Talk:Aggregative game

Copyright violation in the lead

Note that the second paragraph in the lead looks like a copyright violation of the third paragraph in this web page. I will thus delete this paragraph. The rest of the article needs to be checked for other copyright violations. --Mark viking (talk) 19:58, 11 October 2013 (UTC)

That specific paragraph was written by Alex Dickson who is one of the people who has been part of putting this entry together. This puts us in a somewhat strange situation... Perhaps a reference to his webpage would solve the problem? I will reinsert and add a reference (or a footnote with a reference). There are no other copyright issues, I can ensure you of that. — Preceding unsigned comment added by 90.217.220.213 (talk) 22:27, 11 October 2013 (UTC)

Apologies, I was not logged in when I wrote the previous paragraph. I will hold off for a bit with reinserting until a solution has been suggested. — Preceding unsigned comment added by AggregativeGames (talk • contribs) 22:36, 11 October 2013 (UTC)

Just to be clear, I am not accusing you of any malfeasance; I know you are acting in good faith and we're both trying to improve the encyclopedia. You are a new editor and there is a learning curve to figure out what is and is not acceptable at Wikipedia. This article is a good start on the topic of aggregative games. We just need to clear up this significant problem.

Wikipedia takes copyright (and plagiarism) very seriously. References are good to give proper attribution and avoid plagiarism, but they are not good enough to satisfy copyright restrictions. See Wikipedia:Copyrights for the general approach to copyrights and see WP:COPYOTHERS for what needs to be done to be able to use such text. Basically we would need explicit permission from Alex Dickson to use this text under an appropriate license. A much better alternative is to write the prose in your own words, based on reliable sources. Dickson's personal statement would not be considered a reliable source, per WP:RS, as there is no peer review for a personal web site. Better would be a summary of applications from peer-reviewed papers and especially reviews or surveys, as these are good secondary sources. Thanks, --Mark viking (talk) 22:56, 11 October 2013 (UTC)

Thanks a lot for your guidance, much appreciated. I will write it in my own words based on published articles. Thanks also for adding mean field game theory to the see also section. AggregativeGames (talk) 09:08, 12 October 2013 (UTC)

This article is 'much ado about nothing'

The set of aggregative n-person games is essentially the same as the set of all n-person games. Alternatively, the definition is too broad and requires some additional constraints.
Consider an arbitrary n-person game where each player i has a set T_i of at most $2^{\aleph _{0}}$ pure strategies. For each i in {1, 2, ... n}, let

$S_{i}\subseteq \left\{\sum _{k=0}^{\infty }b_{i}(k)\,2^{-(k(n+1)+i)}\,\,\vert \,\,b_{i}:\omega \rightarrow \{0,1\}\right\}\subset \mathbb {R} \,.$

Since the cardinality of these sets is $2^{\aleph _{0}}$, we can fix a bijective mapping J_i from T_i to S_i and we can identify these strategies with each other. Notice that for each element of the joint strategy $S=S_{1}\times S_{2}\times \ldots \times S_{n}$ of the aggregative game, there is a distinct and unique value of

$\sum _{j=1}^{n}s_{j}\,,$

that is, the function from the set S of joint strategies to their aggregative sums is injective. So given the sum, we can recover the entire joint strategy. And from that we can get the joint strategy of the original non-aggregative n-person game. Thus we can assign the payoff of the original game to the aggregative game without violating the condition of being aggregative. Conclusion, all games are aggregative games. So there is nothing gained by restricting consideration to aggregative games, since there is no such restriction in fact. JRSpriggs (talk) 14:45, 26 October 2013 (UTC)

Aggregative games with strategic substitutes admit a pure strategy Nash equilibrium without assuming convex best-response correspondences. Not all games of strategic substitutes admit a pure strategy Nash equilibrium. It follows that not all games are aggregative. I don't have time to go into any more detail but read for example Kukushkin (1994, Economics Letters Vol 46(1), pp 23-26) - I think that paper is set within the finite strategy set setting you speak of [the Wiki entry is NOT by the way]. I'm sure from there you'll figure out where you go wrong. If you're able to identify anything that should be said in the Wiki entry that will clarify to other people who might otherwise conclude like you did, that would be a great help and improve the entry I think. Oh and as an aside: When you wrote your piece there, did you at some point ask yourself "Hmmm... a whole bunch of peer-reviewed articles have been published in top journals over the last 35 years or so, so perhaps I could be wrong"? AggregativeGames (talk) 15:13, 26 October 2013 (UTC)

I am not wrong. Either you have left something important out of the definition in this article OR your whole field of study is hogwash. JRSpriggs (talk) 16:27, 26 October 2013 (UTC)

Listen, I am not going to communicate with someone who is childish and rude. As for your observations, these are trivial and well known (even in the continuum case - in fact, rereading your post I think you are using the cardinality of the continuum and so are speaking of this case). Please read the literature! If you do not have anything constructive to add, please do not waste other people's time. This is peer-reviewed material you are speaking of and it is properly referenced. It's how Wikipedia works. Thankfully, your personal opinions and back of the envelope logic is inadmissable on Wikipedia. If you think you have a point, submit a note to one of the journals on the reference list. This will then land on a professor's table with a little luck. If it land's on mine, I'll do my refereeing duty and explain things to you. That's how these things work. It is NOT something I wish to do on a Wiki talk page (well, I might have, but not with someone who behaves the way you do). AggregativeGames (talk) 13:25, 28 October 2013 (UTC)

A little bit of less-technical explanation for broader audiences?

Would be nice to see some real-world examples of aggregative games. Some illuminating discussions involving these examples would be even more nice. Pretend that you are talking to an undergraduate student explaining this new topic. For instance, summation over elements of a set probably makes zero sense to most people.