Whoops. Github link was truncated https://github.com/olendor... - Steve Koch

This presumes fixed strategies and rational decisions I presume? So there are also marketing effects in here as well? Not just what are the percentage of players in each camp but the perceived percentage? - Cameron Neylon

Important theory... now many tend to think that Closed Science only takes advantage of Open Science... game theory can provide some (theoretical) evidence for that.... interesting! - Egon Willighagen

Open science has many "players". Do the arguments hold if I am Player 1 and the crowd is Player 2? - Matthew Todd

If you haven't already, you should check the literature on game theory and collective action problems (e.g., http://scholar.google.com/scholar... ) Open science is an example of a collective action problem. - Michael Nielsen

@Michael, I haven't read any background yet. Rob has, I'm sure, as he used this in his Ph.D. research in evolutionary biology (experiment + modeling/theory). I'm hoping I can get his attention / contribution on this thread soon! I don't have any background in game theory. But, as far as I understand, the analysis Rob's done so far is the most basic first step, and tit for tat (TFT) non-collective is the starting point (and it's easy to solve analytically). I agree that the competition between open science and closed science is much much more complicated. And I think if this kind of approach is useful, complications should be added. Rob has done a lot of those things, and maybe some people noticing this have also. Even with this very simple, most basic analysis, I think it helped me a bit to see aspects of the competitive landscape. I bet with the next layer of complexity added (such as collective action) a lot more clarity can be added. At this point I don't add much intellectually to the idea, except for a perspective as a player in the game. - Steve Koch

@Mat I am not sure. I'm going to see if I can get Rob to chime in here! - Steve Koch

@Cameron, I think this starting point is fixed strategies, either "defect" or "tit for tat." Like I said in one legend, I can't remember what "temptation to defect" means exactly. I don't think perception is modeled in this basic starting point. I sent an email to Rob urging him to chime in on this thread, so I hope he can! - Steve Koch

Good to see this being tackled in a more formal way, but sure, the simple 2x2 matrix is only the first step. For instance, collaboration can well occur behind closed doors. - Daniel Mietchen

Side issue: Wouldn't something like Octave or R be a better fit to an open project than MATLAB? - Daniel Mietchen

Totally agree open coding platform would be better. Right now there's not much code at all, since it's analytical that Rob did. (Rob, can you post snapshot images of your calculations, if any?) Since right now it's just plotting, R would be good. (I added the text to his images via powerpoint, just for convenience.) I am tempted later tonight to make the pots in R. A further aside: I know Rob, during his PhD or postdoc work wrote a lot of code for game theory simulations including spatial information (so that agents could spread from one community to another). I think he's lost this code (irony!), but it was in C. I think a similar implementation for open science would add perspective. Either geographically, but more fun would be spread of open science from sub-fields. E.g., from Astronomy to drug design (just an example of one community to another) - Steve Koch

A somewhat related project is Lee Worden's "Mathematics of Direct Democracy" at http://rockethub.com/project... (or, more detailed, at http://lalashan.mcmaster.ca/theobio... ) - see also https://plus.google.com/u... on link to collective action problems. - Daniel Mietchen

Rob posted some thoughts / responses on the github wiki: https://github.com/olendor... - Steve Koch