On the Volunteer Dilemma I: Continuous-time Decision

It is assumed that there is a group of unrelated individuals taken at random from a large population which is exposed to the same time-continuous threat of dying. Accumulated loss of each player increases as the game goes on until at least one participant volunteers to take some extra risk on its own. The risk is taken by a volunteer in order to stop the threat may or may not depend on the time of volunteering. This situation can be modeled as an n-player War of Attrition, which ends when one of the players volunteers. We called this sort of generalization, ieThe (n-player) volunteer dilemmalr. Indeed, a two-player volunteer dilemma is equivalent to the original War of Attrition. It was further assumed that both the risk for the volunteer and the in- tensity of the risk of waiting are time dependent according to some integrable function, this instead of being con- stants as assumed in the original War of Attrition model of Maynard Smith. Necessary and sufficient conditions for a strategy to be a Nash stra...