What is Japan "grey market", may I ask?
I just bought a brand new, full price WM1AM2 from a (seemingly) reputable, many units sold Japanese seller on eBay. That's not what's considered grey market, right?
Assuming you are not in Japan, that would be grey market. Companies have authorized distributors for each country, and all products are supposed to go through them.
If you buy a product outside of regular channels, i.e. you import a Japanese Walkman to the US, then that is grey market, as you have bypassed the authorized distribution channels.
- Warranty is usually with the country that the product was distributed to. A Japan Walkman would have warranty in Japan, and grey market shops may take it and ship it back to Japan for the warranty, and then ship it back. They may charge for this, or may do it no charge, as a big grey market operation would be shipping stock back and forth regularly anyways.
- or the grey market shops would have their own repair shop. They will usually charge for parts.
- If the product has International warranty, then you could get local warranty. Some PCs may have this. DAPs, probably unlikely
EDIT: The other situation is that there is no warranty at all, or a very limited warranty to cover failure within a few days/weeks
In general, a grey market purchase is attractive if there is a substantial cost savings, or the product is only available grey market, or there is something you want from the grey market product. i.e. The Sony WM1xm2 from Japan has a different sound than the product released for other countries. This is probably true, as the original WM1x had different sounds for different Region Codes that were set in the firmware. This was a subtle sound difference, but it did exist.