If a certain company sells a product to customer A for $10, could the
company legally tell customer B (during a private negotiation) that
customer A paid more than they actually did in an attempt to have
customer B pay more?
The mere attempt is largely inconsequential and unlikely actionable. However, at least in some jurisdictions (example: California), that sales tactic may be actionable when it results in a transaction the customer would have declined were it not for the false statement of price reduction(s). The recent opinion Hansen v. Newegg.com Americas, Inc., 25 CalApp.5th 714 (2018) will be of interest to you, although I explain below some deficiencies in the Hansen opinion.
For additional case law, some of which might differ from Hansen, see the results of this query.
As applied to "former prices", I personally find the underlying legislation (and/or how courts "interpret" it) at odds with contract law, one of the prima facie elements of fraud, and the economics notion of utility.
Contract law definitely governs sales. Although any deceit or attempt thereof contravenes the covenant of good faith required in contract law, the scope of contracts generally is limited to the interests of the parties as per the transaction(s) between them. The amount that customer A truly paid for the product is not relevant to customer B's genuine interest in, need for, or use of the product itself. You will notice that this point coincides with Newegg's argument in Hansen at 727.
Even if customer B proves economic injury, another contentious point would be that of reasonable reliance: Was it reasonable for customer B to rely on the company's representation about how much it charged customer A? (Mis-)Representations of significant magnitude should prompt customer B to try to make sense of the advertised price gap. The gap could stem from possible difference of circumstances and/or in the quality of the product, whence customer B's light acceptance of the misrepresentation contradicts the reasonableness of his reliance and/or the relevance of the misrepresentation itself.
The Hansen court blatantly cheated at 730-731 by tweaking Kwikset and positing that
reasonable people can and do attach importance to [a product's former
price] in their purchasing decisions.
(brackets in original)
The Kwikset excerpt at issue actually reads:
the Legislature has by statute made clear that whether a product is
manufactured in the United States or elsewhere is precisely the sort
of consideration reasonable people can and do attach importance to in
their purchasing decisions.
That is, whereas the controversy Kwikset centered on a (mis-)representation of "Made in the USA", the Hansen court altered the quote to force it into the very different issue of "former prices". This time the infringement favored customers (particularly the plaintiff Hansen), but that judicial tweaking exemplifies the propensity, impropriety, and generalized danger of judges indulging in lawmaking (and in altering the record on appeal).
To be fair, Hansen at 723 alludes to the wording used in advertisements of price reductions. However, that analysis might be inapplicable to the situation you describe because the misrepresentation about customer A (that is, customer A in particular) does not imply the duration and/or generality inherent in the terms cited from Cal. Code Regs., tit. 4, § 1301.
The concept of utility also strikes the position that former prices charged elsewhere (customer A) influences the benefit customer B obtains henceforth from a new, similar product. The rationale is very straight-forward: Does your sole assumption/belief/knowledge that "yesterday someone else bought an apple at a higher price" change whatsoever the taste or nutritional value of the apple you bought and consumed today? Clearly the answer is No.
Furthermore, in Economics, it is very well known that a rational agent's decisions are determined by
- the principle of Decreasing Marginal Utility (the utility that he
has obtained so far from that good/service or its substitutes);
- his current budgetary constraints; and
- his expectations about the future.
Unlike the bracket-law made up by the Hansen court, former prices allegedly charged to third parties really does not defraud a customer and does not subject him to economic injury.
what laws are there in place to prevent these deceptive sales tactics?
That depends on each state or jurisdiction. You will identify the corresponding statutes by reading the court opinions.