<p>Chess is EXPTIME-Complete, which makes it significantly harder than NP-Complete problems.</p>

<p>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.</p>

<p><strong>Edit:</strong> 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.</p>

<p>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.</p>

<p><a href="http://web.stanford.edu/~jacksonm/papersarticles.html" rel="nofollow">http://web.stanford.edu/~jacksonm/papersarticles.html</a> <br/>
<a href="http://econ.duke.edu/people/kranton/networks" rel="nofollow">http://econ.duke.edu/people/kranton/networks</a> <br/>
<a href="http://www.econ.vt.edu/cvsandresearch/hallercv.pdf" rel="nofollow">http://www.econ.vt.edu/cvsandresearch/hallercv.pdf</a></p>

CC BY-SA 3.0
2016-07-09T17:50:58.590Z
The chess part seems like a comment on a comment by someone other than the OP why is it in the answer...?
Giskard
CC BY-SA 3.0
2016-07-09T18:18:41.550Z
Can you please reference some links on economic networks and strategic network formation? Thanks.
Jack Maddington
CC BY-SA 3.0
2016-07-09T18:53:25.093Z
@JackMaddington- See my revision for some starting points.
ml0105
CC BY-SA 3.0
2016-07-10T07:05:45.623Z
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.
Shane
CC BY-SA 3.0
2016-07-09T17:42:32.000Z
2016-07-09T18:53:02.357Z
2016-07-09T18:53:02.357Z
ml0105
<p>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.</p>
<p><em>In particular, how can I model the way goals interact?</em></p>
<p>I guess the model could get arbitrarily complex, but cannot imagine anything nontrivial as given in standard game theory books. Thanks.</p>

CC BY-SA 3.0
2016-07-09T09:20:08.567Z
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.
Shane
CC BY-SA 3.0
2016-07-09T09:24:55.200Z
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. (?)
Jack Maddington
CC BY-SA 3.0
2016-07-09T09:26:13.320Z
There would have to be a description of moves by each player and pools on Facebook to see how things are going. (?)
Jack Maddington
CC BY-SA 3.0
2016-07-09T09:27:35.173Z
How hard would it be to build such a model to predict the outcome of the game?
Jack Maddington
CC BY-SA 3.0
2016-07-09T09:32:21.667Z
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.
Shane
CC BY-SA 3.0
2016-07-09T09:34:58.183Z
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!
Shane
CC BY-SA 3.0
2016-07-09T09:40:57.830Z
Then what would a practical model used by politicians look like. I once read on the new scientist magazine out a game theorist being able to predict election results.
Jack Maddington
CC BY-SA 3.0
2016-07-09T10:47:21.027Z
@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.
Giskard
<game-theory><dynamic-games><cooperative-game-theory>
World as a society of interlinked multiplayer individuals
Jack Maddington
# World as a society of interlinked multiplayer individuals

(Asked by: username_0 on 2016-07-09)

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.

**Tags:** game-theory, dynamic-games, cooperative-game-theory
> **Comments:**
> **username_1**: 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.  
> **username_0**: 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. (?)  
> **username_0**: There would have to be a description of moves by each player and pools on Facebook to see how things are going. (?)  
> **username_0**: How hard would it be to build such a model to predict the outcome of the game?  
> **username_1**: 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.  
> **username_1**: 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!  
> **username_0**: Then what would a practical model used by politicians look like. I once read on the new scientist magazine out a game theorist being able to predict election results.  
> **username_2**: @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.  

---

## 1 answers

### Answer by username_3 on 2016-07-09. Score: 2

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>

> **Comments:**
> **username_2**: The chess part seems like a comment on a comment by someone other than the OP why is it in the answer...?  
> **username_0**: Can you please reference some links on economic networks and strategic network formation? Thanks.  
> **username_3**: @JackMaddington- See my revision for some starting points.  
> **username_1**: 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.  

---

