Decentralized Resource Allocation Mechanisms in Decentralized Resource Allocation Mechanisms in Networks

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  • Decentralized Resource Allocation Mechanisms in

    Networks

    Tudor Stoenescu

    Information Science and Technology Caltech

  • Organization of the Talk

    Major issues of resource allocation in networks Overview of fundamental issues in decentralized resource allocation Development of two network pricing mechanisms Implementation in networks Conclusions

  • Motivation

    Integrated services networks support the delivery of a variety of services to their users Diversity of information imposes different requirements on the delivery methods – (audio, video, file transfer)

  • Challenge

    Design of resource allocation strategies which guarantee the delivery of different services, each with its own Quality of Service (QoS) requirement, maximize some performance criterion (e.g. network's utility to its users) and satisfy the network’s informational constraints

    – Issue: Compatibility with individual objectives

  • Key Network Features

    Informationally decentralized system formed by two types of agents:

    Users Network

  • Users’ Informational Constraints

    Preferences over the set of services offered by the network are private information.

    – Preferences are expressed by a utility function

    Users are unaware as well as uninterested in the delivery method used for the requested services Users are unaware of the other users requesting services from the network

  • Network Informational Constraints

    Network manager knows the network topology and the network's resources – link capacities, buffer size

    Network manager is unaware of the number of users that may request services, as well as the users' utilities

  • Decentralization of information

  • Major issue

    If information were centralized one could use Math Programming methods

  • Major issue

    If information were centralized one could use Math Programming methods But it is not…

  • Major issue

    If information were centralized one could use Math Programming methods But it is not… Can we find ways of implementing the centralized design and still satisfy the informational constraints?

  • Major issue

    If information were centralized one could use Math Programming methods But it is not… Can we find ways of implementing the centralized design and still satisfy the informational constraints? If we find a method of implementing the centralized design, can we guarantee that the agents will follow this method?

  • Organization of the Talk

    Major issues of resource allocation in networks Overview of fundamental issues in decentralized resource allocation Development of two network pricing mechanisms Implementation in networks Conclusions

  • Decentralized Resource Allocation Background

    Early 1800’s (beginning of the socialist debate) Late 1800’s – Walrasian school (Pareto, Barone,…) World War I – German economy von Mises – economic calculation (1920’s) Socialist economists of the 1930’s

    (Taylor, Dickinson, Lange, Lerner,…) von Hayek – rebuttal to the socialist arguments

  • von Hayek’s arguments regarding the weakness of socialist economies

    Amount of information exchange and calculation needed by a central-control system to determine an optimal resource allocation may be too great. Incentives provided by the market economy could not be reproduced by any socialist system.

  • Mechanism Design

    Realization Theory – Informational efficiency – Complexity of information processing

    Implementation Theory

  • Mechanism Design (Realization Theory)

    E

  • Mechanism Design (Realization Theory)

    E A

  • Mechanism Design (Realization Theory)

    E A π

  • Mechanism Design (Realization Theory)

    E

    M

    A π

    µ h

  • Mechanism components

    E – Environment A – Action Space M – Message Space π – Goal correspondence µ – Equilibrium message correspondence h – Outcome function

  • Requirements

    1. For each element of the environment there exist a non-empty set of feasible actions.

  • Requirements

    1. For each element of the environment there exist a non-empty set of feasible actions.

    2. For each element of the environment the set of feasible actions satisfying the goal correspondence π is non-empty.

  • Requirements

    1. For each element of the environment there exist a non-empty set of feasible actions.

    2. For each element of the environment the set of feasible actions satisfying the goal correspondence π is non-empty.

    3. The actions generated by π also satisfy some sort of optimality criteria.

  • Requirements

    1. For each element of the environment there exist a non-empty set of feasible actions.

    2. For each element of the environment the set of feasible actions satisfying the goal correspondence π is non-empty.

    3. The actions generated by π also satisfy some sort of optimality criteria.

    Requirements 1-3 are constraints on the problem type considered.

  • Requirements

    4. For all ∅≠∈ )(, eEe µ

  • Requirements

    4. For all

    5. (non-wastefulness)

    ∅≠∈ )(, eEe µ

    Eeeeh ∈∀⊆ ),())(( πµ

  • Requirements

    4. For all

    5. (non-wastefulness)

    A mechanism satisfying requirements 1 - 5 is called goal realizing.

    ∅≠∈ )(, eEe µ

    Eeeeh ∈∀⊆ ),())(( πµ

  • Requirements

    6. Unbiasedness - mechanism should not favor one group of agents over another.

  • Requirements

    6. Unbiasedness - mechanism should not favor one group of agents over another.

    7. Essential single-valued - for any environment, the rules of the process leads the system to a uniquely determined allocation

  • Requirements

    6. Unbiasedness - mechanism should not favor one group of agents over another.

    7. Essential single-valued - for any environment, the rules of the process leads the system to a uniquely determined allocation

    A mechanism satisfying requirements 4 through 7 is called satisfactory.

  • Requirements

    8. Privacy preserving - all the agents generate their equilibrium messages based only on their own information about the environment.

  • Requirements

    8. Privacy preserving - all the agents generate their equilibrium messages based only on their own information about the environment.

    9. Spot threadedness of µ - the correspondence has a continuous selection around every point in the domain

  • Requirements

    8. Privacy preserving - all the agents generate their equilibrium messages based only on their own information about the environment.

    9. Spot threadedness of µ - the correspondence has a continuous selection around every point in the domain

    0.a11a12a13… 0.a21a22a23… 0.a31a32a33…

    0.a11a21a31a12a22a32…

  • Requirements

    8. Privacy preserving - all the agents generate their equilibrium messages based only on their own information about the environment.

    9. Spot threadedness of µ - the correspondence has a continuous selection around every point in the domain

    A mechanism satisfying requirements 8 and 9 is called regular.

  • Desired property

    A mechanism is said to be informationally efficient if it is goal realizing and regular and it has a message space of a dimensionality which is minimal among all the other goal realizing and regular mechanisms

  • Implementation Theory

    Studies the constrains on the design of mechanisms imposed by the divergence of individual incentives from the performance objective Question: – Can we design a noncooperative game that

    implements the social choice rule in some sort of equilibrium messages (Nash, Bayesian, subgame perfect, undominated strategies, etc.) ?

  • Implementation Issues

    NEEEE ×××= ...21

    E A π

  • Implementation Issues

    NMMMM ×××= ...21 NEEEE ×××= ...21

    E A

    M

    π

    h

  • Implementation Issues

    NMMMM ×××= ...21 NEEEE ×××= ...21

    E A

    M

    π

    R h

    ( ) ( ) EeNimemheRemh iii ∈∀∈∀− ],...,2,1[),()()( **

    ( ))(),...,(),(:)( **2*1* emememem N= ( ))(),...,(),(),(),...,(:)( ** 1* 1*1* emememememem Niiii +−− =

    ii Mm ∈

  • Implementation Issues

    NMMMM ×××= ...21 NEEEE ×××= ...21

    EeeeRh ∈∀⊆ ),())(( π

    E A

    M

    π

    R h

    ( ) ( ) EeNimemheRemh iii ∈∀∈∀− ],...,2,1[),()()( **

    ( ))(),...,(),(:)( **2*1* emememem N= ( ))(),...,(),(),(),...,(:)( ** 1* 1*1* emememememem Niiii +−− =

    ii Mm ∈

  • Organization of the Talk

    Major issues of resource allocation in networks Overview of fundamental issues in decentralized resource allocation Development of two network

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