The name is absent

hold is that U ( ) be strictly concave
i

on X and x and(if U ∈ 6^,2) that
1                      i

In the homogeneous oligopoly case A. 2 is equivalent to a much used
condition in the literature on Cournot equilibrium (see e.g. Friedman (1982)
p. 496, assumption 3 and the references therein) namely

7                                                                  7

ð p( )             ðp( )                   ðp( )           ð C. ( )

---------- X. + --------- < O and --------- - ------------ < O
∂χ² ɪ дх                5x           ∂χ²

Î

It can be readily seen that A. 2 implies that the best reply function is
decreasing, i.e. the assumption of Strategic Substitutes in terminology of
Bulow, Geanakoplos and Klemperer (1985). Finally, we state our third
assumption.

Assumption 3: U ( ) is strictly decreasing on x VieI.
-------------------------------------- i

This assumption will be only used in Propositions 2, 3 and 5. If U ( )

1
were strictly increasing in x, the reverse conclusions would be true. In the
Cournot case A.3 requires a strictly decreasing inverse demand curve.

Notice that A.l and 2 plus a compactness requirement imply the existence
of an unique N.E. and that under A.l and 3 any interior N.E. can be shown to
be inefficient, i.e. there is a strategy vector for which all players are
better off (for proofs of these facts see Friedman (1977) pp. 25-6 and 169-71.
See Kukushkin (1993) for a more general result on the existence of a N.E. ).

13

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