There are obviously elements of existentialism which have influenced a lot of Auster's work, particularly 'The New York Trilogy' and 'Leviathan'. However, I feel that the theories of Spinoza have had a greater influence on the aforementioned texts.
As a result, in 'The New York Trilogy', Auster (perhaps unwittingly) highlights the flaws in Sartre's 'free will/bad faith' argument. In other words, even if some of the decisions we make feel as though they may be undetermined, it is a fallacy; we can never be free from the determining influence of 'cause' and 'effect'.