Assuming by function you refer to the "agents'" \Phi, where do they make the assumption that it is injective? I see nothing to the effect in the text, and the functions in the counterexample on page 6 are not injective.
Oh, oops. I was reading their statement:
This interpretation is incorrect
without the additional hypothesis that V (x) is
a one-to-one function.
as - all of the phi functions must be one-to-one. Looks like they made the same assumption that I would have.
This was bothering me though so thanks for your response.
