Hi Johana,
Thanks for the post and sorry to take so long to respond (I had a bit of a computer melt down!). Anyway, in case you haven't already got this worked out, the key to working out the area of overlap between two polygons is to use the UNION tool (in the TOOLBOX window, go to ANALYSIS TOOLS> OVERLAY> UNION), but before you can do this, you need to make sure that you have some sort of identifier for each polygon (so when you run the UNION tool you know which of the polygons that are created originate from each home range polygon). You also need to calculate the area of the whole polygon for each individual. So, first open the attribute table of your first polygon data layer, and then click on the TABLE OPTIONS in the top left hand corner of the TABLE window. Select ADD FIELD and add a new field as a double with the precision of 16 and a scale of 3 (this allows it to have 16 digits, 3 of which can be after the decimal point). Make sure you name this field with a name that identifies the individual it represents (e.g. Area_1). Next, right click on the name of this new field, and select CALCULATE GEOMETRY. This will allow you to calculate the total area of the polygon.
Repeat this for the attribute table of the second polygon data layer, making sure you use a name of the new field that will identify the area as belonging to the second individual (e.g. Area_2).
Once you have done this, you are ready to use the UNION tool, Open this tool, and select your two polygon data layers as the INPUT FEATURES and then run the tool. This will create a new polygon data layer which has three types of polygon. One the the area of the combined polygons where only individual 1 is present, a second which represents only the areas where individual 2 is present, and a third which represents the areas of overlap.
You can now open the attribute table of this new data layer, and work out the size of the overlap. This is done by adding a new field called AREA_OL (for overlap), and then calculating the area of each type of polygon using the CALCULATE GEOMETRY tool. You will now have fields in the attribute table which give you the total area of each individual's minimum convex polygon, and the area of the overlap (which will be represented by the line in the attribute table which has a value for area for the field AREA_1 and the field AREA_2. Divide the value in the field AREA_OL by the value in AREA_1 and multiply by 100. This will; give you the percentage of the area of individual 1 that overlaps with the home range of individual 2. Repeat this for the fields ARTEA_OL and AREA_2, and you will get the percentage of the area of individual 2 that overlaps with the home range of individual 1.
Sorry again for taking so long to reply to your post and I hope this helps. If it doesn't or you get stuck with anything, just post a message back on this thread (and I'll hopefully get back to you sooner than this time!).
Good luck with your research.
All the best,
Colin