Contests with multiple rounds

This paper studies contests where players have the ßexibility to add to their previous efforts after observing their rivals’ most recent effort in an intermediate stage. It is found that (1) contrary to previous Þndings, the Stackelberg outcome where the underdog leads and the favorite follows cannot be an equilibrium. (2) There are multiple subgame perfect equilibria all occuring on the underdog’s usual one-shot reaction function in-between and including the oneshot Cournot-Nash and Stackelberg outcome with the favorite leading. (3) The total equilibrium effort is typically greater than or equal to what a one-shot Cournot-Nash play would predict; and (4) in settings where players can choose whether or not to disclose their early actions to the rival, both the favorite and the underdog disclose in equilibrium. Applications in sports, lobbying, and R&D races are discussed. JEL ClassiÞcation: C72;D72