# How do open AI models affect incentive to race?

I see it said sometimes that open models contribute to AI race dynamics. My guess is that they don’t, and if anything, reduce AI race dynamics.

I will consider a simplified model that only takes into account the cost of training a model, not the cost to deploy it (which tends to be small relative to revenue anyway). Let f(x) map a training expense x to a “value per day per customer” of the trained model, under the assumption that the training makes efficient use of the cost. That is, a customer values using an AI model trained with x compute at $f(x) per day.

I assume there are n identical customers here; of course, there are complexities where some customers value AI more than others, incentivizing price discrimination, but I’m abstracting this consideration out. (In general, variation in how much customers value a product will tend to increase consumer surplus while reducing revenue, as it makes it harder to charge customers just under the maximum amount they’re willing to pay.)

I’m also assuming there is only one company that trains closed models for profit. This assumption is flawed because there is competition between different companies that train closed models. However, perfect competition assumptions would tend to reduce the incentive to train models. Suppose two companies have closed models of equivalent expense x. They each want to charge slightly less than the minimum of f(x) and the competitor’s price, per customer per day. If each competitor undercuts the other slightly, the cost will approach 0. See the Traveler’s Dilemma for a comparison. The reasons why this doesn’t happen have to do with considerations like differences in models’ performance on different tasks, e.g. some models are better for programming than others. If models are sufficiently specialized (allowing this sort of niche-monopolization), each specialized type of model can be modeled independently as a monopoly. So I’ll analyze the case of a closed model monopoly, noting that translation to the real world is more complex.

Suppose the best open model has compute x and a company trains a closed model with compute y > x. Each customer will now spend up to f(y) - f(x) per day for the model; I’ll assume the company charges f(y) - f(x) and the customers purchase this, noting that they could charge just below this amount to create a positive incentive for customers. So the company’s revenue over m days is nm(f(y) - f(x)). Clearly, this is decreasing in x. So the better the open model is, the less expected revenue there is from training a closed model.

But this is simply comparing doing nothing to training a model of a fixed cost y. So consider instead comparing expected revenue between two different model costs, y and z, both greater than x. The revenue from y is nm(f(y) - f(x)), and from z it is nm(f(z) - f(x)). The difference between the z revenue and the y revenue is nm(f(z) - f(y)). This is unaffected by x.

This can model a case where the company has already trained a model of cost y and is considering upgrading to z. In this case, the open model doesn’t affect the expected additional revenue from the upgrade.

Things get more complex when we assume there will be a future improvement to the open model. Suppose that, for k days, the open model has training cost x, and for the remaining m-k days, it has training cost x’ > x.

Now suppose that the closed AI company has already trained a model of cost y, where x < y < x’. They are considering upgrading to a model of cost z, where z > x’.

Suppose they do not upgrade. Then they get nk(f(y) - f(x)) revenue from the first k days and nothing thereafter.

Suppose they do upgrade, immediately. Then they get nk(f(z) - f(x)) revenue from the first k days, and n(m-k)(f(z) - f(x’)) from the remaining days.

Clearly, increasing x’ past y will result in less revenue for the upgrade in comparison to not upgrading. So the announcement of the upgrade of the open model to x’ compute will reduce the incentive to race by training a closed model with z compute.

So in this simplified analysis, release of better open models reduces the incentive to race, or does nothing. This is overall not surprising, as intellectual property laws are motivated by incentivizing production of intellectual property, and open content tends to reduce the value of intellectual property.

There are a number of factors that could be taken into account in other analyses, including:

Effects of open models on ease of training closed models

Substitution effects between different model niches (i.e. a model with an absolute advantage at mathematics may still be useful for writing essays)

Effects of uncertainty over open model releases

Different customers valuing the AI differently, driving price discrimination

Non-straightforward incentives such as prestige/recruitment from releasing models

Oligopoly dynamics

Time discounting

Changes in customer demand over time

It should go without saying that effects on race dynamics are not the only relevant effect of open model releases. Isolating and estimating different effects, however, will help in making an overall evaluation.

I suggest that someone who still believes that open models increase race dynamics clarify what economic assumptions they are using and how they differ from this model.