It varies based on the channel in question. Our normal behaviour is the highest minstay for the full stay will be used, although not all channels support it like this. 

For Booking.com, we set the MinLos as a function of the length of stay must comply with the minimum stay of each days within the stay (as if it were a separate stay).

Here is the full documentation from Booking.com on this subject:

The 'minimumstay' element functions as a restriction and defines the minimum stay (through) for the given room for the given date for the given rate category. If a booking takes place on this day a minimum stay (for the whole booking) of this amount of days is required. Each day in a stay has a room and rate category ID associated with it. Each set of consecutive days with the same rate category ID in a stay, must comply with the minimum stay setting of each of those days in that set (as if it were a separate stay). Please note this minimum stay restrictions has an effect on any given day of a booking.

Here is the full documentation from Expedia on this subject:

Expedia supports two different methods to apply minimum and maximum length of stay restrictions. Arrival-based restrictions: Minimum and maximum length of a hotel stay which the system calculates by reading the LOS configured for the requested arrival date. Stay-through based restrictions: Minimum and maximum length of a hotel stay which the system calculates by reading all days of the requested stay and applying the most restrictive values from any of those days. This is a hotel-level setting in Expedia system, and any Expedia market managers can modify this setting. If you are not sure which setting applies to your hotel, please contact your account manager / expedia support team; you can use the following emails:

• eqcss@expedia.com for new activations
• hothelp@expedia.com for existing connections