Jumping back in guys

Appreciate your clarifications @lesigh and you giving us the reply and opportunity to express our views more clearly.

In general, we all agree Fast Lane is an interesting concept and innovative one even. So it’s exciting.

Our remarks are humbly shared as risk management is our bread and butter and we know it’s always easier to imagine (bad) scenarios and find mitigation avenues, before deployment than after.

I think we are landing on common ground for most points here but there are still a few things I’d like to convey.

**Regarding Point 2 in particular**:

The reward concept is well understood. What we’re saying is that this incentive mechanisms might not be a good one because of externalities it generates on Bancor users (due to positive network externalities on arbitrageurs). It is a crucial point since we agree on Point 1 that the normie Bancor user will likely not use Fast Lane by lack of competitive tech and exp in the arbitrage market.

So postulating the following:

The way I see it is that if arbitrageurs (or anyone for that matter) use the contract, it is a significant win for Bancor.

is true, but in my opinion the real question is not whether it is a win or not, we agree that’s a win. The question is how do we ensure the arbitrageurs actually use it. What’s in it for them? Why go through the extra step of using it? Where and how do we place the incentives?

Consider the following plausible scenario:

- a professional arbitrageur (most certainly a bot) is finding an arbitrage on a pool having 0.5% fees and consider going through Fast Lane to execute it.
- doing the math, it turns out the expected arbitrage profit is 10% of the trade volume, so that the reward for arbitrageur is 1%, amounting in our example to 100BNT => just equals the announced fixed cap (we exclude gas fees for the sake of simplicity)
- it’s clear, the incentive for the arbitrageur to execute on Fast Lane depends on the cost of an external execution. At the very least this cost is superior or equal to the pool fee of 0.5%.
- the bargain for the arbitrageur is then the following:
- choice1: get an uncertain profit of max 1% by going thru Fast Lane (but leaving out the control over execution) or
- choice2: get an uncertain profit of max 9.5%=[10% arb profit - 0.5% trade fee], (altho when accounting for the other execution costs the profit is certainly below 9% but surely higher than 1%), while controlling the execution as he’s used to.

- In terms of game theory, all things being equal, the second choice is always the Nash equilibrium (which is not Pareto optimal) and is a non-coordination. This is due to the positive externality the arbitrageur benefits from the other users actually using the Fast Lane => the more users use or try to use the Fast Lane, the more the arbitrageur is incentivized not to use it since a professional arb bot will always be better at this game than Fast Lane and win the competition.
- the expected return of this lottery for the arbitrageur a key dimension. Assuming the duplet [p, 1-p] as probabilities of gain from choice 1 and choice 2 respectively, the
**expected return** (still excluding other costs) is E(R)=p*1% + (1-p)*9.5%, where R is the profit.
- As a rule of thumb, due to technological advance and experience, 1-p is likely twice as high as p → p=0.33. Then E(R)=0.33 * 1% + 0.66 * 9.5% = 6.7%. The reasoning holds if p=0.5.

Fast Lane creates a positive network externality, i.e. it gives free ride on fees to all Bancor and non-Bancor users. And since the 100BNT fixed Cap profit (choice1) will almost always be lower than the Arbitrageur’s expected profit in that scenario, the arbitrageur is in fact pushed to not use the Fast Lane. In the end, arbitrageur is extracting value from the network, backfiring a negative effect to the users of Fast Lane: arbitrageur exploits the positive externality brought by Fast Lane freely.

It’s kind of counter-intuitive that in this scenario the exploit consists in not using the Fast Lane, but what’s at play is that Fast Lane (with such a fixed cap) increases the Arbitrageur’s chance of gain within the non-coordination leg because the other less advanced and informed users will want to use Fast Lane since their E(R) is much lower (probability of success in choice2 is way lower for them).

*Remark*:

*The opposite scenario would be a high fixed cap: say the expected arbitrage profit is 5% of the trade volume, and the announced fixed cap is set at 50% of that, then choice1 yields 2.5% and choice2 yields 4.5%. Then using the same probabilities, the E(R) equals 3.8%. What we see here is that the differential between choice1 and choice2 is now far lesser, hence lower incentive for the Arbitrageur to not use Fast Lane.*

The most effective way to execute this incentive mechanism is by introducing a flexible subsidy/tax (respectively) mechanism into Fast Lane, which can boil down to increasing/reducing (respectively) the final extracted value to a level that is break-even with a function of the expected return E(R) of the identified arbitrage.

Also, the fixed cap entering in the calculation of E(R) should be expressed in % of trade volume, not in BNT amount, to ensure it’s homogeneous with the expected arbitrage profit. The probabilities in E(R) can be left at 0.33/0.66 and be refined afterwards, or even be distributed across a range and picked randomly to avoid further exploit.

In the above first scenario, the extracted value could be set to 6.7% at execution time of the arbitrage trade. Since the arb generates an expected profit of 10%, the protocol will retrieve 3.4% to be burned. This is less than the initial 9% resulting from the application of the proposal, but it **maximizes the usage** of the bot by arbitrageurs and therefore the effectiveness of Fast Lane on the long run.

Doing so, the risk of arbitrageur going outside Fast Lane and frontrunning Fast Lane users is minimized and the Fast Lane usage is maximized.