The Edgeworth Conjecture with Small Coalitions and Approximate Equilibria in Large Economies

We revisit the connection between bargaining and equilibrium in exchange economies, and study its algorithmic implications. We consider bargaining outcomes to be allocations that cannot be blocked (i.e., profitably re-traded) by coalitions of small size and show that these allocations must be approximate Walrasian equilibria. Our results imply that deciding whether an allocation is approximately Walrasian can be done in polynomial time, even in economies for which finding an equilibrium is known to be computationally hard.Comment: 26 page

The Edgeworth Conjecture with Small Coalitions and Approximate Equilibria in Large Economies

We revisit the connection between bargaining and equilibrium in exchange economies, and study its algorithmic implications. We consider bargaining outcomes to be allocations that cannot be blocked (i.e., profitably re-traded) by coalitions of small size and show that these allocations must be approximate Walrasian equilibria. Our results imply that deciding whether an allocation is approximately Walrasian can be done in polynomial time, even in economies for which finding an equilibrium is known to be computationally hard

The Edgeworth Conjecture with Small Coalitions and Approximate Equilibria in Large Economies

We revisit the connection between bargaining and equilibrium in exchange economies, and study its algorithmic implications. We consider bargaining outcomes to be allocations that cannot be blocked (i.e., profitably re-traded) by coalitions of small size and show that these allocations must be approximate Walrasian equilibria. Our results imply that deciding whether an allocation is approximately Walrasian can be done in polynomial time, even in economies for which finding an equilibrium is known to be computationally hard

Perfect Competition

In his 1987 entry on ‘Perfect Competition’ in The New Palgrave, the author reviewed the question of the perfectness of perfect competition, and gave four alternative formalisations rooted in the so-called Arrow-Debreu-Mckenzie model. That entry is now updated for the second edition to include work done on the subject during the last twenty years. A fresh assessment of this literature is offered, one that emphasises the independence assumption whereby individual agents are not related except through the price system. And it highlights a ‘linguistic turn’ whereby Hayek’s two fundamental papers on ‘division of knowledge’ are seen to have devastating consequences for this research programmeAllocation of Resources, Perfect Competition, Exchange Economy

Perfect Competition

In his 1987 entry on ‘Perfect Competition’ in The New Palgrave, the author reviewed the question of the perfectness of perfect competition, and gave four alternative formalisations rooted in the so-called Arrow-Debreu-Mckenzie model. That entry is now updated for the second edition to include work done on the subject during the last twenty years. A fresh assessment of this literature is offered, one that emphasises the independence assumption whereby individual agents are not related except through the price system. And it highlights a ‘linguistic turn’ whereby Hayek’s two fundamental papers on ‘division of knowledge’ are seen to have devastating consequences for this research programme.Allocation of Resources; Perfect Competition; Exchange Economy

Herbert Scarf: a Distinguished American Economist

Herbert Eli Scarf (born on July 25, 1930 in Philadelphia, PA) is a distinguished American economist and Sterling Professor (Emeritus as of 2010) of Economics at Yale University. He is a member of the American Academy of Arts and Sciences, the National Academy of Sciences and the American Philosophical Society. He served as the president of the Econometric Society in 1983. He received both the Frederick Lanchester Award in 1973 and the John von Neumann Medal in 1983 from the Operations Research Society of America and was elected as a Distinguished Fellow of the American Economic Association in 1991.

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

A Core-equilibrium Convergence in an Economy with Public Goods

This paper deals with a core-equilibrium equivalence in an economy with public goods where preferences of consumers display warm glow effects. We demonstrate that provided that each consumer becomes satiated to other consumers provision, it holds that, for a sufficiently large economy, the set of Edgeworth allocations is non-empty. Moreover, we show that an Edgeworth allocation could be decentralized as a warm glow equilibrium.Competitive equilibrium, Warm glow, Public goods, Edgeworth, Core, Decentralization

Core-Equivalence for the Nash Bargaining Solution.

Core equivalence and shrinking of the core results are well known for economies. The present paper establishes counterparts for bargaining economies, a specific class of production economies (finite and infinite) representing standard two-person bargaining games and their continuum counterparts as coalition production economies. Thereby we get core equivalence of the Nash solution. The results reconfirm the Walrasian approach to Nash bargaining of Trockel (1996). Moreover we establish the same speed of convergence as is known from Debreu (1975) and Grodal (1975) for replicated pure exchange economies and for regular purely competitive sequences of economies, respectively.

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