A Strategy-proof Pricing Scheme for Multiple Resource Type Allocations
Summary (3 min read)
1 Introduction
- Currently, there is growing interest in large scale resource sharing [5].
- Users of such systems share their resources such as compute cycles, files, and bandwidth, while benefiting from the services provided by the network.
- Increasingly, peer-to-peer systems, mobile computing, e-commerce and grid computing develop into such multi-agent systems where each entity tries to maximize its own benefit [5, 17].
- The authors investigate how mechanism design and computational economies can be used to create a pricing scheme for strategy-proof resource allocation, both fast and efficient in the context of large distributed systems where an agent can both provide and consume resources of more than one type.
- Section 5 presents a summary of related work, and Section 6 concludes this paper.
2 Preliminaries
- A market refers to the environment, expressed in terms of rules and mechanisms, where resources within an economy are exchanged.
- Different markets may employ distinct mechanisms for setting the prices of the traded resources.
- The allocation with the best economic efficiency, also called Pareto-optimal, is achieved when, given an allocation, no Pareto improvement can be performed [6].
- Informally, best economic efficiency is achieved when social welfare is maximized.
- The concept of economic efficiency is different from the engineering approach commonly used in computer science.
2.1 Mechanism Design
- The authors use mechanism design [12] as a framework to create an incentive compatible pricing scheme for resource allocation.
- This section provides an overview of essential concepts in mechanism design and introduces the notations used in their proofs.
- Thus, by ensuring that agents stand to gain from participation, the mechanism provides incentives for rational agents to get resources and requests into the system.
- A Pareto-optimal resource allocation is achieved when the total welfare of all agents is maximized.
- Indeed, VCG mechanisms are not budget-balanced [13] and require a third-party agent (called a market-maker) to mediate between seller and buyer agents and to provide the surplus or deficit budget.
3 Proposed Pricing Mechanism
- Resource allocation is a complex process, which can be divided in several independent steps, such as resource location, pricing, allocation administration, etc.
- Thus, the authors consider a virtual economy in which common currency provides the basis for a utilitarian function that can be exploited by their mechanism.
- Market-based Resource Allocation Problem Given a market containing requests submitted by buyers and resources offered by sellers, each participant is modeled by a rational agent i with private information ti.
- This is an optimization problem, since the output specification is given by a positive real valued objective function, g(x, t), and the output ominimizes g, also known as More formally.
- An allocation is determined by a market-maker agent and represents an exchange between one buyer agent and at least one seller agent.
3.1 Winner Determination for Multiple Resource Types
- The authors scheme is designed for pricing and allocation of multiple resource types in dynamic markets, where buyer and seller agents may join and leave at any time.
- The authors describe the buyer request and seller available resource, and their strategy for selecting winners.
- The authors use tRdb to denote the buyer’s maximum declared price, as opposed to tRb which is the private maximum price.
- Furthermore, the authors present the proofs for the properties achieved by their mechanism.
3.4 Achieved Properties
- Theorem 1. The proposed mechanism is individual rational.
- From Equation 3, the authors see that seller utility is always positive.
3.5 Generalized Algorithm and Example
- Assume a market consisting of buyer requests and seller available resources published to a market-maker agent, together with their reserved prices, ti (private information).
- For each resource type (line 4), the market-maker sorts the seller queue for that resource type based on the reserved price, ts (line 5).
- Finally, the authors compute the buyer payment pb (line 13) and inform the winners of the allocation if their welfare is greater than 0 (lines 14–15).
- A solution that is pareto-optimal, but not budget-balanced, may be achieved using VCG payments for both buyers and sellers, as below.
4 Evaluation
- Welfare measures the economic efficiency and the algorithm runtime represents the computational efficiency.
- Global efficiency for buyers is defined as the total number of successful buyer requests, and for sellers as the average resource utilization of all seller agents, i.e. total resources utilized over total available seller resources.
- Using simulation, the authors first compare their mechanism with traditional auctions.
- The authors evaluate the impact of untruthful users in a balanced market under different market conditions.
- For simplicity, the authors consider a centralized implementation characterized by a single market-maker agent to which sellers and buyers submit their requests and available resources.
4.1 Comparison with Traditional Auctions
- For comparison with traditional one-sided auctions, the authors have developed a discrete-event auctions simulator with a request queue holding all outstanding buyer requests, and a resource queue containing seller agents published resources.
- First, the authors consider a balanced market to study the impact of untruthfulness on global efficiency of buyers, i.e. total number of successful buyer requests.
- Next, the authors compare the proposed scheme with traditional onesided auctions under different market scenarios.
- Market conditions are modeled by varying the arrival rates of buyers and sellers.
- Table 4 compares 10,000 buyer requests under different market scenarios and with different market diversity.
4.2 Comparison with Combinatorial Auctions
- In this section the authors compare the proposed scheme with combinatorial auctions using the open-source combinatorial auctions simulator jCase [16].
- The authors select for comparison the pure VCG and the Threshold algorithms proposed by Parkes et al. [13].
- Each buyer request consists of many resource types sampled from a uniform distribution between 1 and 10.
- Overall, their scheme is comparable to combinatorial auctions both in economic efficiency, measured in terms of overall welfare, and global efficiency, average seller resource utilization and percentage of successful buyer requests.
- 1The authors experiments are performed on a 8-core Intel Xeon, 1.86 GHz server with 4GB RAM.
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Cites background from "A Strategy-proof Pricing Scheme for..."
...Making combinatorial auctions is a NPComplete problem, as mentioned in [14]....
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...In [14], the market agent will select an alternative from a given set of choices to maximise his utility function....
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...A strategy-proof pricing scheme for multiple resource type allocations is presented in [14]....
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References
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"A Strategy-proof Pricing Scheme for..." refers background in this paper
...However, one thing to note is that achieving pareto-optimality usually requires an algorithm with exponential complexity, making the trade-off both in terms of budget-balance (-2-2+5 yields in $1 deficit in the case of VCG payments), and computational efficiency....
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2,435 citations
"A Strategy-proof Pricing Scheme for..." refers background in this paper
...However, one thing to note is that achieving pareto-optimality usually requires an algorithm with exponential complexity, making the trade-off both in terms of budget-balance (-2-2+5 yields in $1 deficit in the case of VCG payments), and computational efficiency....
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...However, it has been shown that no budgetbalanced system that provides incentives can maximize the overall welfare [10]....
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