line, eg both -1, can you just choose any one of them as your pivotal column

5. also if you form your linear problem for the column player in game theory and then solve it, the value of the game you obtain will still be the value of the game to the row player right?

thnx alot
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Pork and Beans
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#2
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1. Yes, a row dominates if the values are all greater than or equal to the other row.

2. Not too sure what you mean. Which zero? Unless you mean your final answer, which they probably won't care about, because there is 0 going there, after all.

3. I think by definition, a minimum cut will be saturated if the network's at maximum flow. Don't quote me on that though, it's been a while since I've done flows. If the network isn't at maximum flow, then the cut wouldn't be saturated.

4. Yup.

5. Yes, the value of a zero-sum game is the same for both players.
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bonbon
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Report 11 years ago
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For number 2:

I have seen mark schemes where they have expected you to put the 0 in yourself if the solution is degenerate - so probably best to do it I guess.
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aash18
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Report Thread starter 11 years ago
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(Original post by Pork and Beans)
1. Yes, a row dominates if the values are all greater than or equal to the other row.
this is what i thought and this is what the book says but in the june 2008 paper the definition of dominance is given as 'for each row the element in column x must be less than the element in column y' (for column x to dominate column y)...it doesnt say anything about being equal
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Ronan Laker
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(Original post by Pork and Beans)
5. Yes, the value of a zero-sum game is the same for both players.
I think the value of the game for one player is the negative for the other player, so if 1 for player A then value of game is -1 for B
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Ktulu666
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From the textbook, a minimum cut can only pass through 2 types of arcs:

Saturated arcs that flow out of the cut i.e: they flow into the region containing the sink.
OR
Empty arcs that flow into the cut i.e: they flow into the region containing the source.

If you can find a cut which only passes through arcs as described above then it is a minimum cut.
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Ktulu666
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#7
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(Original post by aash18)
this is what i thought and this is what the book says but in the june 2008 paper the definition of dominance is given as 'for each row the element in column x must be less than the element in column y' (for column x to dominate column y)...it doesnt say anything about being equal
I think the book may be kind of wrong here (and it wouldn't be the first time). Actually think about what a dominance argument is. It is 'all possible outcomes from me selecting option A are as good or better than those from me selecting option B.' Now, if I were playing a game where option A would win me £10 in event 1, £24 in event 2 and win me -£30 in event 3 (i.e: a loss), but option B would win me £12 in event 1, £34 in event 2 and win me £-30 in event 3, common sense dictates you should play B. In event 1, you will win more, in event 2, you will win more and in event 3 you will lose the same amount, so why wouldn't you opt for B?
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