If you pay out a percentage x of the difference it once again becomes profitable to be strategic about what you report. In particular, you want to guess the difference with the second best solution and then adjust your price up by that amount. That way you get reimbursed the full amount instead of only a percentage x. Let’s call this mixed price auction (a term I got from this paper).
We could also consider the case where solvers are simply reimbursed their reported price: this would be a first price auction. Here you get the same strategic behavior where you want to guess the next best solution and be as close as possible above it. I think first price is still an improvement on the status quo because it allows for price forming. That is, solvers need to be strategic about their pricing, but they only get to charge a good margin where there is little competition, so the rewards will reflect the incremental value brought by the solver (and if the reward is high, attract additional development in that area).
Still, the mixed price auction would be better than the first price auction in my opinion, because it means that a solver that is not strategic (ie just ‘naively’ reports it’s private beliefs) will be able to capture a positive margin. This lowers the barrier to entry. Also, being strategic becomes less lucrative in general, so solvers should dedicate less resources to it.
The idea of fitting the surplus in the fixed token rewards is interesting, though hard to reason about because your payoff now depends on all other auction. I assume you mean that if the reserved cow is enough we pay out according to second price rule, if not we scale down by a percentage x until it fits?
My intuition would be that the following would happen in equilibrium: whenever there is not enough reserve to cover the bonus rewards, solvers have an incentive to be strategic (through overreporting their price). This happens until the paid out rewards are decreased to the reserved level. One implication of this is that any marginal entrant will have no incentive to be strategic, as to them the auction functions exactly like a second price auction. In other words, you could have a couple of sophisticated players pushing the auction into second price territory, and capturing some profits in the process, but once you are there, they have no advantage over less sophisticated solvers. This would be a good thing I guess.
Note that overall the DAO+users don’t pay anything less to solvers. It’s just shifting from the ‘bonus for having a good algorithm’ line item to the ‘compensation for execution cost and risk’ line item.
In the end, the best way to lower the cost is to have more competition. Anyone can see the solutions settled on chain, so if one solver is getting crazy profits settling a particular kind of batch, there is an incentive for others to compete on those batches and bring the margin down in the process.
On the collusion question: yes the second price mechanism is susceptible to collusion of the type you described, but so is basically any other mechanism (eg first price). If a solver can coordinate with the competition to overreport their price to get more bonus, they can also just overreport their own price by the same amount and guarantee a higher margin. I think the answer here is to have enough competition as well: collusion only works if all agents comply. If one of them defects they pick up all the batches instantly.