The game theory of how algorithms can drive up prices

However, Walmart now displays in store and online for pickup prices on their website. I walked into the Walmart and paid $1.11 more than if I were to have ordered it via the app on my phone or website for pickup.

And Walmart was very upfront about it, and I knowingly paid $1.11 more because their online order and pickup option sometimes makes you wait 20min+ for a Walmart employee to come out and give you what you bought (even after it says your order is ready for pickup).

Regulators can already police the data used as inputs in decision-making in industries like insurance, so policing the algorithms that operate on that data doesn't seem like too much of a reach.

How enforceable is policing which data can be used as inputs though?

It's common for insurance companies to price based on age and sex (e.g. teenage boys will typically pay higher car insurance premiums than similar aged girls). Presumably insurers are not allowed to price on a factor such as race. Unlike collusion, overt use of a variable like 'race' in a pricing model could be detected and enforced via a company whistleblower.

But how would a regulator find/prove algorithmic collusion?

In an extreme case, regulators could ban all use of competitors' data in a sellers' pricing models. But that seems extreme and unproductive since it could stop price wars (downward prices), as well as muting good effects of the 'invisible hand' (higher prices attracting more market entrants and greater investment)

One of my first thoughts as well. If you're big enough, you collect so much data and run so many experiments all the time that you know exactly what you'd do if/when there's any competitor on the scene. Not only is there no need to talk to them and make backroom deals, but barely any need to even observe them. You priced like they did/would/could at some point already anyway. At a certain scale and if you already know the price that the market can tolerate.. the most relevant hidden information you want to know is how much cash your competitor has access to. That tells you whether you can win the price-war to sell at a loss for long enough to ruin them, buy them, move on to integrating verticals etc.

Game theory is interesting but also a bad model to the extent that it assumes persistent players with changing strategies, whereas average case in late-stage capitalism is more likely to have players eating players, no new players can enter, players changing rules, etc. As a CS nerd I still like a game theoretical approach better than most econ, but at some point we need to give up on tidy formulas and closed-form answers, and go all in on messy simulations.