Over the last couple of days I’ve been thinking a lot about direct incentives. As far as I can tell, the idea has lost favor with a large part of the community. And I think it’s important that we determine whether or not they’re effective.

I’ve been having a discussion with @fei.saver on another thread that’s convinced me that direct incentives fail in at least one important scenario. That conversations starts with this post: Reweight Without Reweights (using cumulative deviation) - #6 by Inaniel

I’ve learned that to have any meaningful discussion about whether direct incentives are effective we need to be more precise about what we’re looking to achieve with them. So I’m making this post in the hopes that we can have a discussion about what a “good pair” of direct incentives is.

I’ve already discovered that some of the definitions that I first thought of are impossible. For example, I thought a “good pair” of direct incentives would at least **(1)** mint less than it burns, **(2)** reward buyers and punish sellers relative to an unincentivized market, regardless of the sequence of purchases and sales in the market, and **(3)** prevent drainage of PCV under extreme sell pressure.

It turns out this definition is too strong. @fei.saver showed me that any pair of direct incentives that satisfies (1) fails (2). Here’s why:

Suppose there’s a perfectly elastic sell pressure up to marginal price p. That is, sellers are willing to sell any FEI until the marginal price of FEI on the market is p.

In an unincentivized market, sellers will sell until the marginal price of FEI on the market is p. In this case, this marginal price of FEI is both the price to buy and the price to sell. So, after all the sell pressure has been released, buyers can buy FEI at p.

In a market incentivized by direct incentives satisfying (1), sellers will sell until the marginal selling price of FEI on the market is p. If b is the marginal burn punishment for selling FEI, this means sellers will sell until the unincentivized marginal buying price of FEI on the market is p + b. If m is the marginal mint reward for buying FEI, the only way for the marginal buying price to be better than in the unincentivized case is for b < m. But m < b by (1), so (2) cannot be satisfied.

The immediate variation that came to mind is to tweak the definition to give probabilistic guarantees. That is, instead of (2), we’d want a “good pair” to satisfy **(2’)**: reward buyers and punish sellers relative to an unincentivized market with probability at least 1/2 + \epsilon for some \epsilon > 0 over the space of all sequences of purchases and sales in the market.

I know: this starts looking exceedingly abstract. But I think the question of whether “good pairs” that satisfy (2’) exist is important. If the answer’s yes, then it’s possible we can worry about finding “good pairs” with larger and larger \epsilon. We can try to determine how close to \epsilon = 1/2 we can get. If the answer’s no for every choice of \epsilon, then we can lay the quest for direct incentives to bed.

In any case, I know there’s still a lot of work to be done to make the ideas I’m describing precise. But I wanted to share what I’ve been thinking to see if anyone wants to join me on this exploration.

Any ideas? Better definitions? Counterarguments to the fact that the original definition is too strong?