3

Do you lose as in magic? Do you reshuffle your discard pile?

6

If the Corporation player attempts to draw from his empty R&D deck, he loses the game. From the rules PDF, page 3:

...the Runner wins if the Corporation must draw a card from his empty draw deck

The Runner simply loses the ability to draw more cards if his Stack is empty, but it's not a game-ender. You don't reshuffle.

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