Timeline for Infinite games: are they well defined?
Current License: CC BY-SA 2.5
17 events
| when toggle format | what | by | license | comment | |
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| May 18, 2018 at 17:13 | history | edited | DukeZhou |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 2, 2011 at 7:28 | answer | added | Michael Greinecker | timeline score: 2 | |
| Oct 10, 2010 at 22:00 | comment | added | Wadim Zudilin | Andres, thanks for the link to your interesting talk! | |
| Sep 11, 2010 at 2:45 | comment | added | Andrés E. Caicedo | Wadim, I recently gave a talk aimed at graduate students on the subject of games, particularly on infinite games. You may find it at my page, andrescaicedo.wordpress.com/talks | |
| Jul 19, 2010 at 23:27 | comment | added | Wadim Zudilin | In the case of the PL game I carefully followed the reference. I am now convinced that L has a wining strategy and P does not, and the example is especially nice as it helps to prove a nontrivial analytic theorem. | |
| Jul 19, 2010 at 21:46 | comment | added | Mark Bell | Actually Wadim, I think the conclusion of the question was that even though it it appears that $P$ has a winning strategy actually the proofs given were flawed and $L$ does. It turns out this is not a case of there being "winning strategies for both players". However, this doesn't mean that there isn't another game where both players have winning strategies. | |
| Jul 17, 2010 at 9:14 | comment | added | Wadim Zudilin | Thanks everybody for valuable comments! @Andres, I wonder whether I get a chance in the nearest year to follow the book (but I promise to have it on my desk!) but the arXiv preprint is a really nice piece (why don't you answer?!). @Joel, your answer there is indeed very nice (plus having Eve and Adam as players is remarkable). @Raja and Andreas, I remain not convinced: both players in an infinite game follow wining strategies and on each finite step (even in the discrete situation) it is hard to agree on who wins! In that special game, the epsilon-delta language can possibly give a solution. | |
| Jul 17, 2010 at 3:48 | comment | added | Andreas Blass | BlueRaja's comment is correct if the sequence of moves is well-ordered, because then you can define the play of one strategy against another by induction along that well-ordering. But when the set of moves is not well-ordered, as in the "continuous" games mentioned by Andres Caicedo, then there may not exist a play of the game in which both players follow their strategies. In such a case, they might both have winning strategies. | |
| Jul 17, 2010 at 2:50 | comment | added | BlueRaja | I don't see how they could both have winning strategies, infinite or not: if they both use their winning strategy, the sequence of points is well-defined, and either it converges in $D^{2}$ or it doesn't. | |
| Jul 16, 2010 at 19:50 | comment | added | Joel David Hamkins | Related MO question: mathoverflow.net/questions/23375/… | |
| Jul 16, 2010 at 15:50 | answer | added | Carl Mummert | timeline score: 14 | |
| Jul 16, 2010 at 15:39 | answer | added | Charles Matthews | timeline score: 3 | |
| Jul 16, 2010 at 14:50 | answer | added | Tony Huynh | timeline score: 2 | |
| Jul 16, 2010 at 14:46 | comment | added | Andrés E. Caicedo | Wadim, you may want to take a look at the following paper by Bollobas, Leader, and Walters, where an example is giving of a ("continuous") game where both players have winning strategies: arxiv.org/abs/0909.2524 For "discrete" games, set theory has studied infinite games for a while, and they are an essential tool in modern research. A book like Jech's "Set Theory" should give you a nice overview. | |
| Jul 16, 2010 at 14:14 | comment | added | Andrea Ferretti | I was about to ask something like this. :-) | |
| Jul 16, 2010 at 14:07 | history | asked | Wadim Zudilin | CC BY-SA 2.5 |