Time polynomial Arrow-Debreu market equilibrium

• US 7,584,111 B2
• Filed: 11/19/2004
• Issued: 09/01/2009
• Est. Priority Date: 11/19/2004
• Status: Expired due to Fees

• Current Assignee: Microsoft Technology Licensing LLC (Microsoft Corporation)
• Original Assignee: Microsoft Corporation
• Inventors: Jain, Kamal
• Primary Examiner(s): Sterrett; Jonathan G
• Application Number:
  US10/994,182
• Publication Number:
  US 20060116917A1
• Time in Patent Office: 1,747 Days
• Field of Search: 705/7
• US Class Current: 705/7.25
• CPC Class Codes: G06Q 10/06 Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
• CPC Class Codes: G06Q 10/06315 Needs-based resource requirements planning or analysis
• CPC Class Codes: G06Q 30/0204 Market segmentation
• CPC Class Codes: G06Q 30/0206 Price or cost determination based on market factors

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.

Claims

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;

$\forall <br><br>j<br><br>\text{;<br><br>}<br><br><br><br>\underset{i}{\sum <br><br>}<br><br>x_{\mathrm{ij}}=1$ $\forall <br><br>i,j<br><br>\text{;<br><br>}<br><br><br><br>x_{\mathrm{ij}}\ge <br><br>0$ $\forall <br><br>i,j<br><br><br><br>\mathrm{such}<br><br><br><br>\mathrm{that}<br><br><br><br>u_{\mathrm{ij}}><br><br>0;<br><br><br><br>{\mathrm{LOGp}}_i-{\mathrm{LOGp}}_j\le <br><br>\log \left(\frac{\underset{k}{\sum <br><br>}<br><br>u_{\mathrm{ik}}<br><br>x_{\mathrm{ik}}}{u_{\mathrm{ij}}}\right);<br><br>$

wherein x_ij is the amount of goods j consumed by a participant i,

wherein u_ij is the number of goods j that is wanted by a participant i,

wherein u_ik is the number of goods of i that is wanted by k,

wherein x_ik is the amount of goods of k consumed by a participant i,

wherein p_j is the price of j th goods, and

wherein p_i is the amount of money spent by i.

2. The article of manufacture of claim 1, wherein the convex program instantiates Arrow-Debreu theory.

3. The article of manufacture of claim 1, wherein the convex program treats linear utility functions.

4. The article of manufacture of claim 1, wherein the convex program treats non-linear utility functions.

5. An apparatus for allocating a gamut of resources across a spectrum of users, comprising:

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;

$\forall <br><br>j<br><br>\text{;<br><br>}<br><br><br><br>\underset{i}{\sum <br><br>}<br><br>x_{\mathrm{ij}}=1$ $\forall <br><br>i,j<br><br>\text{;<br><br>}<br><br><br><br>x_{\mathrm{ij}}\ge <br><br>0$ $\forall <br><br>i,j<br><br><br><br>\mathrm{such}<br><br><br><br>\mathrm{that}<br><br><br><br>u_{\mathrm{ij}}><br><br>0;<br><br><br><br>{\mathrm{LOGp}}_i-{\mathrm{LOGp}}_j\le <br><br>\log \left(\frac{\underset{k}{\sum <br><br>}<br><br>u_{\mathrm{ik}}<br><br>x_{\mathrm{ik}}}{u_{\mathrm{ij}}}\right);<br><br>$

wherein x_ij is the amount of goods j consumed by a participant i,

wherein u_ij is the number of goods j that is wanted by i,

wherein u_ik is the number of goods of k that is wanted by k,

wherein x_ik is the amount of goods of k consumed by a participant i,

wherein p_j is the price of j th goods, and

wherein p_i is the amount of money spent by i.

6. The apparatus of claim 5, wherein the convex program treats linear utility functions.

7. The apparatus of claim 5, wherein the convex program treats non-linear utility functions.

8. The apparatus of claim 5, wherein the users provide requests to handle bodies of digital information of different sizes via a data-handling network, and the resources comprise data handling capabilities.

9. The apparatus of claim 5, wherein the users provide requests to store bodies of data of different sizes in a memory system, and the resources comprise memory resources.

10. The apparatus of claim 5, wherein the users provide requests to transmit bodies of information of different sizes via a data transmission system, and the resources comprise data transmission system descriptors.

11. The apparatus of claim 5, wherein the users provide requests to transmit bodies of information of different sizes via a data transmission system, each of the bodies represents one or more or digital representations of text, video, pictorial and audio data and the resources comprise data transmission system descriptors, including one or more of:

bandwidth;

capacity, loading and throughput.

12. An apparatus for allocating a gamut of resources across a spectrum of users, comprising:

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;

$\forall <br><br>j<br><br>\text{;<br><br>}<br><br><br><br>\underset{i}{\sum <br><br>}<br><br>x_{\mathrm{ij}}=1$ $\forall <br><br>i,j<br><br>\text{;<br><br>}<br><br><br><br>m_i<br><br>u_{\mathrm{ij}}\le <br><br>p_j<br><br>\underset{k}{\sum <br><br>}<br><br>u_{\mathrm{ik}}<br><br>x_{\mathrm{ik}}$ $\underset{j}{\sum <br><br>}<br><br>p_j\le <br><br>\underset{i}{\sum <br><br>}<br><br>m_i$ $\forall <br><br>i,j<br><br>\text{;<br><br>}<br><br><br><br>x_{\mathrm{ij}}\ge <br><br>0$ $\forall <br><br>j<br><br>\text{;<br><br>}<br><br><br><br>p_j\ge <br><br>0;<br><br>$

wherein x_ij is the amount of goods j consumed by a participant i,

wherein m_i is the amount of money of the i th buyer,

wherein u_ij is the number of goods j that is wanted by i,

wherein u_ik is the number of goods of i that is wanted by k,

wherein x_ik is the amount of goods of k consumed by a participtant i, and

wherein p_j is the price of j th goods.

13. The apparatus of claim 12, wherein the convex program implementation employs linear utility functions.

14. The apparatus of claim 12, wherein the convex program implementation employs non-linear utility functions.

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:

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;

$\forall <br><br>j<br><br>\text{;<br><br>}<br><br><br><br>\underset{i}{\sum <br><br>}<br><br>x_{\mathrm{ij}}=1$ $\forall <br><br>i,j<br><br>\text{;<br><br>}<br><br><br><br>x_{\mathrm{ij}}\ge <br><br>0$ $\forall <br><br>i,j<br><br><br><br>\mathrm{such}<br><br><br><br>\mathrm{that}<br><br><br><br>u_{\mathrm{ij}}><br><br>0;<br><br><br><br>{\mathrm{LOGp}}_i-{\mathrm{LOGp}}_j\le <br><br>\log \left(\frac{\underset{k}{\sum <br><br>}<br><br>u_{\mathrm{ik}}<br><br>x_{\mathrm{ik}}}{u_{\mathrm{ij}}}\right);<br><br>$

wherein x_ij is the amount of goods of j consumed by a participant i,

wherein m_i is the amount of money of the i th buyer,

wherein u_ij is the number of goods of j that is wanted by i,

wherein u_ik is the number of goods of i that is wanted by k,

wherein x_ik is the amount of goods of k consumed by a participtant i, and

wherein p_j is the price of j th goods.

16. The article of manufacture of claim 15, wherein the convex program instantiates Arrow-Debreu theory.

17. The article of manufacture of claim 15, wherein the convex program treats linear utility functions.

18. The article of manufacture of claim 15, wherein the convex program treats non-linear utility functions.