  Fairness is well studied in the context of resource allocation. Researchers
have proposed various fairness notions like envy-freeness (EF), and its
relaxations, proportionality and max-min share (MMS). There is vast literature
on the existential and computational aspects of such notions. While computing
fair allocations, any algorithm assumes agents' truthful reporting of their
valuations towards the resources. Whereas in real-world web-based applications
for fair division, the agents involved are strategic and may manipulate for
individual utility gain. In this paper, we study strategy-proof mechanisms
without monetary transfer, which satisfies the various fairness criteria.
  We know that for additive valuations, designing truthful mechanisms for EF,
MMS and proportionality is impossible. Here we show that there cannot be a
truthful mechanism for EFX and the existing algorithms for EF1 are manipulable.
We then study the particular case of single-minded agents. For this case, we
provide a Serial Dictatorship Mechanism that is strategy-proof and satisfies
all the fairness criteria except EF.
