The War of Attrition
Two parties involved in a costly dispute
E.g. two animals fighting over prey
Each animal chooses time at which it intends to give up
Once an animal has given up, the other obtains all the prey
If both animals give up at the same time then they split the prey equally.
Fighting is costly: each animal prefers as short a fight as possible.
Also a model of bargaining between humans.
Let time be a continuous variable that starts at 0 and runs indefinitely.
Assume value to party i of object in dispute is vi > 0; value of
half of object is vi/2.
Each unit of time that passes before one of parties concedes costs each party one unit of payoff.