  In blockchain systems, the design of transaction fee mechanisms is essential
for stability and satisfaction for both miners and users. A recent work has
proven the impossibility of collusion-proof mechanisms that achieve both
non-zero miner revenue and Dominating-Strategy-Incentive-Compatible (DSIC) for
users. However, a positive miner revenue is important in practice to motivate
miners. To address this challenge, we consider a Bayesian game setting and
relax the DSIC requirement for users to Bayesian-Nash-Incentive-Compatibility
(BNIC). In particular, we propose an auxiliary mechanism method that makes
connections between BNIC and DSIC mechanisms. With the auxiliary mechanism
method, we design a transaction fee mechanism (TFM) based on the multinomial
logit (MNL) choice model, and prove that the TFM has both BNIC and
collusion-proof properties with an asymptotic constant-factor approximation of
optimal miner revenue for i.i.d. bounded valuations. Our result breaks the
zero-revenue barrier while preserving truthfulness and collusion-proof
properties.
