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

Hotelling Tax Competition

This paper shows how competition among governments for mobile firms can bring about excessive differentiation in levels of taxation and public good provision. Hotelling’s Principle of Minimum Differentiation is applied in the context of tax competition and shown to be invalid. Instead, when an equilibrium exists, differentiation of public good provision is maximized. Non-existence of equilibrium, which is possible, is a metaphor for intense tax competition. The paper also shows that, to some extent, perfect tax discrimination presents a solution to the existence problem created by Hotelling tax competition, but that the efficiency problem of Hotelling tax competition is exacerbated.hotelling, limit tax, perfect tax discrimination, tax competion

ADVANCES IN THE THEORY OF LARGE COOPERATIVE GAMES AND APPLICATIONS TO CLUB THEORY : THE SIDE PAYMENTS CASE

In a series of papers (Kovalenkov and Wooders 2001a, Games and Economic Behavior, 2001b,Mathematics of Operations Research, and 1997, Journal of Economic Theory to appear), the authors have developed the framework of parameterized collections of games and also that of parameterized collections of economies with clubs. These papers apply to collections of games with nontransferable utility and similarly to economies with clubs and general preferences. The game theoretic framework encompasses the earlier `pregame' framework (cf., Wooders 1994b Econometrica) and also earlier models of economies with clubs and with possibly multiple memberships in clubs (cf. Shubik and Wooders 1982). In this paper, we consider the special case of games with side payments and illustrate the application of our more general results in this special, and much simpler but still important, framework. The motivation for this line of research is developed and application to environmental problems is discussed.cooperative games ; clubs ; core ; approximate cores ; widespread externalities ; multiple memberships ; local public goods

SOCIAL CONFORMITY AND BOUNDED RATIONALITY IN ARBITRARY GAMES WITH INCOMPLETE INFORMATION : SOME FIRST RESULTS

It has been frequently observed, in both economics and psychology, that individuals tend to conform to the choices of other individuals with whom they identify. Can such conformity be consistent with self interested behaviour? To address this question we use the framework of games with incomplete information. For a given game we first put a lower bound on * so that there exists a Nash *-equilibrium in pure strategies consistent with conformity. We also introduce a new concept of conformity that allows players to conform and yet perform different actions. This is achieved by the endogeneous assignment of roles to players and by allowing actions to be conditional on roles. We conclude by relating our research to some experimental literature.

Social Conformity and Bounded Rationality in Arbitrary Games with Incomplete Information: Some First Results

In has been frequently observed, in both economics and psychology, that individuals tend to conform to the choices of other individuals with whom thy identify. Can such conformity be consistent with self-interested behaviour? To address this question we use the framework of games with incomplete information. For a given game we first put a lower bound on e so that there exists a Nash e-equilibrium in pure strategies consistent with conformity. We also introduce a new concept of conformity that allows players to conform and yet perform different actions. This is achieved by the endogenous assignment of roles to players and by allowing actions to be conditional on roles. We conclude by relating our research to some experimental literature.Social Conformity, Bounded Rationality, Arbitrary Games

On Equilibrium in Pure Stategies in Games with Many Players

We introduce a framework of noncooperative games, allowing both countable sets of pure strategies and player types, in which players are characterized by their attributes and demonstrate that for all games with sufficiently many players, every mixed strategy Nash equilibrium can be used to construct a Nash "-equilibrium in pure strategies that is ‘"-equivalent’. Our framework introduces and exploits a distinction between crowding attributes of players (their external effects on others) and their taste attributes (their payoff functions). The set of crowding attributes is assumed to be compact; this is not required, however, for taste attributes. For the special case of at most a finite number of crowding attributes, we obtain analogs, for finite games, of purification results due to Pascoa (1993a,b,1998) for games with a continuum of players. Our main theorems are based on a new mathematical result, in the spirit of the Shapley-Folkman Theorem but applicable to a countable (not necessarily finite dimensional) strategy space.

An explicit bound on " for nonemptiness of "-cores of games

We consider parameterized collections of games without side payments and determine a bound on E so that all suffciently large games in the collection have non-empty E-cores. Our result makes explicit the relationship between the required size of E for non-emptiness of the E-core, the parameters describing the collection of games, and the size of the total player set. Given the parameters describing the collection, the larger the game, the smaller the E that can bechosen