Price Taking Equilibrium in Club Economies with Multiple Memberships and Unbounded Club Sizes

This paper develops a model of an economy with clubs where individuals may belong to multiple clubs and where there may be ever increasing returns to club size. Clubs may be large, as large as the total agent set. The main condition required is that sufficient wealth can compensate for memberships in larger and larger clubs. Notions of price taking equilibrium and the core, both with communication costs, are introduced. These notions require that there is a small cost, called a communication cost, of deviating from a given outcome. With some additional standard sorts of assumptions on preferences, we demonstrate that, given communication costs parameterized by ε > 0, for all sufficiently large economies, the core is non-empty and contains states of the economy that are in the core of the replicated economy for all replications (Edgeworth states of the economy). Moreover, for any given economy, every state of the economy that is in the core for all replications of that economy can be supported as a price-taking equilibrium with communication costs. Together these two results imply that, given the communication costs, for all sufficiently large economies there exists Edgeworth states of the economy and every Edgeworth state can be supported as a price-taking equilibrium.Competitive pricing, Clubs, Local public goods, Hedonic coalitions, Edgeworth, Tiebout hypothesis, Core

COMPETITIVE PRICING IN SOCIALLY NETWORKED ECONOMIES

In the context of a socially networked economy, this paper demonstrates an Edgeworth equivalence between the set of competitive allocations and the core. Each participant in the economy may have multiple links with other participants and the equilibrium network may be as large as the entire set of participants. A clique is a group of people who are all connected with each other. Large cliques, possibly as large as the entire population, are permitted ; this is important since we wish to include in our analysis large, world-wide organizations such as workers in multi-national firms and members of world-wide environmental organizations, for example, as well as small cliques, such as two person partnerships. A special case of our model is equivalent to a club economy where clubs may be large and individuals may belong to multiple clubs. The features of our model that cliques within a networked economy may be as large as the entire population and individuals may belong to multiple cliques thus allow us to extend the extant decentralisation literature on competitive pricing in economies with clubs and multiple memberships (where club sizes are uniformly bounded, independent of the size of the economy).social networks ; competitive pricing ; cliques ; clubs ; Edgeworth equivalence ; core

Endogenous bourse structures

Using a club theory approach, this paper provides an equilibrium model in which traders must belong to at least one bourse in order to trade assets. We show, by means of examples, that: 1) traders’ complementarities in preferences and endowments can determine the formation of both large bourses and bourses that are small dark pools of liquidity; 2) bourse formation costs explain the existence of bourses with incomplete markets. For this bourse economy equilibrium is shown to exist generically. We also analyze the welfare implications of considering instead a monopolist bourse that can or cannot exclude and distinguish among traders.Bourse structures, Traders' complementarities, Technology, Dark liquidity pools, Demutualization, Efficiency, Inter-bourse arbitrage, Monopolistic bourse, Market incompleteness

Competitive pricing in socially networked economies

In the context of a socially networked economy, this paper demon-strates an Edgeworth equivalence between the set of competitive allocations and the core. Each participant in the economy may have multiple links with other participants and the equilibrium network may be as large as the entire set of participants. A clique is a group of people who are all connected with each other. Large cliques, possibly as large as the entire population, are permitted; this is important since we wish to include in our analysis large, world-wide organizations such as workers in multi-national firms and members of world-wide environmental organizations, for example, as well as small cliques, such as two-person partnerships. A special case of our model is equivalent to a club economy where clubs may be large and individuals may belong to multiple clubs. The features of our model that cliques within a networked economy may be as large as the entire population and individuals may belong to multiple cliques thus allow us to extend the extant decentralisation literature on competitive pricing in economies with clubs and multiple memberships (where club sizes are uniformly bounded, independent of the size of the economy)

Anonymous Price Taking Equilibrium in Tiebout Economies with Unbounded Club Sizes

We introduce a model of a local public goods economy with a continuum of agents and jurisdictions with finite, but unbounded populations. Under boundedness of per capita payoffs we demonstrate nonemptiness of the core of the economy. We then demonstrate that the equal treatment core coincides with the set of price-taking equilibrium outcomes with anonymous prices - that is, prices for public goods depend only on observable characteristics of agents. Existence of equilibrium follows from nonemptiness of the core and equivalence of the core to the set of equilibrium outcomes. Our approach provides a new technique for showing existence of equilibrium in economies with a continuum of agents.Tiebout, Clubs, Jurisdictions, F-core, Core-equilibrium equivalence, Edgeworth equivalence, Continuum economies with clubs, Crowding types, Core, Equal treatment core

