We consider an asymmetric duopoly producing a homogeneous commodity and fac
ing 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 har
d currencies, maximizes its revenue. The second asymmetry involves a securi
ty (or diversification) constraint which states that the second player is n
ot allowed to sell more than a certain proportion of the quantity sold by i
ts rival. This game is an abstraction of the European natural gas market du
ring the eighties. Cournot and Stackelberg equilibria are characterized and
compared. An assessment of the impact on consumers and producers of the se
curity constraint is also made. (C) 2001 Elsevier Science B.V. All rights r
eserved.