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The generalized Stackelberg equilibrium of the all-pay auction with complete information


We characterize the equilibrium of the all-pay auction with general convex cost of effort and sequential effort choices. We consider a set of n players who are arbitrarily partitioned into a group of players who choose their efforts ‘early’ and a group of players who choose ‘late’. Only the player with the lowest cost of effort has a positive payoff in any equilibrium. This payoff depends on his own timing vis-a-vis the timing of others. We also show that the choice of timing can be endogenized, in which case the strongest player typically chooses ‘late’, whereas all other players are indifferent with respect to their choice of timing. In the most prominent equilibrium the player with the lowest cost of effort wins the auction at zero aggregate cost.

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Corresponding author

Correspondence to Kai A. Konrad.

Additional information

We thank Dan Kovenock and Luis C. Corchón for discussion and helpful comments. The usual caveat applies. Wolfgang Leininger likes to express his gratitude to Wissenschaftszentrum Berlin (WZB) for its generous hospitality and financial support.

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Konrad, K.A., Leininger, W. The generalized Stackelberg equilibrium of the all-pay auction with complete information. Rev. Econ. Design 11, 165–174 (2007).

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  • Sequential all-pay auction
  • Complete information
  • Generalized cost
  • Generalized Stackelberg game

JEL Classification

  • D72
  • D74