The game theory of how algorithms can drive up prices

Very interesting. I looked at stability in learning agents in artificial markets back in the late 90s for my PhD and concluded that at least the systems I worked with weren't stable - they were prone to bubbles and crashes.

Very interesting to see that there is a class of stable systems that force high prices.

Would be interesting to understand if the no swap regret systems studied also give stable results when it is an N player game rather than a 2 player game

I had the same question about N-player settings. My intuition is the more players, the more competition and the more chaotic the dynamics, and the harder it would be for any strategy like they describe to emerge. But intuitions can be wrong.

In any event, it would be interesting to know how the dynamics change with increases in the number of players — I wondered if it might provide some kind of rationale for having a certain number of competitors in a market.

The researcher says

> this strange strategy will maximize your profit. “To me, it was a complete surprise”

It doesn't seem like such a surprise that algorithms that use information about rivals to optimising profit tend to price high.

Consider a small town with two gas stations, you own one. You can set the price (high or low) in the morning and can't change it until the next day. Your goal is to optimise profit for the next 1000 days. On day one you price high (hoping your rival will). But your rival prices low and wins lots of business. On day two, you price high again (hoping your rival will have seen your prices and cooperate). If your rival prices high, you both stay high for the most of the next 998 days (there's some incentive to 'cheat' and price low, but that is easily countered by the rival pricing low). If your rival priced low on day 2, you have to start pricing low too. But occasionally you'll price high to try to 'nudge' your rival to price high to avoid low-low. If they eventually understand, you can both price high for the rest of the 1000 days. Critically, even if stuck at the low-low equilibrium, you'll keep trying to 'nudge' high periodically. The frequency with which you try to 'nudge' will depend on the ratio of profit for high-high vs low-low. If you both make extreme profits when pricing high-high, you have more incentive to 'nudge', but if the difference isn't great, you won't nudge as often.

Seems obvious pricing high will be attempted in proportion to the reward relative to pricing low.

The researchers' conclusion seems reasonable:

> it’s very hard for a regulator to come in and say, ‘These prices feel wrong’”

and

> what can regulators do? Roth admits he doesn’t have an answer.

(i.e. in practical terms, there's no way regulators can police what algorithms sellers use - I can't think of exceptions to this, but perhaps there are some special cases)

> Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price.

I always found this statement to be rather wishful. Individual lowering of prices makes sense if and only if your competitor is capable of saturating the market. Otherwise, demand elasticity becomes very relevant. Sure, your competitor may take the larger share of the market, but then you can compensate with higher per item profit.

The common wisdom is that in properly functional markets there's enough supply with n-1 market participants, therefore given a market signal of one participant lowering their prices the last one standing without lowering prices gets kicked out of the market, making maintaining prices the losing move. Yet, if the rest of the market does not react to the signal, the one lowering their prices hurts their profits and possibly kicks themselves out of the market. Making price maintenance, and depending on elasticity maybe even jacking of prices, the winning move in the presence of this signal.

Turns out the probability of either move being the winning move is dependent on probability of other market participants colluding/defecting. However, since lowering the prices hurts the profit a rational market participant would conclude that the rest of the market is inclined, even if a little bit, not to lower their prices in reaction given price cutting signal and similarly a bit more inclined to raise the prices given price hike signal.

You can see this happening all the time on Amazon these days if you use a price tracker. Most items are swapping between two prices that are maintained for periods and little peaks just a little bit lower and higher to test response. Then when you take that and look across different countries stores you can see they are running different pricing and running tests globally while the price is being sustained in others.

Enormous amounts of price testing with a very clear strategy that is easy to see in pricing charts.