Myrna Holtz Wooders

Group formation in economics : networks, clubs, and coalitions

Broad and diverse ranges of activities are conducted within and by organized groups of individuals, including political, economic and social activities. These activities have become a subject of intense interest in economics and game theory. Some of the topics investigated in this collection are models of networks of power and privilege, trade networks, co-authorship networks, buyer–seller networks with differentiated products, and networks of medical innovation and the adaptation of new information. Other topics are social norms on punctuality, clubs and the provision of club goods and public goods, research and development and collusive alliances among corporations, and international alliances and trading agreements. While relatively recent, the literature on game theoretic studies of group formation in economics is already vast. This volume provides an introduction to this important literature on game-theoretic treatments of situations with networks, clubs, and coalitions, including some applications.

Networks and farsighted stability

Networks and Farsighted Stability By Frank H. Page, Jr. Department of Finance University of Alabama Tuscaloosa, AL 35487 USA fpage@cba.ua.edu Myrna H. Wooders Department of Economics University of Warwick Coventry CV4 7AL UK M.Wooders@warwick.ac.uk Samir Kamat Portfolio Management Group Wachovia Corporation Atlanta, GA 30303 USA samir.kamat2@wachovia.com The main contribution of this paper is to provide a framework in which the notion of farsighted stability for games, introduced by Chwe (1994), can be applied to directed networks. In particular, we introduce the notion of a supernetwork. A supernetwork is made up of a collection of directed networks (the nodes) and uniquely represents (via the arcs connecting the nodes) agent preferences and the rules governing network formation. By reformulating Chwes basic result on the nonemptiness of farsightedly stable sets, we show that for any supernetwork (i.e., for any collection of directed networks and any collection of rules governing network formation), there exists a farsightedly stable directed network. We also introduce the notion of a Nash network relative to a given supernetwork, as well as the notions of symmetric, nonsimultaneous, and decomposable supernetworks. To illustrate the utility of our framework, we present several examples of supernetworks, compute the farsightedly stable networks, and the Nash networks. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

THE EPSILON CORE OF A LARGE REPLICA GAME

Abstract Sufficient conditions are given for large replica games without side payments to have non-empty approximate cores for all sufficiently large replications. No ‘balancedness’ assumptions are required. The conditions are superadditivity, a boundedness condition, and convexity of the payoff sets.

The core of a game with a continuum of players and finite coalitions: The model and some results

Abstract In this paper we develop a new model of a cooperative game with a continuum of players. In our model, only finite coalitions - ones containing only finite numbers of players - are permitted to form. Outcomes of cooperative behavior are attainable by partitions of the players into finite coalitions: this is appropriate in view of our restrictions on coalition formation. Once feasible outcomes are properly defined, the core concept is standard - no permissible coalition can improve upon its outcome. We provide a sufficient condition for the nonemptiness of the core in the case where the players can be divided into a finite number of types. This result is applied to a market game and the nonemptiness of the core of the market game is stated under considerably weak conditions (but with finite types). In addition, it is illustrated that the framework applies to assignment games with a continuum of players.

Competitive equilibrium and the core in club economies with anonymous crowding

In club economies with anonymous crowding, competitive equilibrium states of the economy are efficient and coincide with the core when there is only one private good. Anonymous admission prices permit consumers with different tastes to share facilities. Consumers might do so when their demands for facility size and crowding coincide, in which case sharing is efficient. Thus, similarity of demands is the relevant consideration for efficiently grouping consumers with different tastes.

Strategic Basins of Attraction, the Path Dominance Core, and Network Formation Games

Given the preferences of players and the rules governing network formation, what networks are likely to emerge and persist? And how do individuals and coalitions evaluate possible consequences of their actions in forming networks? To address these questions we introduce a model of network formation whose primitives consist of a feasible set of networks, player preferences, the rules of network formation, and a dominance relation on feasible networks. The rules of network formation may range from non-cooperative, where players may only act unilaterally, to cooperative, where coalitions of players may act in concert. The dominance relation over feasible networks incorporates not only player preferences and the rules of network formation but also assumptions concerning the degree of farsightedness of players. A specification of the primitives induces an abstract game consisting of (i) a feasible set of networks, and (ii) a path dominance relation defined on the feasible set of networks. Using this induced game we characterize sets of network outcomes that are likely to emerge and persist. Finally, we apply our approach and results to characterize the equilibrium of well known models and their rules of network formation, such as those of Jackson and Wolinsky (1996) and Jackson and van den Nouweland (2005).

A Tiebout theorem

Abstract Tiebout (1956) has conjectured that when public goods are local rather than pure, competitive forces tend to make local governments provide the public goods in a near-optimal manner. He hypothesized that ‘the greater the number of communities and the greater the variety among them, the closer the consumer will come to fully realizing his preference position’. In this paper, a model with potential ‘entry’ of jurisdictions is considered. In equilibrium, no firm could enter, form a new jurisdiction, and charging possibly discriminatory admittance fees, earn a positive profit. A Tiebout-type entry equilibrium with lump-sum taxes is shown to exist for all sufficiently large economies. An equilibrium jurisdiction structure and the associated lump-sum taxes are constrained only by the property that entry is unprofitable. The equilibrium is of the type suggested by Tiebout in that equilibrium states of the economy are approximately optimal and, the larger the economy and the smaller the costs of forming a jurisdiction, the closer an equilibrium is to an optimum. To characterize the Tiebout equilibrium, we develop another specific equilibrium concept, called a competitive equilibrium. In this equilibrium, agents pay Lindahl prices for the local public goods, and receive payments (possibly negative) for their effects on the production and/or consumption possibilities of the other agents. The competitive equilibrium states of the economy are Pareto-optimal. It is shown that the Tiebout equilibrium states of the economy converge to the competitive states as the economy grows large and jurisdiction formation costs, small.

Continuum economies with finite coalitions: Core, equilibria, and widespread externalities

Abstract We develop a new model of a continuum economy with coalitions consisting of only finite numbers of agents. The core, called the f -core, is the set of allocations that are stable against improvement by finite coalitions and feasible by trade within finite coalitions. Even with widespread externalities—preferences depend on own consumptions and also on the entire allocation up to the null set—we obtain the result that the f -core coincides with the Walrasian allocations. Without widespread externalities, the f -core, the Aumann core, and the Walrasian allocations all coincide; however, with widespread externalities there is no obvious natural definition of the Aumann core.

Equivalence of Games and Markets

The author proves an equivalence between large games with effective small groups of players and games generated by markets. Small groups are effective if all or almost all gains to collective activities can be achieved by groups bounded in size of membership. A market is an exchange economy where all participants have concave, quasi-linear payoff functions. The market approximating a game is socially homogeneous--all participants have the same monotonic nondecreasing, and 1-homogeneous payoff function. The authors results imply that any market (more generally, any economy with effective small groups) can be approximated by a socially homogeneous market. Copyright 1994 by The Econometric Society.

Tiebout Economies with Differential Genetic Types and Endogenously Chosen Crowding Characteristics

Abstract We consider a Tiebout economy with differential crowding and public projects in which agents are distinguished by their tastes and genetic endowments. Agents choose which crowding characteristic, for example, a skill, they wish to express, and this affects their value to other members of their jurisdiction, club, firm, etc. An agents choice is influenced both by his genetic endowment, which affects his cost of acquiring crowding characteristics, and by his preferences over which crowding characteristic he expresses. We show that if small groups are strictly effective, the core is equivalent to the set of anonymous competitive equilibrium outcomes, but that the core generally contains taste-homogeneous jurisdictions. Journal of Economic Literature Classification Numbers: H41, H72.