Project Waterloo is the first game project from Microsoft Research played on Facebook.
“The game is played by two players; each has 100 troops at their disposal and needs to allocate those troops among five battle fields. Once both players have allocated their troops, the winner is determined by finding which of the two players has won more battles. A battle is won by having allocated more troops to it than the opponent.
The game is complex from a game-theoretic perspective, involves randomized strategies, and can be approached by reasoning about the opponent's reasoning. We have also found it to be fun, engaging, and slightly addictive. It is thus a great test case for studying actual strategic behavior of people on Facebook.”
Check out this Facebook game app at http://apps.facebook.com/msrwaterloo