I had this scenario today where I played not to win but to just accumulate all the cards. The other player (just the two of us) was playing to win. You can argue this is unsportsmanlike however I was curious to see the outcome! I countered all their moves to the point there was no more cards left to pick up. The rules say to reshuffle the discard pile and use it as a new pickup pile. So we reshuffled and I continued to pick up cards without playing (except sporadically to force my opponent to pick up new cards or change the colour).
We repeated this until I held all the cards except two, which were held by my opponent. I deduced the colour they held (yellow and red), and the card on discard was blue (and I decided to pick up, so that final discard card became my pick up card). At that point there are no more cards to pick up.
There's nothing that I can see in the rules to specify what happens in this situation. So, how should it be handled? Is this a stalemate/tie? Is it decided by who has the fewest cards left? etc. Has anyone been so foolish to try this approach before?