Has there been a successful implementation of Nash-Equilibrium in big data problems like suggesting a best buy in a stock market, in traffic monitoring systems or crowd control systems. All the above mentioned scenarios have competitive environments and one needs to get the best possible solution in them, which should suit well for Nash-Equilibrium cases.
This question isn't terribly clear. Data analysis and strategic modeling (game theory) are different tasks. Nash equilibrium is a way of understanding the incentives they have by assuming a set of players with assumed utility function and making deductive inferences about what they ought to do to maximize those utility functions given their interaction. Data analysis is an inductive process.
There are a number of ways game theory and data analysis might interact, here are the easy top two:
- Someone might use data to infer players' utility functions (I'm sure this exists in econometrics-land somewhere; also, political scientists have a technique called "ideal point estimation," to infer political preferences from voting behavior---which you can easily google to learn more);
- Someone might use game theory to generate behavioral predictions which are testable by data.
Thinking about the specific kinds of cases you mention, the obvious application would be in the stock market one. Suppose you have a ML model that can reliably predict the market behavior of other people at time T from a given feature set. Then the consumer of the ML model might have an optimal purchase at T-1, and finding that optimal purchase is going to be strategic.
But combining the two approaches might just break the ML. This is really interesting to think about... musing out loud...
Consider the simple case of a two-player market in one stock. Player 1 wants to buy at T-1 if player 2 will be buying at T (because the price will go up); player 1 wants to sell at T-1 if player 2 will sell at T (because the price will go down). The naive approach for player 1 is "use my ML model to predict what player 2 will do, then do it first at T-1." But, of course, P1's behavior at T-1 is itself observable by P2, and changes P2's behavior (the price has gone up); moreover, by definition P1's behavior at T-1 can't be a feature of the ML model used to predict P2's behavior at T, because it's behavior that is chosen on the basis of the ML prediction. All sorts of fun puzzles begin here, but none of them look real good...
I have a very limited knowledge of game theory, but hope to learn more. However, I think that potential applications of Nash equilibrium in the context of big data environments, implies the need of analyzing a large number of features (representing various strategic pathways or traits) as well as large number of cases (representing significant number of actors). Considering these points, I would think that complexity and, consequently, performance requirements for Nash equilibrium in big data applications grow exponentially. For some examples from the Internet load-balancing domain, see paper by Even-Dar, Kesselman and Mansour (n.d.).
The above-mentioned points touch only the volume aspect of 4V big data model (an update of Gartner's original 3V model). If you add to that other aspects (variety, velocity and veracity), the situation seems to become even more complex. Perhaps, people with econometrics background and experience will have some of the most comprehensive opinions on this interesting question. A lot of such people are active on Cross Validated, so I will let them know about this question - hopefully, some of them will be interested to share their view by answering this question.
Even-Dar, E., Kesselman, A., & Mansour, Y. (n.d.). Convergence time to Nash equilibria. Retrieved from http://www.tau.ac.il/~mansour/course_games/nash-load.pdf