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You can play it on the web here:

http://www.ecb.europa.eu/ecb/educational/economia/html/index.en.html

Or you can get the iOS version to play on your phone or iPad. You get one tool: the interest rate. Which is kinda stupid, in a way, because they are pretending that all other policy, including open market operations, are unavailable. *shrug* "Events" can happen (oil crisis, severe weather, new technology reducing dependence on oil, etc.) more or less outside your control and other events seem to occur as a result of your actions (stock market boom/crash, housing crash, etc.).

If you're wondering, how'd'ya find out about that, hunh? Well, the answer should be obvious: I searched for a central banking game.

I've been in the mood for a new game lately; I'm also going to try Ticket to Ride.

ETA still more: An excellent review of Economia here: http://thinkprogress.org/yglesias/2011/11/18/372102/economia-the-game-of-terrible-monetary-policy-lessons/

I can't speak to the formula he offers, but the verbal description of the game's mechanics is exactly correct, as is his assessment that it accurately reflects the behavior of the ECB. Of course, the problem is this is exactly the strategy you land on when you only let yourself have the one tool (Bank Rate, interest rate, discount rate, whatever you call it).

ETA: Schmoop has a text game where you get to be the Fed and make decisions. It's a multiple choice, narrative quiz and basically you get to be Volcker. Sort of. It's nice that they recognize the three major categories of action you can take at the Fed: adjusting the discount rate, open market operations (buying and selling securities) and adjusting the reserve requirement.

http://www.shmoop.com/money-banking/game.html

ETAYA: This looks like an RPG for bankers:

http://www.libow.lv/en_banking_game/

Bizarrely BofE centric.

The Fed actually has a bunch of games but to the extent you can play any of them online they are all remarkably horrible. If you find a fun one, let me know.

Want an example? Prepare to be offended:

http://www.clevelandfed.org/learning_center/online_activities/barter_island/index.cfm

This one is like a weaker version of Economia:

http://www.frbsf.org/education/activities/chairman/