DP1564 The Generalized War of Attrition

Author(s): Jeremy I. Bulow, Paul Klemperer
Publication Date: January 1997
Keyword(s): 'Strategic Independence', 'Twoness', Auctions, Natural Monopoly, Oligopoly, Political Decision Making, Standards, War of Attrition
JEL(s): D43, D44, L13, O30
Programme Areas: Industrial Organization
Link to this Page: www.cepr.org/active/publications/discussion_papers/dp.php?dpno=1564

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.