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If you were to take a game-theoretic model of a world in which each individual tried to optimize their utility function / goals then how would you go about designing a computer simulation of the people's interactions as they try to optimize their goals.

In particular, how can I model the way goals interact?

I guess the model could get arbitrarily complex, but cannot imagine anything nontrivial as given in standard game theory books. Thanks.

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    $\begingroup$ As you suggest, this would be arbitrarily complex. In any case, the point of game theory is generally not to take a complex real world situation and write it down exactly as game, which will often be infeasible. Rather, in game theory, we create simplified models of real world examples in the hopes that our models distill the key strategic components of the real world scenario. If we do a good job in distilling the real world example into a model, then our predictions from the model may be useful in predicting outcomes in the real world example also. $\endgroup$ – Shane Jul 9 '16 at 9:20
  • $\begingroup$ We could create say 80 key roles (e.g. jobs), each with a weight representing their relative respective weight in society, and see how these interact (and we may even be able to guess election results or other variables such as percentage of people going to war, jail, psychiatric hospitals, concentration camps, etc.) as a result,. How can we run a simulation of this "simplified" scenario. It must sure be possible, I'm sure politicians have someone paid to do that analysis for them. (?) $\endgroup$ – Jack Maddington Jul 9 '16 at 9:24
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    $\begingroup$ Very difficult. You would need to determine all of the possible actions for each of your players. Even if each agent has only two possible actions and the game is static, that's still $2^{80}$ possible outcomes (a number with 24 digits). If you have them interacting repeatedly, then the number of possible outcomes would blow up further. I don't want to be the bearer of bad news, but you're biting off more than is possible to chew. $\endgroup$ – Shane Jul 9 '16 at 9:32
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    $\begingroup$ Take chess as an example. A fairly simple game (much simpler than the real world). We know how to solve chess -- it's not particularly difficult. The problem is that it is thought that there are more possible paths of play in chess than atoms in our universe. Even with supercomputers, it is currently computationally infeasible to solve chess. Quantum computing could perhaps make solving chess possible. But if you want to build a model that's more complicated than chess, as it seems you do, I'd suggest you think twice! $\endgroup$ – Shane Jul 9 '16 at 9:34
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    $\begingroup$ @JackMaddington That (the game theorist being able to predict results) sounds like it is probably untrue. Most election forecasts use advanced statistics and econometrics. Newspapers are actually a very bad place to get informed on technical issues. $\endgroup$ – Giskard Jul 9 '16 at 10:47
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Chess is EXPTIME-Complete, which makes it significantly harder than NP-Complete problems.

Perhaps you are interested in the study of economic networks. Strategic network formation sounds like a good starting point. A lot of the work examines when certain classes of graphs arise under pure strategy Nash equilibria. There are exponentially many pure strategies. Enumerating the vertices of the polytope is likely not feasible.

Edit: Some of the big names in the area include Matthew O. Jackson, Rachel Kranton, Sanjeev Goyal, and Hans Haller. I would start with their papers. In particular, Matthew O. Jackson has a book on the subject.

Here are links to their homepages/CVs so you can scout out their publications. Economic networks are a pretty hot area at the moment, so you can likely look at journals like Econometrica to see what is being published.

http://web.stanford.edu/~jacksonm/papersarticles.html
http://econ.duke.edu/people/kranton/networks
http://www.econ.vt.edu/cvsandresearch/hallercv.pdf

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    $\begingroup$ The chess part seems like a comment on a comment by someone other than the OP why is it in the answer...? $\endgroup$ – Giskard Jul 9 '16 at 17:50
  • $\begingroup$ Can you please reference some links on economic networks and strategic network formation? Thanks. $\endgroup$ – Jack Maddington Jul 9 '16 at 18:18
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    $\begingroup$ @JackMaddington- See my revision for some starting points. $\endgroup$ – ml0105 Jul 9 '16 at 18:53
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    $\begingroup$ This is a good answer. Still, realistically, I don't think it will be of much use to the OP. Endogenous network formation is a pretty nascent (and potentially quite exciting) field but it's still largely theoretical. If the OP's interested in forecasting elections, he would be far better off reading directly on that subject (statistics, econometrics, and Nate Silver stuff), as denesp suggested in a comment. I don't see game theory or networks being particularly useful in this direction beyond in a very abstract setting. $\endgroup$ – Shane Jul 10 '16 at 7:05

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