I wrote a research paper "A mathematical model of the Mafia game" (arXiv:1009.1031 [math.PR]). However, I do not know where to publish it. As an undergraduate studying majorly physics, I have little knowledge of mathematical journals. Moreover, its not easy for me to classify its subject.

The paper itself is generally "using applied mathematics (and physicist's approach) to model a party game (psychology)". Just to give some of its features:

  • Uses pure death process and gives its closed-form solution
  • Is elementary and didactic (a tricky use of generating functions, Wallis formula, ...)
  • Somehow "cool" topic

I thought about The American Mathematical Monthly. Besides the obvious advantages I see two drawbacks:

  • In AMM there are usually an old results in a nice/didactic/cool form or short findings
  • It won't reach to psychologists who might investigate the Mafia game experimentally

Can you recommend me any proper journal? (popular mathematics, mathematics and psychology, ...?) Any other advice are appreciated as well.

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    $\begingroup$ Try one of the journals that has already published papers on the game. Forget submitting the paper to the Monthly. Most readers of the Monthly probably won't know about or have an interest in this topic. (Unless you play the game I think it is hard to care about it; that is a one-way implication.) $\endgroup$ – KConrad Sep 9 '10 at 0:41
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    $\begingroup$ Undergraduates are rarely successful in publishing papers without strong mentoring. Getting a couple of lines of advice on the internet is not enough. I'd go and have a chat with one of your professors. $\endgroup$ – Andy Putman Sep 9 '10 at 1:12
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    $\begingroup$ While I completely agree that it is uncommon for undergraduates to publish any papers, and nobody here has explicitly discouraged publication of this work, I would strongly encourage wider publishing of undergraduate work. As with this case, undergraduates are often quite interdisciplinary in their research, which has been greatly lacking in some fields. For example, in quantum computing, many publications disregard basic concepts of physics, whereas many other publications disregard basic concepts of computer science. A fresh perspective could help bring fields together. $\endgroup$ – Neil Dickson Sep 9 '10 at 7:58
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    $\begingroup$ The Monthly is not limited to expository papers; original research is welcomed there too. I think that the Monthly is a reasonable place to try, though as I mention in my answer below, the Intelligencer would be my first recommendation. Regarding the problem of reaching psychologists, I wouldn't worry too much about that. The best way to get your paper noticed by psychologists is to contact them directly, and then it doesn't matter where the paper is published so long as it is readily available. Given that the content of your paper is mostly mathematical, a math journal is appropriate. $\endgroup$ – Timothy Chow Sep 10 '10 at 18:11
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    $\begingroup$ @TimothyChow Well, quite a few time ago I sent it to the AMM and then (after getting rejected) to the Mathematical Intelligencer, . In both cases one reviewer was enthusiastic and the other wrote in the spirit "technically correct, but I don't think it is of interest to the readers" (a statement that leave little room for discussion). At that point I decided to keep it on arXiv. $\endgroup$ – Piotr Migdal Dec 30 '18 at 22:14

I have only glanced at your paper, but one possibility is to submit it to The Mathematical Intelligencer, in particular to Michael Kleber, who edits the "Mathematical Entertainments" column. This is a great place for serious mathematical analysis of problems with a recreational flavor. The Intelligencer has a wide readership, which is what you want for your article.

By the way, contrary to some other commentators, I don't see any reason why you necessarily need to find a mentor just because you're an undergraduate. Your paper seems to be well-written enough. Of course it doesn't hurt to find a mentor but what matters is the quality of your writing and not your employment status.

Also, regarding KConrad's comment that only existing players of the game will find it interesting, I don't believe that this is true. First of all, as you note, Mafia is in fact a pretty well-known game. Secondly, the subtlety of the game means that there is a lot of interesting mathematics buried in it. If your article can draw more mathematicians into studying it, that would be a very good thing.

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    $\begingroup$ Very helpful answer, +1. $\endgroup$ – Hailong Dao Sep 10 '10 at 17:48
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    $\begingroup$ Thanks for both a journal suggestion and some encouragement. I thought about value of my paper and saw its not for psychologists (with the current results for a too idealized game). The Mathematical Intelligencer sounds nice. Just curious, why you recommend it me more than AMM (even if its softer and prefers shorter papers)? And one more question - as I see MI prefers short papers - should I vasty reduce its size or somehow persuade to publish a longer one? $\endgroup$ – Piotr Migdal Sep 10 '10 at 19:07
  • $\begingroup$ I think the Entertainments column of the Intelligencer is a better fit because of the recreational flavor of your subject matter. As for the length of the paper, that is a question you can ask Kleber (or Vakil, the other editor of that column). $\endgroup$ – Timothy Chow Sep 10 '10 at 20:07

Here is another paper on Mafia published in Annals of Appl. Prob.:

Mark Braverman, Omid Etesami, Elchanan Mossel, "Mafia : A Theoretical Study of Players and Coalitions in a Partial Information Environment", Annals of Appl. Prob. 18(3), 2008

ps: I agree with Andy Putman's comment under the question.

