contestants that consists out of those m contestants with the lowest δ values that
satisfy the following inequality:
(m — 1)δP < ^ δp for all i ∈ M and for P ∈ {ET, AA} . (24)
j∈M
From the definition of the share function in Eq. (22) the equilibrium effort level
of contestant i can be calculated as e*(P) = z*∕αp = si(Z*)Z*/αP. Inserting the
expression for Z* leads to Eq. (10).31
B References
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31 Stein (2002) derives a similar expression in a rent-seeking framework where the contestants are
heterogeneous with respect to valuations instead of marginal costs.
25