As this may be of use to others as well, I will try to provide some general points on journal selection for an `average' paper.
One obvious general approach to take is (i) to look where the references of your paper were published (and I note that there are lots still unpublished so here that may raise a problem... so check on whether they have now been published).
(ii) Look at, or estimate, the publication backlogs where available and make your decision on those grounds. (You have a delicate balancing act ahead as your idea of a two month acceptance is really hard to achieve and may need revising!)
(iii) Look at other journals similar to those found by (i), e.g. by iterating (i) on the recent papers in your reference list. Electronic journals tend to be quicker to publication, and probably also to acceptance, than traditional ones, of course, so (ii) will be biased in that direction to some extent.
(iv) Finally I have not read the introduction to your paper but often introductions are crucial in 'selling' a paper to the referee. If you say what the paper sets out to do, clearly and concisely, then your chances of getting a referee's report more quickly, and one which will be positive, will increase.
(v) The paper was submitted to Arxiv last November. That means you have a certain distance from it. Do a critical health check on it from the point of view of wording, sentence structure, spelling, etc., before sending it to any journal. Get a friend or colleague to do a quick read of intros etc. so as to get a second opinion on wording. Think of the poor referee, make their job easier. They need to be able to evaluate the paper fairly quickly. Check, yourself, for typos (and, of course, don't trust spell checking programs on this). My reaction to writing a report when there are clearly lots of typos is to put it off for a few weeks... therefore longer turn around time.
Finally I feel that your should have put the question in a different form. Specific journal suggestions are hardly the responsibility of MO but your general point on how to select journals for such a paper is a valid one .
There seem good advantages in POD (Print On Demand) publishing. I discuss some issues in POD at http://pages.bangor.ac.uk/~mas010/orderbook.html
I have found createspace a good publisher for my book "Topology and Groupoids"; they are an amazon.com company, and this has the implication that the royalty rates are good (black and white, 6" x 9", 200 pages, price 20.00 dollars, gives $8.75 royalty). Non exclusive contract.
You should consult the book "The Fine Print", written by a copyright lawyer, Mark Levine.
All the publicity, and sending out review and complimentary copies, has to be done by you - this is a typical downside to any self publishing.
Later: Another disadvantage is that many libraries and institutes buy anything issued by a major publisher, but have to be persuaded to buy a book which does not have the cachet of having satisfied the refereeing process of a major publisher. The advantage of this amazon.com company is that the royalty is direct on the published price for amazon sales.
Later: I have found another problem, as a UK resident, namely that the USA Inland Revenue insists that 30% tax be deducted, as against the lowest UK rate of 20%, unless you can get a USA Income Tax Number allocated: in view of the difficulties I have had in doing this, I think you would need to employ a professional who knows all the ropes. However, this is a marginal problem in my case.
Best Answer
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.