Hmm, if Dan or Bethany happen to be reading this, why split the surplus proportional to the bids when making a joint purchase rather than split it equally? An equal split seems fairer at first glance, and that mechanism definitely hits the Myerson-Satterthewaite bound in equilibrium if both people act non-cooperatively. The proportional split mechanism is messy enough I can’t see the equilibrium immediately, so I’m curious if there is some advantage to it I’m not seeing.
Great question, and upon reflection (I actually looked this up in my PhD dissertation just now!) I agree. I actually can’t remember the last time Bethany and I used a joint purchase auction. For some reason it never comes up—we just each buy things and don’t worry about joint ownership. If we did disagree about whether to buy a household item we’d probably just straight up yootle for whether to buy it (with the cost split 50⁄50 if we did).
Hmm, if Dan or Bethany happen to be reading this, why split the surplus proportional to the bids when making a joint purchase rather than split it equally? An equal split seems fairer at first glance, and that mechanism definitely hits the Myerson-Satterthewaite bound in equilibrium if both people act non-cooperatively. The proportional split mechanism is messy enough I can’t see the equilibrium immediately, so I’m curious if there is some advantage to it I’m not seeing.
Great question, and upon reflection (I actually looked this up in my PhD dissertation just now!) I agree. I actually can’t remember the last time Bethany and I used a joint purchase auction. For some reason it never comes up—we just each buy things and don’t worry about joint ownership. If we did disagree about whether to buy a household item we’d probably just straight up yootle for whether to buy it (with the cost split 50⁄50 if we did).
If this is something that can be looked up in your PhD dissertation, where can I get a copy?
Edit: here (pdf)