Markets for Influence

Proposition 1 A standard Tullock contest characterised by the payoff function
given in (1) is strategically equivalent to a Cournot oligopoly game with demand
function p = -^-— and cost function Ci (qf) = q? .

Σ ¾

J=I

2.1 Imperfectly competitive markets as contests

The interpretation of contests as taking places in markets, which is afforded
by the proposition above, may be turned around. Participants in oligopolistic
markets may be considered as taking part in a contest for market share. In the
case where the elasticity of demand is unitary, this interpretation is represented
by the isomorphism given above. More generally, oligopolistic markets may be
considered as analogous to contests where the strategic choices of the players
determine both the value of the prize (total revenue) and the probability of
winning (market share).

One important implication of this literature, which has received only lim-
ited attention in the industrial organization literature, is that, in determining
the rent accruing to participants, the cost function is just as important as the
choice of strategic variable. Depending on the cost function, any outcome in
the range from perfect competition to joint monopoly pricing may be sustained
as a Cournot equilibrium.

3 Tullock Contests as Markets for Influence

The results derived above suggest that individual behavior in Tullock contests
may usefully be related to the behavior of firms in imperfectly competitive mar-
kets. To pursue this idea further, it seems natural to consider more carefully the
idea, familiar from public-choice theoretic discussions of political processes, that
contests represent a particular kind of market, namely a market for influence.
If this analogy is taken seriously, the participants in contests may be regarded
as buyers in oligopsonistic markets. To formalize the idea, we need to define
concepts analogous to prices, quantities, and supply schedules.

To address this task, we introduce the idea of a price of influence which is
given by the inverse demand function

p(θ₁,θ₂,...,θ_n) = ∑ θi
i

where θ_i is the influence acquired by player i and p is the unit price of influence.
In the electoral case, for example, we might adopt the interpretation that p is
the price paid by the candidates for each vote and θi the total number of voters
induced to vote for candidate i. Accordingly, the expenditure for player i is

ɛi = pθi, i = 1, 2...n.

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