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

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.

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).basins of attraction, network formation games, stable sets, path dominance core, Nash networks

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

On the theory of equalizing differences Increasing abundances of types of workers may increase their earnings

The theory of equalising differences recognises that wage differentials may be required to equalise the attractiveness of alternative occupations. We examine this theory using the Conley/Wooders 'crowding types'' model. The crowding types model distinguishes between the tastes of a player and his crowding type, those attributes of the player that directly effect the well-being of other players in the same club - a player''s skill, productivity or personality are examples. A club can be interpreted as firm in which the job attributes are the club goods thus, the crowding types model, with its distinction between tastes and crowding types, provides a natural environment in which to study equalising differences. In contrast to results for earlier models, we demonstrate that even when small groups of players are strictly effective in a strong sense, an increase in the abundance of players of one crowding type can increase the core payoffs to players of that crowding type.cooperative game theory

Relaxing Tax Competition through Public Good Differentation

This paper argues that, because governments are able to relax tax competition through public good differentiation, traditionally high-tax countries have continued to set taxes at a relatively high rate even as markets have become more integrated. The key assumption is that firms vary in the extent to which public good provision reduces costs. We show that Leviathan governments are able to use this fact to relax the forces of tax competition, reducing efficiency. When firms can ‘vote with their feet’ tax competition leads firms to locate in ‘too many’ jurisdictions. A ‘minimum tax’ further relaxes tax competition, further reducing efficiency.asymmetric equilibrium ; core-periphery ; non-renegotiable minimum tax ; tax competition ; tax harmonization

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