A non-zero-zum War of Attrition

The division of a cake by two players is modelled by means of a game of timing in which the players have a probability of learning when their opponent acts. It is shown that the game has a unique Nash equilibrium when both players are non-noisy but that there are many Nash equilibria including pure ones when at least one of the players is noisy. Explicit expressions for the strategies used in these Nash equilibria are obtained.This work was carried out while Dr. Garnaev was visiting the University of Southampton on a Postdoctoral Fellowship of The Royal Society of London.