The name is absent

b) Models of strategic interaction among firms like technological
competition (see Loury (1979)), the problem of the commons (see Dasgupta and
Heal (1979) pp. 55-78) and pollution games, and

c) Models focusing on internal organization of firms or the like as
contribution and revelation games and principal-many agents models.

In all the above cases uncertainty, taxes and payoff functions different
from profit functions (i.e. sales) are allowed.

We first prove that the best reply functions of a game satisfying the
aggregation axiom and the strategic substitution condition do not have any
structural property beyond that they depend on the sum of strategies of the
remaining players and that they are decreasing (Theorem 1). This result can be
used to motivate the need of our strong concavity assumption. Assuming the
latter we show that:

1) An increase in the number of players, a) decreases the value of the
strategy of any incumbent, and increases the sum of all strategies
(Proposition 1). b) Decreases the payoff of incumbents (Propositions 2-3).

2) A shift raising the marginal payoff curve of a player, say i, a)
increases the sum of strategies and the strategy of player i, and decreases
the strategy of any other player (Proposition 4). b) Increases the payoff of
player i and decreases the payoff of any other player (Proposition 5).

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