SFB 303 Discussion Paper No. B-196

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.
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Creation-Date: November 1991
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