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# D2 Game Theory Chapter Issues watch

1. Referring to chapter 5 of Edexcel's D2 text book, "Game Theory",

Could anybody explain how to select the correct intersection, when solving graphically, that gives the highest minimum winnings? This is when finding the optimum mixed strategy for the player with 2 options in a 2 x 3 game.

I'm fine formulating the expected winning / probability equations etc, just am unsure of the aim; maximise V(A) by testing the equations with their respective probabilities? sketch a feasible region, eliminate certain intersections?

I understand it sounds self explanatory however the latest edition of Edexcel's D2 maths text book, pages 150/151 in particular, are unclear as to what the strategy is.

2. (Original post by tea_light)
...
This may help Post #2 for some of it.
3. (Original post by ghostwalker)
This may help Post #2 for some of it.
Yes, that correlates my explanation exactly. Thank you.

I didn't realise that you must consider;

V(A) <= (a)p+(b)
V(B) >= (a)q+(b)

Giving the "start from the bottom up" and vice versa ideas, more specifically check the intersection(s) that are actually inside/along the edge of the feasible region.

4. (Original post by tea_light)
Yes, that correlates my explanation exactly. Thank you.

I didn't realise that you must consider;

V(A) <= (a)p+(b)
V(B) >= (a)q+(b)

Giving the "start from the bottom up" and vice versa ideas, more specifically check the intersection(s) that are actually inside/along the edge of the feasible region.

Still no luck, I attempted doing a couple of questions and only a few were correct: most likely by chance.

Could you explain the process of selecting the optimal intersection please? Looking at mark scheme for the solomon press papers,

e.g. Paper F Q4 (b) http://papers.xtremepapers.com/Edexc...n%20F%20MS.pdf

They state, "it is not worth player A considering strategy I", how is this decided? I know of dominance arguments but I cannot see an obvious dominant move.

Thanks again.
5. (Original post by tea_light)
...
Sorry for the delay. I don't have a valid argument for this.

Looking at the two diagrams in the attachemnt.

I think the significant thing is that the bottom line only involves two of the three possible strategies.

If we drop I, then clearly our new bottom line (2nd diagram) is no worse than the original line (1st diagram), and in some cases it's superior.

However one could ask why not drop III? And I don't have an answer without during some research.

Edit: See next post.
Attached Images

6. (Original post by tea_light)
...
Finally - hopefully.

When considering a 2xn game we look at the maximum point on the lower envelope.

When considering an mx2 game we look at the minimum point on the upper envelope.

Only found that from some old books I had - Googling was rubbish!
7. (Original post by ghostwalker)
Finally - hopefully.

When considering a 2xn game we look at the maximum point on the lower envelope.

When considering an mx2 game we look at the minimum point on the upper envelope.

Only found that from some old books I had - Googling was rubbish!
Hi guys i'm stuck on this also, What do you mean by the envelope?
8. (Original post by tee-jay)
Hi guys i'm stuck on this also, What do you mean by the envelope?
The envelope is the lowest (or highest) line between the two sides. It will be made up of parts of the straight lines that go from one side to the other.

One such is the line in dark green I referenced in post #2.
9. I know this is a year out but I had a problem with this section of the D2 textbook also and ghostwalker's explanation helped greatly. It should be pointed out however that the 'envelope' that ghostwalker refers to doesn't change if you use the method in the D2 book, it is always the bottom one. This is due to the fact that in the solomon question linked, it uses the negative values in the matrix even when calculating B's optimal mixed strategy, whereas in the D2 textbook is simply takes the same equations and tells you to multiply them all by -1. This results in the same probability values and an 'envelope' the is always on the bottom.

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Updated: February 26, 2014
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