Did Existenz influence Inception?

As Mnementh points out, it's probably impossible to say with certainty until he joins the site, but it seems as though he hasn't explicitly made mention of it yet. He has said that:

"The whole concept of avatars and living life as someone else, there's a relationship to what we're doing, but I think when I first started trying to make this film happen it was very much pulled from that era of movies where you had 'The Matrix,' you had 'Dark City,' you had 'The Thirteenth Floor' and, to a certain extent, you had 'Memento' too. They were based in the principles that the world around you might not be real."

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The Matrix was 1999; Dark City 1998; Thirteenth Floor 1999; Memento 2000, so eXistenZ (1999) falls neatly in that "era of movies" he talks about. It's conceivable that it was an influence along with the ones he mentioned, but him not explicitly bringing it up leads me to believe it was not, or at least not a major one. He hadn't seen Last Year at Marienbad (1961) to which Inception also drew a lot of comparison.

I tend to think that the dream/reality layers idea is not that original or uncommon and that there are plenty of previous works that build on it without necessarily being an influence on those which follow. For instance the Scrooge McDuck comic people said Inception ripped off.

All speculation of course :)

The concept of layered realities does seem very similar. Take for example the following scenes.

In the scene below, the viewers of the movie already think they are within the game (1 layer deep) and are going to boot into a next layer. This can be seen as similar to when Cobb and others were in the van about to jump again. So in both cases, the viewer needs to keep track of where reality in the movie starts and where the new layer of reality begins.

_{Images are used for the critique of Existenz}

Here we have the first possible jump and once the viewers reach the end they begin to question whether this was indeed the first pod entry. This is similar to questioning whether Cobb was already a layer deep before booting in on the airplane.

_{Images are used for the critique of Existenz}

Here is where it gets tricky, let's call this the jump into limbo. In Existenz, only one character actually uses the pod. So did that character go one more layer deep or did both characters jump back up a layer? This can be compared to the snow mountains layer to the jump to Fischer's layer and finally to limbo. No one is sure that Cobb did indeed escape limbo for the whole show. That is, Cobb could have been in limbo for the entire show.

_{Images are used for the critique of Existenz}

The next feature that can be compared is the idea of a kick, where in Existenz it is shown as a pause of game whereas in Inception the user supposed thrown up a level/layer.

The final item is that of the user/gamer imparting their own images/thoughts into the game. That weird gun that was used in the opening is shown in the later layers. So this most likely means that the game uses the thoughts of a person to advance the dynamic play. Thus it shows the same psychotic effect as in Inception because the player will need some sort of "totem" to hold on to what they believe to be reality.

I believe the idea of layering (questioning the present reality) predates both of these films such that both of these movies could have gotten influence from earlier books/scripts/movies. Though the similarity between films is quite remarkable.