1 Introduction
Tullock’s (1980) seminal contribution marks the beginning of a large research
effort aimed at understanding some economic interactions, typically referred to
as contests, where agents spend resources in order to get ahead of their rivals
and win a prize. Economic interactions that have been studied in this literature
include elections, litigation, internal labour market tournaments, sales contests,
R&D races, and rent seeking.1
This note shows that the standard formulation of the Tullock rent-seeking
game, where individuals choose effort or resources to win a prize, is strategically
equivalent to a Cournot oligopoly game where the elasticity of demand is unitary
and firms choose quantity to maximise their profits. We derive the associated
isomorphism and show how alternative specifications of the success function
in the Tullock contest correspond to specifications of the cost function for
oligopolists. Conversely, oligopolistic markets may be regarded as a generalized
class of contests.
This result has an important implication; it suggests that the exclusive fo-
cus of the Tullock contest literature on effort or resources as the strategic vari-
able might be misleading. There is an obvious contrast with oligopoly models,
where both prices and quantities (Bertrand or Cournot models) were considered
as possible strategic variables even before the game theory revolution that has
dominated the field of industrial organisation over the last three decades. More
recently, a number of papers have proposed alternative strategic variables, such
as supply curves (Klemperer and Meyer, 1989) and markups (Grant and Quig-
gin, 1994). In addition, there have been numerous attempts to motivate the
choice of particular strategic variables, for example as outcomes of a multistage
game (Kreps and Scheinkman, 1983). These issues have received comparatively
less systematic attention in the contests literature.
The contests literature does examine games for which the equilibria resem-
ble Bertrand. For example, when the contest success function is discontinuous,
complete dissipation of rent (equivalent to zero profits in the oligopoly case) is
an equilibrium outcome. However, our result shows that even confining atten-
tion to the standard success function with probability proportional to relative
effort, alternative choices of the strategic variable can yield the full gamut of
equilibrium outcomes from Cournot to Bertrand.
This finding leads us to explore the relationship between contests and mar-
kets more carefully. We argue that a natural economic interpretation of contests
may be presented in terms of oligopsonistic markets for influence. The influence
variable may be interpreted as electoral support, legal expertise, connections
within labour markets and so on. As markets for influence become more com-
petitive, the implicit price of influence increases and the net rent shared by
purchasers of influence decreases. Once again, this interpretation leads to an
isomorphism with a model of imperfect competition, in this case that of firms
acting as oligopsonists in a factor market.
1For a recent survey of the literature see, for example, Konrad (2007).