Equilibria in an Asymmetric Duopoly Facing a Security Constraint
by
Michèle Breton
H.E.C. Montréal
Coauthors: Georges Zaccour (H.E.C. Montréal)

We consider an asymmetric duopoly producing a homogeneous commodity and facing a competitive demand. Our model incorporates two asymmetries. The first one is relative to the performance indices. Indeed, we assume that one of the player maximizes its profit and the second one, being eager to earn hard currencies, maximizes its revenue. The second asymmetry involves a security (or diversification) constraint which states that the second player is not allowed to sell more than a certain proportion of the quantity sold by its rival. This game is an abstraction of the European natural gas market during the eighties. Cournot and Stackelberg equilibria are characterized and compared. An assessment of the impact on consumers and producers of the security constraint is also made.

In the general model, it is shown that both equilibria exist. In the Stackelberg case, wheteher the security constraint is active or not depends on demand elasticity. A linear-quadratic illustration is given where it is shown that in both modes of play, the proposed security constraint punishes the revenue maximizer and rewards the profit maximizer, at the expense of the consumer. Indeed, under both modes of play, there is a loss in consumer surplus with respect to absence of rationing. It is argued that the presence of a security constraint should lead naturally to a Stackelberg paradigm.

Date received: June 17, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafi-95.