Time polynomial Arrow-Debreu market equilibrium
First Claim
1. An article of manufacture comprising computer-readable media having computer-readable code embodied therein, wherein the computer-readable code is configured to cause one or more processors to perform acts of:
- determining a spectrum of participants in a market, the spectrum comprising consumers of goods of a particular type;
defining a gamut of goods of the particular type;
including ranges of value units over which respective products related to the gamut command; and
invoking a convex program to determine a particular number of value units for a specific product related to the gamut, at which a market in which the spectrum participates will clear;
the convex program is represented by;
wherein xij is the amount of goods j consumed by a participant i, wherein uij is the number of goods j that is wanted by a participant i, wherein uik is the number of goods of i that is wanted by k, wherein xik is the amount of goods of k consumed by a participant i, wherein pj is the price of j th goods, and wherein pi is the amount of money spent by i.
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Accused Products
Abstract
A concept for providing a process and apparatus for allocating a gamut of assets/resources across a spectrum of consumers is described. The concept includes an apparatus for allocating resources across a spectrum of users. The apparatus includes one or more processors and a memory coupled to the one or more processors. The memory is configured to store data representative of characteristics and capabilities of the resources and describing needs of the spectrum. The memory further includes computer readable code configured to cause the one or more processors to perform acts of: estimating current requests from the spectrum for the resources; comparing the current requests to the capabilities and characteristics; and allocating the resources with respect to the requests in conformance with a convex program implementation of Arrow-Debrue theory.
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Citations
18 Claims
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1. An article of manufacture comprising computer-readable media having computer-readable code embodied therein, wherein the computer-readable code is configured to cause one or more processors to perform acts of:
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determining a spectrum of participants in a market, the spectrum comprising consumers of goods of a particular type; defining a gamut of goods of the particular type; including ranges of value units over which respective products related to the gamut command; and invoking a convex program to determine a particular number of value units for a specific product related to the gamut, at which a market in which the spectrum participates will clear; the convex program is represented by; wherein xij is the amount of goods j consumed by a participant i, wherein uij is the number of goods j that is wanted by a participant i, wherein uik is the number of goods of i that is wanted by k, wherein xik is the amount of goods of k consumed by a participant i, wherein pj is the price of j th goods, and wherein pi is the amount of money spent by i. - View Dependent Claims (2, 3, 4)
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5. An apparatus for allocating a gamut of resources across a spectrum of users, comprising:
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one or more processors; a memory coupled to the processor, the memory being configured to store data representative of the resources and needs of the spectrum, the memory further comprising computer-readable code configured to cause the one or more processors to perform acts of; estimating current requests from the spectrum for the resources; comparing the current requests to the data; and allocating the resources with respect to the requests in conformance with a convex program implementation of Arrow-Debreu theory; the convex program represented by; wherein xij is the amount of goods j consumed by a participant i, wherein uij is the number of goods j that is wanted by i, wherein uik is the number of goods of k that is wanted by k, wherein xik is the amount of goods of k consumed by a participant i, wherein pj is the price of j th goods, and wherein pi is the amount of money spent by i. - View Dependent Claims (6, 7, 8, 9, 10, 11)
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12. An apparatus for allocating a gamut of resources across a spectrum of users, comprising:
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one or more processors; a memory coupled to the processor, the memory being configured to store data representative of the resources and needs of the spectrum, the memory further comprising computer-readable code configured to cause the one or more processors to perform acts of; estimating current requests from a spectrum of participants for resources; characterizing a gamut of resources that can be made available to the participants; and allocating portions of the gamut across the spectrum using a convex program implementation of Arrow-Debreu theory; the convex program represented by; wherein xij is the amount of goods j consumed by a participant i, wherein mi is the amount of money of the i th buyer, wherein uij is the number of goods j that is wanted by i, wherein uik is the number of goods of i that is wanted by k, wherein xik is the amount of goods of k consumed by a participtant i, and wherein pj is the price of j th goods. - View Dependent Claims (13, 14)
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15. An article of manufacture comprising computer-readable media having computer-readable code embodied therein, wherein the computer-readable code is configured to cause one or more processors to perform acts of:
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determining a spectrum of participants in a market, the spectrum comprising consumers of goods of a particular type; defining a gamut of goods of the particular type; including ranges of value units over which respective products related to the gamut exchange command; and invoking a convex program to determine a particular number of value units for a specific product related to the gamut, at which a market in which the spectrum participates will clear; the convex program represented by; wherein xij is the amount of goods of j consumed by a participant i, wherein mi is the amount of money of the i th buyer, wherein uij is the number of goods of j that is wanted by i, wherein uik is the number of goods of i that is wanted by k, wherein xik is the amount of goods of k consumed by a participtant i, and wherein pj is the price of j th goods. - View Dependent Claims (16, 17, 18)
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Specification