scholarly journals Concave Generalized Flows with Applications to Market Equilibria

2012 ◽  
Author(s):  
Laszlo A. Vegh
Keyword(s):  
Generalized Flows ◽  
Market Equilibria

scholarly journals Computing Large Market Equilibria Using Abstractions

2021 ◽  
Author(s):  
Christian Kroer ◽  
Alexander Peysakhovich ◽  
Eric Sodomka ◽  
Nicolas E. Stier-Moses
Keyword(s):  
Practical Problem ◽  
Market Design ◽  
Matrix Completion ◽  
Fair Division ◽  
Problem Size ◽  
Solution Quality ◽  
Computing Power ◽  
Large Market ◽  
Market Equilibria

Computing market equilibria is an important practical problem for market design, for example, in fair division of items. However, computing equilibria requires large amounts of information, often the valuation of every buyer for every item, and computing power. In “Computing Large Market Equilibria Using Abstractions,” the authors study abstraction methods for ameliorating these issues. The basic abstraction idea is as follows. First, construct a coarsened abstraction of a given market, then solve for the equilibrium in the abstraction, and finally, lift the prices and allocations back to the original market. The authors show theoretical guarantees on the solution quality obtained via this approach. Then, two abstraction methods of interest for practitioners are introduced: (1) filling in unknown valuations using techniques from matrix completion and (2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market.

scholarly journals Market equilibria and money

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sjur Didrik Flåm
Keyword(s):  
Fixed Point ◽  
Steady State ◽  
Value Added ◽  
Pareto Optimal ◽  
Generalized Gradients ◽  
Market Mechanisms ◽  
Mathematical Arguments ◽  
Second Welfare Theorem ◽  
Market Equilibria ◽  
Welfare Theorem

AbstractBy the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing the second welfare theorem we show that the said solutions may coincide as a common fixed point for one and the same system.Mathematical arguments invoke conjugation, convolution, and generalized gradients. Convexity is merely needed via subdifferentiablity of aggregate “cost”, and at one point only.Economic arguments hinge on idealized market mechanisms. Construed as algorithms, each stops, and a steady state prevails if and only if price-taking markets clear and value added is nil.

scholarly journals Do Sunspots Matter when Spot Market Equilibria are Unique?

Econometrica ◽  
2000 ◽  
Vol 68 (2) ◽  
pp. 435-441 ◽  
Author(s):  
Thorsten Hens
Keyword(s):  
Spot Market ◽  
Market Equilibria
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