Birthday present #2

We're sitting at a table, next to a giant pile of pennies. We play a game.

First, you put a penny on the table. Anywhere's fine, but it can't stick out over the edge.

Next, I put one on, somewhere else. I can, if I want, even touch your penny with mine, but they can't overlap.

We keep doing this until there's no place to put another penny. Last person to be able to put a penny down, wins.

What's a winning strategy, and who's the winner?