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The all-pay auction with cross-shareholdings
(Working paper; Arbeidsnotat, 2007-02)
We consider an all-pay auction between several firms under asymmetric information in which each firm owns a share in its rival. We characterize the equilibrium and show how much these cross-shareholdings serve to dampen competition. Additionally, we explain why the well known relationship between the equilibrium strategies of the standard first price and all-pay auctions breaks down in our setting.