The name is absent

II.- THE MODEL

In this Section we will explain the main concepts which will be used in
the rest of the paper.

Definition 1.- A market game (U ( ), S ) consist of
----------------------- ɪ         i i∈I

a) A set of players (also called agents) I = 1, 2, ..., n.

b) A collection of strategy sets S =R.
i +

c) A collection of payoff functions U : X S ----> R of the form

i i ∈I i

Ufx., x) where x ∈ S. and x = ∑ x.∙

In words, in a market game, the so-called "Aggregation Axiom" holds (see
Dubey, Mas-Colell and Shubik (1980), p. 346), so the (one dimensional)
strategies of the players can be aggregated in an additive way. We remark that
all the Propositions below can be proved if x = f(x ,..., x ) (f( ) strictly
1         n

increasing) introducing suitable concavity assumptions. A market game can be
thought of as a generalization of the well-known Cournot model. In this case
U = p(x)x - C (x ), x being the output of firm i, x total output, p(x) the
i   Iiii

inverse demand function and C (x ) the cost function of firm i. This case will
i i

be used in most examples below. We remark that our approach can deal with a)
payoff functions different from profit (i.e. Welfare-maximizing publicly owned
firms, see Fershtman (1990)), b) symmetric uncertainty (for the Cournot case
see Horowitz (1987)), c) taxes (for the Cournot case see Dierickx, Matutes and
Neven (1988)) and d) in some cases, heterogeneous product (using the trick of
Yarrow (1985), p. 517). Other examples of market games (technological

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