  • $\begingroup$ I considered it (and perhaps should consider it again). The main objection was, is the work valuable for someone interested solely in Applied Probability? I guess not. (In my paper solution is very straightforward and uses no theorems in probability.) $\endgroup$ – Piotr Migdal Sep 9 '10 at 8:41
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    $\begingroup$ You could contact the authors of that paper. I'm sure they'd be delighted to discuss mathematical mafia with you. $\endgroup$ – Tom LaGatta Sep 10 '10 at 17:00

You could consider the journal Involve, which aims at publishing high-quality research paper at least partially written by students. See http://mathscipub.org/ for more details.

  • $\begingroup$ Thanks for info, I will think about it. Is it that readable? (I don't want to publish in a write-only journal.) $\endgroup$ – Piotr Migdal Sep 9 '10 at 9:14
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    $\begingroup$ @Piotr: Bjorn Poonen is one of the founding editors of Involve. Based on that information alone, I am confident that the papers it publishes are readable. $\endgroup$ – Pete L. Clark Sep 9 '10 at 20:15
  • $\begingroup$ @Pete: I (have to) believe. My univ. doesn't provide access to it so I can't judge by myself. $\endgroup$ – Piotr Migdal Sep 10 '10 at 13:25

The MAA also publishes "The College Math Journal", and a brief lookthrough of your paper suggests to me that it is of a good level and topic for that journal. Also, the journal Integers is a "real" math research journal, and has an official policy of being interested in games.

I can't speak for others, of course, but certainly at my grad school (mid 1990s) everyone had played and enjoyed Mafia a couple of times.

  • $\begingroup$ Thanks. Is The College Math Journal better (for me) than The American Mathematical Monthly? And one more: I know that level and style fits for an journal for students, but at the same time I don't know if it is good to publish an original research in an expository journal. Well, the "game" may be misleading (I use neither game theory nor chess/go/whatever-like combinatorics). $\endgroup$ – Piotr Migdal Sep 10 '10 at 17:47
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    $\begingroup$ Just my opinion, but I don't think the CMJ is more appropriate for your paper than the AMM. The level of mathematics in your paper is more at the AMM level. Also, the AMM is much more widely read than the CMJ. If you're going to try one or the other then I would try the AMM first. $\endgroup$ – Timothy Chow Sep 10 '10 at 18:05
  • $\begingroup$ I didn't look closely enough at your paper to judge Timothy's opinion. Certainly, in terms of prestige, AMM is miles better than CMJ. $\endgroup$ – Kevin O'Bryant Sep 10 '10 at 23:43
  • $\begingroup$ On the other hand, with increased prestige comes increased selectiveness: I know instances of papers that were rejected for no good reason by the Monthly, even though they would have made a good fit. Does the Monthly have an official or informal policy of accepting only solicited papers? $\endgroup$ – Victor Protsak Sep 11 '10 at 3:11
  • $\begingroup$ @Victor: I've never heard any rumors of such a policy. Of the three papers I've submitted to the Monthly, two were accepted and none were solicited. They get so many submissions that they reject many good papers, just like the most selective colleges reject many good students for no reason other than their limited capacity. $\endgroup$ – Timothy Chow Sep 11 '10 at 4:13

If you want to reach psychologists with a mathematical background, then you should try the Journal of the Mathematical Psychology. This is the official journal for the Society of Mathematical Psychology. It publishes theoretical work with a decent amount of math usually of the probability/statistics variety. However, you will have to be careful with language (i.e. avoid physics jargon and more sophisticated math jargon) to better appeal to the audience.

  • $\begingroup$ Thanks, surely worth considering. Anyway, do you know anything more related to modeling interactions in a small group? I found Journal of Artificial Societies and Social Simulation (but it is more numerical simulation oriented). $\endgroup$ – Piotr Migdal Sep 10 '10 at 13:30

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