The Generalized War of Attrition
We generalize the War of Attrition model to allow for N + K ﬁrms competing for N prizes. Two special cases are of particular interest. First, if ﬁrms continue to pay their full costs after dropping out (as in a standard-setting context), each ﬁrm’s exit time is independent both of K and of the actions of other players. Second, in the limit in which ﬁrms pay no costs after dropping out (as in a natural-oligopoly problem), the ﬁeld is immediately reduced to N + 1 ﬁrms. Furthermore, we have perfect sorting, so it is always the K -1 lowest-value players who drop out in zero time, even though each player’s value is private information to the player. We apply our model to politics, explaining the length of time it takes to collect a winning coalition to pass a bill
Bulow, Jeremy I. and Klemperer, Paul D., "The Generalized War of Attrition" (1996). Cowles Foundation Discussion Papers. 1390.