Let’s first state our assumptions:

• Very thin membrane, the balloon skin cannot be compressed more than it already is

• Zero trapped air

• Isothermal conditions, water temperature at the bottom of the ocean is the same as the top, that way we don’t need to deal with thermal expansion

• Balloon is a perfect sphere

Calculations:

1. Pressure on the balloon is densitygravitydepth ~= 1000 x 10 x 100 = 1 Mpa or 10 atmospheres

2. The bulk modulus of water is 2.2 Gpa so (change in volume)/(initial volume) = (change in pressure)/(bulk modulus) = 0.0046% decrease in volume

0.0046% decrease in volume is like a 0.015% decrease in radius

So yes the balloon does get a little bit smaller