Hail of Stones Multiplayer
The rules talk about "paying costs" on page 25 and say this (emphasis added):


  Many cards are written in a “pay or exhaust X to do Y” manner. When confronted with such a construct, everything before the word “to” is considered the cost, and everything after the word “to” is considered an effect. Costs can only be payed with cards or resources that a player controls. If an effect is canceled, the cost is still considered to have been paid.


Hail of Stones' text matches the scheme described here, and therefore it doesn't seem that you can exhaust characters that other players control for this purpose.