Endogenous bourse structures

We propose a novel approach to the market microstructure theory, where a bourse is a club that facilitates asset trading among its members. Under the new perspective of club theory, we provide an equilibrium setting where traders must belong to at least one bourse to trade assets. For this bourse economy, we show that equilibrium exists generically, and give positive predictions regarding the formation of a large unique bourse, and/or a bourse with complete markets. We also give examples that illustrate how traders’ attributes and bourse formation costs explain bourse size and composition, market incompleteness, and multiple memberships.Jaime Luque gratefully acknowledges the Spanish Ministry of Education and Science for fiinancial support under grant SEJ2008-03516. This work was partially supported by the “Fundação para a Ciência e a Tecnologia” (Portuguese Foundation for Science and Technology) through PEst-OE/MAT/UI0297/2011 (CMA).

Market games and clubs

The equivalence of markets and games concerns the relationship between two sorts of structures that appear fundamentally different -- markets and games. Shapley and Shubik (1969) demonstrates that: (1) games derived from markets with concave utility functions generate totally balanced games where the players in the game are the participants in the economy and (2) every totally balanced game generates a market with concave utility functions. A particular form of such a market is one where the commodities are the participants themselves, a labor market for example. But markets are very special structures, more so when it is required that utility functions be concave. Participants may also get utility from belonging to groups, such as marriages, or clubs, or productive coalitions. It may be that participants in an economy even derive utility (or disutility) from engaging in processes that lead to the eventual exchange of commodities. The question is when are such economic structures equivalent to markets with concave utility functions. This paper summarizes research showing that a broad class of large economies generate balanced market games. The economies include, for example, economies with clubs where individuals may have memberships in multiple clubs, with indivisibile commodities, with nonconvexities and with non-monotonicities. The main assumption are: (1) that an option open to any group of players is to break into smaller groups and realize the sum of the worths of these groups, that is, essential superadditivity is satisfied and :(2) relatively small groups of participants can realize almost all gains to coalition formation. The equivalence of games with many players and markets with many participants indicates that relationships obtained for markets with concave utility functions and many participants will also hold for diverse social and economic situations with many players. These relationships include: (a) equivalence of the core and the set of competitive outcomes; (b) the Shapley value is contained in the core or approximate cores; (c) the equal treatment property holds -- that is, both market equilibrium and the core treat similar players similarly. These results can be applied to diverse economic models to obtain the equivalence of cooperative outcomes and competitive, price taking outcomes in economies with many participants and indicate that such results hold in yet more generality.Markets; games; market games; clubs; core; market-game equivalence; Shapley value; price taking equilibrium; small group effectiveness; inessentiality of large groups; per capita boundedness; competitive equilibrium; games with side payments; balanced games; totally balanced games; local public goods, core convergence; equal treatment property; equal treatment core; approximate core; strong epsilon core; weak epsilon core; cooperative game; asymptotic negligibility

Heterogeneous Tiebout communities with private production and anonymous crowding

his paper examines, in the context of a multiple types of consumers, a set of necessary and sufficient conditions under which equilibrium and optimum exist, and involve mixing types of consumers in jurisdictions. Pricing includes visa permits for entry. Following Berglas (1976), we assume anonymous crowding and complementarities in production. For a large economy, we prove existence of equilibrium and the first and second welfare theorems. Our simultaneous optimization approach provides a new technique for showing existence of equilibrium in local public good economies with local production and a continuum of agents.Local public goods, Collaborative production, Wages, Anonymous crowding, Visa permits, Societal stratification, Heterogeneous Tiebout communities, Generalized game

Approximate Cores of Games and Economies with Clubs

This presentation focuses on new approachs to large games introduced in five papers by the authors (one with the same title as this abstract). In a new framework of parameterised collections of games with and without side payments, we provide nonemptiness of approximate core, a law of scarcity, and convergence results. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. Our nonemptiness theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. Our convergence results provide a new sort of application of standard theorems from linear programming. The results are applied to a model of an economy with clubs. In contrast to the extant literature, our approach allows widespread externalities -- that is, the payoffs to members of a club may depend on the economy in which the club is situated.

APPROXIMATE CORES OF GAMES AND ECONOMIES WITH CLUBS

We introduce the framework of parameterized collections of games with and without side payments and provide three no emptiness of approximate core theorems for games in parameterized collections. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact electiveness. The theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. The results are applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results.cooperative games ; clubs ; local public goods ; approximate cores ; effective small groups ; parameterized collections of games