The name is absent

without loss of generality we will write the first order condition as a

function of a single t, i.e. T (x , x, t) = 0.
i i

Intuition suggests that in the case of an idiosyncratic shock an increase
in t will increase the strategy of player i and it will decrease those of its
i

competitors. This intuition is formalized in the next Proposition:

Proposition 4: Under A. 1, A. 2 and A. 4 an increase in t., a) increases the
sum of strategies b) increases the strategy of player i and c) decreases the
strategy of any other player in the market.

Proof: Since the proof is fairly analogous to the proof of Proposition 1 we
will indicate only the guidelines. First it is proven that the sum of
strategies can not be constant. Second, if the sum of strategies decreases,
the strategy of all players must increase in order to maintain first order
conditions and this is a contradiction. Thus, the sum of strategies increases.
Again first order conditions of all players except i imply that the strategy
of these players must fall. Therefore the strategy of i must increase л

Of course if the inequality in A. 4 is reversed so are the conclusions of
Proposition 4. An implication of this Proposition is -in contrast with
Supermodular games- the absence of multiplier effects i.e. dx∕dt_j < dx.∕dt.
(see Fudenberg and Tirole (1991) p. 498). The next example -which again refers
to the Cournot model- will show that A. 2 is needed for the result to hold.

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