also governs the specification of the individual effort weights (α1P , . . . , αnP ). With
respect to the ethical perception of the difference in cost functions, there are two
potential interpretations for the source of this heterogeneity.
The first interpretation holds the contestants ethically responsible for their respective
cost function in which case the probability to win the contest game (i.e. the CSF)
should only depend on the vector of exerted effort. In other words, if a contestant i
exerts the same effort level as a contestant j then both contestants should win the
contest game with the same probability. This policy option would therefore treat the
contestants equally with respect to their exerted effort level.
Definition 1 A policy is called equal treatment approach (ET) if:
ei = ej ⇒ pi (e) = pj (e) for all i = j.
For the class of contest games as defined by the CSF in eq. (2) equal treatment implies
that the policy weights (α1ET , . . . , αnET ) must be identical for all players:
αiET = αET for all i ∈ N.
The last line is derived by observing that for all ei = ej it has to be the case that
pi(e) = pj (e). Solving this expression according to eq. (2) for all possible values of
ei = ej yields the above specification for the weight αiET for all i ∈ N .
This policy could also be interpreted as an anonymity principle because it postu-
lates that the contest success function neither depends on the specific names nor on
the exogenous characteristics of the players.10 However, the outcome, i.e. expected
equilibrium utility, of the contest game will indirectly depend on the characteristics of
the players because weaker players will exert less effort in equilibrium.
The second interpretation is based on the perception that the contestants cannot be
held ethically responsible for their heterogeneity, for instance, if it is the consequence
of past discrimination. As heterogeneity affects the cost function for each contestant,
fairness would require that two contestants that face equal disutility induced by the
chosen effort level (that could be different) should have the same probability to win
the contest game. The normative justification for this interpretation is the “moral
10In Skaperdas (1996), theorem 2, this CSF (specified by eq. (2) and the relevant ET weights) is
axiomatized based on a conventional anonymity axiom, comp. footnote 12.