This paper is organised as follows. Section 2 formally defines the strategic
equivalence between the two classes of games. Section 3 then discusses the
implications of such equivalence by recasting contests as markets for influence.
Section 4 concludes.
2 Tullock Contests and Cournot Competition
Our starting point is the most well-known model of contests, namely, the Tullock
rent-seeking game. This class of games can be represented by a set of n players,
who choose effort levels e1,e2,...,en in order to win a prize of fixed value V,
and a parameter R> O. The winner of the contest is the player who spends the
most effort. Player Ps payoff in this class of games is given by:
ɛ^
πi(eι,e2 ,...,en) = V —--ei. (1)
∑ef
J=ι
The equilibria for this family of games (both symmetric and asymmetric, pure
and mixed-strategy) are well-known.2
To develop the isomorphism with oligopoly games, consider now a unit elas-
ticity demand curve with normalisation such that:
V
P = ——
Σ⅞,∙
J=ι
and assume that Ps cost function is given by
player i is
C»(q»)
1
= ¾r . Thus, the revenue for
Vqi
ri = —--
∑q,∙
7
ci
Therefore, we can write Ps payoff as follows :
C X f'7
πi(cχ, c2, ..., cn) = V —----
∑V
J=ι
- ci. (2)
Thus, incentives in the oligopoly game, with Ci as the strategic variable, are
strategically equivalent to those in a standard Tullock contest with ei substituted
for Ci. That is, we have established the following result:
2See, for example, Baye, Kovenock and de Vries (1994). Importantly, Baye and Hoppe
(2003) show that this family of games is isomorphic to certain innovation and patent-race
games. It follows then that our main result also applies to these other classes of games. That
is, there are isomorphisms between oligopoly games and specific innovation and patent-race
games.