Any groups I have been in ask that shares are sold through the group - ie. The Treasurer. It seems to work in a gentlemanly manner - although depending where you are it can take a while to sell shares in the current GA climate.
Anyway - the price is generally decided by the group based on 'market value' ... and not necessarily just sold off to the lowest bidder - after all an individual caves in to a ridiculously low offer just because they need the money quickly it forces down the value of everyone elses share.
Work out the value of the aircraft, deduct any loans (to other group members) or outstanding debt to other parties, amount stashed away for an engine fund or in the bank - and then divide by the number of owners. At last that will give you a feel for the 'right' price.
Nothing to stop seller finding prospective buyers though.
In other circimstances the group might consider buying someone out