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The phrase "a private value" is correct and usable in written English.
It can be used in contexts discussing economics, personal beliefs, or subjective assessments where the value is not shared publicly.
Example: "In negotiations, each party may have a private value for the deal that influences their decision-making."
Alternatives: "a personal value" or "an individual value".
Exact(11)
Let's consider a private value auction.
Is that a common value or a private value?
This paper studies optimal auction design in a private value setting with endogenous information gathering.
So there's nothing subtle about bidding on eBay if it's truly a private value auction.
It's a consumption good, my living in it, that's a private value.
So in the case of a home, it's somewhere between a private value and a common value.
Similar(49)
A private-value asset offers unique value to different bidders.
In contrast, bidders' estimates of the worth of a private-value asset can be quite different.
Yammer was a private-value asset, as it offered a unique opportunity for Microsoft to break into a new technology.
Before entering an auction for an asset, evaluate whether it is a private-value asset or a common-value asset.
In such situations, bidders should consider whether a private-value or common-value asset is at stake.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com