Best price clauses and, to a lesser extent, price-matching guarantees have been the subject of intense regulatory activity in recent years. Here's a fact that is surprising to many, despite there being a significant consensus in the economics profession:

Best price clauses and price-matching guarantees can harm competition and consumers

A best price clause/most favored nation clause/price-parity clause requires a seller listing a price via one venue (e.g. a price comparison website) to ensure that the price listed there is no higher than that available through other similar venues. It is often imposed by venue operators to ensure their venue will attract customers. Common sense suggests that a clause requiring a vendor to be offered the lowest available price should be, at worst, neutral for consumers.

Suppose there are two venues, $A$ and $B$, that a seller can sell through. Suppose both are large suppliers of business to sellers, so simply quitting one of the venues is not a viable option.

Here's the problem: if venue $A$ charges a commission of $c_A$ to sellers who sell through its platform and venue $B$ charges commission $c_B>c_A$ then sellers will set a lower price on $A$ than on $B$ to try to steer consumers to buy through venue $A$ (where it pays lower commission). Thus, a venue can have consumers steered towards it by cutting its commission--venues compete in commission. Moreover, lower commissions (which are essentially a variable cost for the seller) are passed-through to consumers in the form of lower prices.

Now suppose there are best price clauses in effect. If $c_A<c_B$ then sellers can't steer consumers towards $A$ by setting a lower price on $A$ because $B$'s best-price clause requires the price on $B$ to be no higher than that on $A$. Thus, $A$ can no longer attract customers by cutting its commission, and so has no incentive to compete in its choice of $c$. This results in higher $c$s and higher consumer prices. This effect is theoretically robust and empirically well-validated.

A price matching guarantee is a promise from a seller to a consumer of the form "If you find the same product at a lower price elsewhere, I'll beat that better price". Common sense suggests a guarantee to beat the lowest price in the market should be good for consumers. Not necessarily so.

Here's a rough illustration of why: Suppose sellers A and B both have price-matching guarantees and consumers have a preferred seller from whom they buy by default unless the other seller offers a better deal. Normally, sellers would cut their prices to try to attract consumers from their rival. But here that doesn't work! If A cuts its price then the consumers whose default is B can just go to B and get it to match A's reduced price. But this means A has no benefit from lowering its price and will just stick with the same high price that it had all along. The price-matching guarantee has completely killed price competition!