As a case study, I recommend watching this episode of "Golden Balls" , which shows how a player can manipulate a game outcome and defeat the natural Nash equilibria. This is a classic IMO.
It kind of reminds me of the explanation of how the crowd at the Hajj crush (on the front page earlier today) behaved more like a fluid than crowd of communicating agents because the human density was so high.
Schelling's book is a write-up of the theoretical predictions of several different game-theory models. I didn't notice much overlap between the two.
You might also know Oskari as the author of Buzz Tracker
"In 2000 the British government used their help to design a special auction that sold off its 3G mobile-telecoms operating licences for a cool £22.5 billion ($35.4 billion). Their trick was to treat the auction as a game, and tweak the rules so that the best strategy for bidders was to make bullish bids (the winning bidders were less than pleased with the outcome)."
I'm thinking best price for HM Government was paid by UK customers?
C.F. quote below from 
"The auction confrmed our view that industrial-organisation issues are more important than the informational issues on which the auction literature has mostly focused. In particular, the problems of attracting entrants and dealing with alliances and mergers are likely to remain major preoccupations of tele-com-auction designers for the foreseeable future. Tackling such problems sensibly requires high-qualit ymarket research that keeps pace with developments in an industry that can change its clothes with bewildering rapidity. We also need more theoretical work on the industrial-organisation implications of major auctions."
(Basically the high bids lead to mergers & consolidation)
I know Ken, he's exactly like you might expect a leading academic but is basically amazing (and very well liked by his students).
It worked for the govt - it certainly didn't for the customers...
During my econometrics study this explanation helped me to explain it to others without going in to the mathematical details:
- Person A needs to decide what the best strategy is for all strategies of B (circle, on paper, the outcomes for A)
- Person B has to do the same (circle as well)
NE => look for 'box' (ie. outcome) that has two circles (there could be more!)
This leads to (confess, confess).
Anyone unfamiliar with him should at least glance at this Known For section on Wikipedia. https://en.wikipedia.org/wiki/John_von_Neumann
His body of work, breadth of scope, and reach of influence is really only comparable to Newton, Gauss, or Euler.
Edit: Can't forget Gauss.
Don't forget Gauss - he has more contributions than any you've listed, and contributed to a vast number of fields. His 'known for' section is a separate Wikipedia page ;)
http://www.economist.com/blogs/economist-explains - this seems to include some other stuff (which is doubtless interesting as well) but you can skip around to find the economics articles.
> The auction was conducted in a simultaneous ascending auction, similar to the US format with a slight deviation. In the UK's version of the simultaneous individual auction, each high bidder is only allowed to win one of the five auctions whereas in the US, many regions have multiple licences which multiple bidders can win.
1) Enjoy a nice latte
2) Trigger the bomb, killing both
3) Disarm the bomb, stopping the other from triggering it
The min-max strategy is to disarm the bomb, but there's a better Nash equilibrium where both players enjoy their lattes.
But of course it's not the main application. If I remember correctly it is mostly used to find balanced solutions in complex inter-company or inter-government exchanges, considering each side's leverage as well as the assets' values.
It really changed mine and lots of other people's worldview.
EDIT: Irony is a class with enrollment restrictions.
This is not neccessarily the best outcome for the market or the players themselves, see for example the prisoners dilemma (etc).
To me, i would look at it as a two dimensional plot somewhere there would be a statistical point which is the point of equilibrium.
Where these processes would statisticly end up.
Thanks for your participation.
The Economist's full article (behind the paywall) in fact repeats this claim that I consider misleading: "Nash showed that every 'game' with a finite number of players, each with a finite number of options to choose from, would have at least one such equilibrium."
An equilibrium that does not depend on the notion of mixed strategies is called a pure-strategy equilibrium. For an example of a game that has no pure-strategy equilibrium, see https://en.wikipedia.org/wiki/Matching_pennies.
Rarely does this happen in the real world.