A consensus design which doesn't offer a mining reward is attractive in theory, because it prevents the system from centralising due to the compounding profits of the best miners.
In a consensus design utilising PoW with no mining reward (neither block reward nor fees) - is the incentive for timely confirmation enough to guarantee convergence of the system as a whole? Is timely confirmation even well defined in a system with no competition to mine?
The timely confirmation incentive is supposed to encourage the system to converge by having its participants build off the block/transaction with the best score - the idea being that if everybody does this, the chain selection rule will select in favour of them and their transactions will be confirmed more quickly than if they chose any other location to build their blocks.
This is all well and good except for the adversary problem. With no competition to mine, the maximum network hashing rate will be impossible to measure, since although transactions may be incoming at a high rate in a mature currency (and assuming a PoW must be submitted with the transaction) , this rate could still be vastly below that of even just one ASIC* such that any adversary looking to double spend would find the task relatively easy.
This also brings into question the entire way in which transaction acceptability can be bounded. In bitcoin the adversary's hashing power relative to the network as a whole is considered, yielding a probability of the best block being reversed, yet with no competition to mine, the maximum hashing rate of the network as a whole cannot be measured since adversaries have nothing to gain by participating in the network's nominal operations, instead they might chose to lie in wait.
Thoughts?
*) AntMiner S5+ rated at 7,722,000Mh/s, compared to Xeon Phi 5100 rated at 140Mh/s is 55,000 times faster
https://en.bitcoin.it/wiki/Mining_hardware_comparisonhttps://en.bitcoin.it/wiki/Non-specialized_hardware_comparison