Having sexed my share of co-workers (and one boss), yes there is "workplace game." It's a lot like real game. But since you see the person every day you have to moderate yourself differently.
The key for me was to establish myself as the Office Flirt wherever I worked. Talk to all the girls, even the ugly and fat ones. Be outgoing. Mention the date you had last night or the girl outside the office who's chasing you. Pretty soon the impression of you will be that you're a Cassanova.
But don't forget to put "playtime" on hold when push comes to shove. Do your job and do it well. Don't ALWAYS be Mr. Flirt. Sometimes be Mr. Serious, Mr. Busy, etc. I should add that you don't want to go over any lines with what you do/say - and those lines often vary from office to office.
If the people from your office invite you out for drinks, go out but don't get hammered. Definitely have fun, but cut out early. When I was much younger, I'd get drunk and hang out til 2 a.m. thinking I'd be able to take home a similarly drunk chick. Bad idea. Better to take a step backward and save face. As I got older I started leaving without telling anyone, after an hour or so. The next day the girls would be all "where did you go last night??" and I'd just say I had to meet someone.
Finally, if the object of your desires ever says "we shouldn't do this, we work together," AGREE & AMPLIFY. That means you say "you're right - the last time I did this it caused trouble." Back off and don't press. As always, let her come to you.
(I only ever did this at jobs I didn't care much about, or where it was permitted to fraternize. If you value your job, and you think it's a risk to have an office romance, by all means, refrain.)