**Author**: Holtz
Wooders, Myrna**Title**: On Large Games and Competitive Markets 2: Applications**Abstract**: I discuss the consequences of "On Large Games and Competetive
Markets 1: Theory" for economies with collective goods and for
properties of markets in large economies, where the goods to be
marketed are endogenously determined and prices may be hedonic.
For economies with collective goods the main results are: Large
economies with excludable collective goods satisfying effectiveness
of small groups are competetive. When there are sufficiently strong
benefits to increasing group size, so that the group of the whole is
an optimal sharing group, but still effectiveness of small groups
holds, then the Lindahl equilibrium is competetive; the core converges
to the Lindahl payoffs. When more than one group optimally forms for
the purpose of joint consumption by the group members, Lindahl pricing
within groups and Walrasian pricing for agent types is competetive.
In a more general environment, I consider large economies satisfying
the substitution and effectiveness of small groups properties and where the
payoffs to groups depend on the characteristics or attributes of the
members of the groups. An attribute is a point in a finite-dimensional
space. It is assumed that the payoffs to groups are independent of the
economy in which the group is embedded and exclusion from groups is
possible, justifying the assumption of superadditivity of the games
derived from the economies. Asymptotically, the economies are game-
theoretically equivalent to market exchange economies where agents have
continuous, concave, and 1-homogeneous utility functions on attributes.
Even though in the original economy utilities are not necessarily
monotonic non-decreasing in attributes, the "limiting" utility function
on attributes has this property. This follows from the exclusion and
superadditivity properties and holds even though in small economies the
economic structure may be quite distinct from an exchange economy.
Since this work is intended, at this time, primarily to illustrade
applications of "On Large Games and Competetive Markets 1: Theory", I
have concentrated on discussion rather than proofs and omitted some
proofs which follow from previous results in the literature. Moreover,
I have exposited some previous research to illustrade further properties
of economies with collective goods. As the reader will observe, the
paper has not been edited for terseness - at this time my aim is to
collect ideas and results. I note that both Sections 2 and 3 can be read
separately from each other.
Further results and applications will appear in "On large Games and
Competetive Markets 3: Further Results and Applications". In that
paper, the relationship between effectiveness of small groups and
Ostroy's no-surplus condition is established; boundedness of essential
group sizes implies that games with "enough" players of each type
typically have a no-surplus property (altough feasible no-surplus
payoffs may not exist) and large games satisfying effectiveness of
small groups typically have approximate no-surplus payoffs. Also, when
effectiveness of small groups is satisfied, approximate core payoffs
satisfy a monotonicity property.**Keywords**:
**JEL-Classification-Number**:**Creation-Date**: November 1991

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