How do you define your ICP attributes when serving multiple markets, segments, varying levels of price sensitivity where typically the buyer profile is the same?

You want your ICP to give you a good sense for all of the above. Its hard to give you specifics, because this will vary by org. 

We defined our ICP per product (we have 8 products in our B2B portfolio), pulled sales data for the past 365 days, and did an in-depth analysis on that to define a few things such as:

• Top segments we win in (and trends over time) for each product (SMB, Mid-market, Enterprise)
• Top industries or verticals where we have been closing the most deals, with the highest AOV (per product)
• Top geographies (with the most deals closed or highest AOV) (Per product)
• Top personas/roles/seniority of buyer types purchasing each product

Once you have your complete list of attributes, you want to cut this data in different ways to see where you see some trends and patterns that tell you a good story about who your ideal customer is, and how they buy. I also like to do repeat this process over the course of time to see how things are shifting;

This is a tough one. Each market will need to have a tailored approach but don't make it more complicated than it needs to be.

At PayFit, we have similar pricing and packaging structure across all our countries, but the actual numbers will differ based on local dynamics. We also include some service add-ons specific to each market when needed. However, the overall target market (SMB) and product (payroll + talent management) will be the same. 

It's also easier for monitoring business performance. If you have too many different pricing plans across countries, it will be a hassle to understand your data.

Focus on a specific type of audience with similar problems, create the offering to meet their needs, adjust pricing for the local market, and keep the packaging structure as close as possible.

Even when you may be servinf different markets or segment with the same type of buyer. The needs of these segments are going to vary. 

A VP of Ecommerce at a D2C 200 person startup is solving for inherently different needs than a VP of Ecommerce at Nike. 

The D2C startup has a smaller budget and many SMB/Mid-market competitors to choose from. The MNC can pay a lot more and its likely that it is considering only a handful of vendors to solve its problem.

The startup requires agility, perhaps an ability to self-serve the product, more simplicity and good support. The big MNC may need reliability at scale, more dedicated professional services and enhanced governance features. 

In fact only the title of your buyer is the same, everything else varies in the ICP for these two segments, i.e. company size, consumer base, volume of annual orders sold, etc. 

I would argue that, if you think the "buyer profile is the same" when there are so many important differences, that you need to refine (or redefine) what the buyer profile actually is. Properly defining the buyer profile in and of itself should account for many of these factors. Often, answering (or partially answering) the question of what problem you solve for each stakeholder is instrumental in developing that profile because you'll discover certain patterns that help in doing so.