I was thinking about the following scenario on my way home today.
Paul and Mary are returning from a vacation abroad. Upon arriving back in the United States, they realize that the airline has damaged the antiques that they purchased on their trip. The airline is more than happy to compensate them for their loss but doesn’t have any sense of how much the objects are worth. They don’t want to ask Paul and Mary to set the price because they’d be prone to inflating it. So, instead they devise a scheme in which both Paul and Mary must choose a dollar amount between $2 and $100. If they both write the same amount then that will be the price they will each receive. However, if they write different amounts then they will each be given the smaller amount. But the person who wrote the smaller amount will get a reward of $2 while the person who wrote the larger amount will get a $2 penalty. For instance, if Paul chooses $30 and Mary chooses $36, Paul will get $32 and Mary will get $28.
What amount would you choose?