Timeline for Five Front Battle
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 16, 2010 at 1:58 | answer | added | Jason Bandlow | timeline score: 1 | |
| Jan 7, 2010 at 16:55 | answer | added | David E Speyer | timeline score: 13 | |
| Jan 7, 2010 at 16:31 | comment | added | David E Speyer | @Thorny: For 3 fronts, notzeb's final solution works. forums.xkcd.com/viewtopic.php?f=3&t=43065#p1702833 Of course, he may have posted this after you made your comment. | |
| Jan 7, 2010 at 16:29 | comment | added | Ilya Nikokoshev | The winning strategy is almost certainly quasipolynomial on a triangle (4-symplex in $n=5$) case, so computer solution is entirely plausible. | |
| Jan 7, 2010 at 13:28 | comment | added | David E Speyer | A nice computer experiment might be to replace the game by a discrete approximation where each general has N soldiers that cannot be subdivided. This is a finite dimensional, zero sum, two player game, so there must be software to find a minimax strategy. Looking at the limit of these strategies as N goes to infinity might give us some insight. | |
| Jan 7, 2010 at 11:48 | comment | added | Thorny | The space of probability distributions on the standard triangle $x_1+x_2+x_3=1$ is not finite dimensional, so I would not place great hopes on a computer-based solution. It is not clear at all what kind of probability distribution would be a good candidate for satisfying the requirements, either. | |
| Jan 7, 2010 at 11:23 | comment | added | Kevin Buzzard | ...However, actually finding the compact convex set is a problem that is best solved by computer in general, and the answer you get might well be very messy. So, for me, this question says "can someone who does game theory put this problem into a standard computer program which solves these sorts of things and then tell me the answer, bearing in mind that there is a chance that the answer spat out will be non-intuitive and the proof that it works will be "the computer says it works". Is this how this sort of question works? I always thought that it was. | |
| Jan 7, 2010 at 11:21 | comment | added | Kevin Buzzard | Are the following comments correct? Perhaps a game theorist can back me up or shoot me down. The problem above is just a 2-player zero sum game, and the space I can play on is a compact convex set, so general theory tells me that there is a compact convex subset and a probability distribution on this subset that will do the job you want (and I think one of the possibilities for the subset will be defined by linear equations and inequalities and the probability distribution on this set can I think even be taken to be Lebesgue measure or indeed any measure at all)... | |
| Jan 7, 2010 at 10:05 | comment | added | Thorny | I have to point out that the problem with 3 fronts is not solved in the link, the given strategies all perform worse than needed. | |
| Jan 7, 2010 at 6:13 | history | asked | zeb | CC BY-SA 2.5 |