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The first term is not defined. As you noted earlier the integral does not converge, so how can we divide something that doesn't exist by 2n?

Yep, that is the same thing just written differently unfortunately.

A brief lapse of my bos hiatus. Sy, your ideas are quite good although I do have one significant issue with your third page. You attempt to show that the alpha-integral tends to zero as n->inf by showing that the integrand tends to zero for each theta in (0,pi) as n->inf. This is in general...

Sure about the first question? What about the game with payoff (0,0) for each strategy profile? That has exactly mn equilibria.

5 for second set.

Nope, sign up now. Its only been running for a week.

I feel posting here isn't violating my bostirement too badly. How is everyone finding the course? I got 9 for the first week but I had looked at similar things to that weeks material before. About to look at this weeks stuff.

None, wasn't particularly interested in economics and there were a lot of other courses I was more keen on. Game theory itself has always interested me in a way though.

Yeah, I figured that some 'nice' strategy which still punished greedy behaviour by opponents would be best.

I haven't done much of this before so may be way off base but I think that trust is an important issue in the long-term version. Making choices to steal most or all of the time will lead to a rational opponent moving to stealing most of the time regardless of his initial intentions. If you prove...

When treating it as a one-off game with a stranger at least. If played repetitively or with a friend etc I think it is a little less clear cut.

However fast you like, think about the things you have read and play around with the games. Would advise against shooting ahead even if the material seems slow for now.

Re: HSC 2013 4U Marathon This method does work for your question although it is not all that fast. I will post this solution and more about this method and it's limitations tomorrow, it was one of my favourite ways of doing such questions.

Re: HSC 2013 4U Marathon Still not what I meant, the lim should be on the side of the cosines.

Re: HSC 2013 4U Marathon Err, it could be anything? You probably want to say something about a,b,c first.

Re: HSC 2013 4U Marathon Yep, Sy you would want to phrase that question as asking the student to evaluate the infinite product of cosines, what you have written has exactly the problem Goldy mentioned, theta is independent of n.

Probably just a difference in how verbose the author wanted to be in his explanations. Don't fall into the trap of judging difficulty and size of content by length.

you wouldn't.

Re: HSC 2013 4U Marathon Alternatively: Each pair of intersecting diagonals gives rise to a convex quadrilateral with vertices among the vertices of your polygon P (the convex quadrilateral with these two diagonals). Different pairs of intersecting diagonals give rise to different convex...

Re: HSC 2013 4U Marathon I would fancy most peoples chances of drawing several thousand 1 mark graphs over their chances of solving one of those three problems, and not by a small margin.