Timeline for A game on integers
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Apr 21, 2018 at 10:49 | vote | accept | Haoran Chen | ||
| Apr 10, 2018 at 13:21 | comment | added | Joel David Hamkins | @Haoran My argument shows that A can force a win in finitely many moves, for any k and n, with the strategy of always playing the smallest available number. | |
| Apr 10, 2018 at 13:11 | comment | added | Haoran Chen | I believe that $A$ wins the finite game for all finite fixed $k$. However I'm more interested in the strategy of $A$. For example, $A$ can always "steal" a turn by picking $0$ first, then after $B$ picks $k$ integers, picking $M$ sufficiently large that no $iM, i\in\mathbf{R}$ has been picked and continuing to pick multiple of $M$. In this way, all $B$'s numbers in the first turn are in vain. | |
| Apr 10, 2018 at 0:06 | comment | added | Joel David Hamkins | Note that at that question, I realized that the blocking strategy is certainly not exponential, but $g(i)=i-1$ suffices, since at each move $i$, the new number makes $i-1$ pairs with old numbers, and so only this many blocking moves are sufficient. | |
| Apr 10, 2018 at 0:04 | comment | added | Joel David Hamkins | I've posted such question at mathoverflow.net/q/297428/1946. | |
| Apr 9, 2018 at 2:24 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Apr 9, 2018 at 2:18 | comment | added | Joel David Hamkins | I added some remarks and questions at the end. Please vote up this comment if you think I should ask a separate MO question with those questions. | |
| Apr 9, 2018 at 2:17 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Apr 9, 2018 at 2:00 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
I expanded on my answer and asked a question about it.
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| Apr 8, 2018 at 4:23 | comment | added | Steven Landsburg | This is a most beautiful answer (speaking as one who played around with this for a little while and didn't come up with anything remotely this clever). | |
| Apr 8, 2018 at 4:01 | comment | added | Joel David Hamkins | In light of Aaron's answer, I wonder if it might be possible to provide good bounds for the length of play to the win when A follows the strategy of always playing the smallest available number? This is a simple-to-describe winning strategy, but is it efficient at winning quickly? I have no idea either way. | |
| Apr 8, 2018 at 3:37 | comment | added | Our | Oh, I see. Thanks for pointing out. | |
| Apr 8, 2018 at 3:30 | comment | added | Joel David Hamkins | @onurcanbektas You may have misunderstood the game. If A plays 3, 6, 9, 12, 15, for example, then she has won, even if player B follows your directions, since this is an arithmetic progression of length 5. en.wikipedia.org/wiki/Arithmetic_progression | |
| Apr 8, 2018 at 3:24 | comment | added | Our | I do not yet know Game Theory, but if $k\leq 2$, and if in every move $B$ picks the integers $n-1$ and $n+1$, where $n$ is the integer what $A$ has picked, how can $A$ ever win ? | |
| Apr 8, 2018 at 3:16 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Apr 8, 2018 at 2:43 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
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| Apr 8, 2018 at 2:37 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |