Timeline for Randall Munroe's Lost Immortals
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 15, 2014 at 15:42 | comment | added | Steven Gubkin | @TimothyChow re: #4, my remark was about the existence of a strategy guaranteeing a win. 2 shows that if you are not a pointmass, you can guarantee a win by writing messages to trap the other player. 4 claims that, without the other person knowing they cannot cross your lines somehow, they could theoretically stay antipodal, so you do not get a guaranteed win. I agree that, just by following a random walk, two players with finite extent will run into each other with probability $1$. | |
| Oct 15, 2014 at 15:36 | comment | added | Timothy Chow | I think Steven is correct if people really are idealized points, but the finite horizon assumption seems to me to be the right one for this problem. Also, I don't think that #4 is correct, because a randomized strategy can be used to break out of any such trap with probability approaching 1. | |
| Oct 15, 2014 at 12:42 | comment | added | Steven Gubkin | @cpast I have not thought a lot about random walks. At a finite time $T$, is your path not a measure zero subspace? If so, do you not have a zero probability of winning at any finite time? Maybe I am thinking about this incorrectly. | |
| Oct 15, 2014 at 4:36 | comment | added | cpast | Given that the surface of the Earth is 2-dimensional, isn't the probability of an infinite random walk hitting any given point actually 1? In particular, then, if the other person stays still, you're almost certain to hit them, not almost certain not to. | |
| Oct 14, 2014 at 23:58 | comment | added | usul | Re: #3 and #4, it depends what you think of as "planning beforehand". We could ask "what is a strategy that succeeds if both players follow it?" We could consider this a sort of equilibrium strategy and it might be reasonable for both players to follow such a strategy even if they have never met or spoken. (Selection among all such strategies is a further problem...) | |
| Oct 14, 2014 at 21:36 | history | edited | Steven Gubkin | CC BY-SA 3.0 |
added 164 characters in body
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| Oct 14, 2014 at 21:15 | history | answered | Steven Gubkin | CC BY-SA 3.0 |