1 Introduction
Consider a principal that needs to buy a good or service and has two procurement alternatives. On the one
hand, it can award an exclusive contract to the agent offering the lowest price, as in a standard Demsetz
(1968) auction. In this case, there will be intense ex ante price competition (‘competition for the field’),
but in the aftermath, the agent will always charge the maximum price allowed by the contract. The other
option is to award two independent supply contracts and rely on ex post competition (‘competition in the
field’). Then agents will consider the probabilities of different ex post duopoly games when negotiating
their contracts. If they anticipate that with high probability there will be intense price competition, they will
participate only if they obtain high profits in the rare cases in which they collude. Thus, the prospect of
intense competition in the field softens competition for the field.2 This motivates the question we address in
this paper: Should the principal contract with one or two agents?
The answer does not seem straightforward. A basic difficulty is that the appropriate specification of the
ex post duopoly game depends on particular aspects of the situation.3 Moreover, many duopoly games have
multiple equilibria and there are no a priori compelling reasons to choose one over another. Nevertheless,
in this paper we obtain a simple sufficient condition that shows unambiguously which option is better. This
condition depends only on the shapes of the surplus function of the principal and the profit function of
each agent, and is independent of the duopoly game played ex post. We then apply this condition to study
three canonical examples—procurement, royalty contracts and dealerships. We find that whenever marginal
revenue is decreasing in the quantities, a Demsetz auction is unambiguously better. Moreover, a planner
who wants to maximize social surplus also prefers a Demsetz auction.
Our point of departure is a standard setting where a principal wants the final price of the good or service
to be as low as possible, but agents prefer the monopoly price. The principal can either run a Demsetz
auction for an exclusive contract, or auction two separate contracts to different agents who then produce
perfect substitutes and compete. With a Demsetz auction, the ex post equilibrium price equals the winning
bid. By contrast, when there are two contracts, the price depends on the outcome of ex post competition.
We do not specify the second stage game, but summarize its outcome as follows: ex ante the equilibrium
price is a random variable with an arbitrary distribution F whose support is bounded above by the maximum
price allowed by the contract. In some states of nature agents will succeed in colluding and prices will be
close to the winning bid; in other states agents will compete intensely and prices will be much lower.4
We assume that the principal and the agents are risk neutral. Nevertheless, the main result of the paper
exploits the fact that a Demsetz auction eliminates variability in the equilibrium price. To get the intuition
2This terminology is due to Chadwick (1859).
3In this paper we abstract from complications due to incomplete contracting and asymmetric information.
4There are several interpretations for F . In one of them, it describes agents’ uncertainty about ex post market conditions and
potential collusive prices. In another, firms always collude at the price that maximizes joint profits, but there is a positive probability
of a successful antitrust case against them, leading to a price equal to marginal costs. Similarly, in the specific case of dealerships,
the upstream firm may try to prevent the double marginalization associated with collusion by penalizing those agreements between
franchisors that are detected.