My understanding of Existentialism is that it's a DIY ("Do It Yourself") philosophy, in which the character of human existence is an intellectually open-ended proposition, and the purpose of life and existence for the individual (as well as the demands placed on the individual and therefore one's response to those...
My understanding of Existentialism is that it's a DIY ("Do It Yourself") philosophy, in which the character of human existence is an intellectually open-ended proposition, and the purpose of life and existence for the individual (as well as the demands placed on the individual and therefore one's response to those demands) is subjective.
This central idea means that the world, and one's place in it, is a matter of personal responsibility. As a principle, this is in contrast to a faith in a higher power or in belief systems that dictate appropriate actions and responsibilities attached to that set of beliefs. Therefore, Existentialism isn't the ideal philosophy for someone seeking external structure and comfort intellectually or as an article of faith.
In Waiting for Godot, there's a line—an aside by one of the tramps—about "faith deferred." The problem with Existentialism is that, for all its advantages in self-determination, it can never determine whether or not the Self is aligned with the Universe (or any aspect of it), since it’s a presupposition of Existentialism to assume that the universe is a vacuum of meaning.
All of the above might indicate that the Existentialist is "a man alone." However, Sartre (a philosopher with a similar world-view to Beckett's) wrote in his play No Exit: "Hell is other people." Despite its misanthropic tone, this statement is not advocating that one avoid flawed human society and go it alone. It actually means that, once again, we make our own reality—for better or for worse. To simplify things, then, we succeed or fail (but—arguably—mostly fail) as part of a group.
In this thought process, one's sense of Self is tied to the image of oneself reflected back by other people. This image can exist within the context of a metaphoric Hell (Sartre) or metaphoric Purgatory (Beckett), but it doesn’t provide escape from others or from the Self.
In Waiting for Godot, Vladimir and Estragon vacillate between being friends and antagonists. Companionship is their buffer against the void confronting them, and yet, within Existentialism, they are responsible for their own expectations. And, since those are constantly dashed, they are consequently responsible for their own defeatism.
Thus, the relationship between Vladimir and Estragon is perfectly in-keeping within an Existentialist reading of the play.