Bid Value Estimation via Differential Equation in Auctions

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Solution Overview

Problem

Current methods for estimating bidder values in auctions lack efficiency and accuracy, particularly in asymmetric auctions where each bidder has a different value distribution, making it difficult to compute optimal bid values without knowledge of other bidders' bids.

Innovation Solution

A method and system that utilize historical auction data to compute a bidder's bid value by solving an ordinary differential equation, which includes the selected bidder's value distribution and a parameter derived from the joint bid distribution, allowing for the estimation of bid values without requiring the value distributions of other bidders.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If traditional methods are used to estimate bidder values, then the approach is simple, but the accuracy and efficiency are insufficient especially in asymmetric auctions

Engineering Contradiction:

Improvebid value estimation accuracyVSAvoidmethod complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent transforms the bid value estimation problem into a differential equation framework, changing the mathematical parameters from simple probability distributions to differential equations involving density functions and joint bid distributions. This allows for more precise estimation of bid values in asymmetric auctions by modeling the relationship between bids and values through differential equations rather than direct probability comparisons.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent introduces a differential equation as an intermediary mechanism between the observed bid data and the desired bid value estimation. The differential equation serves as a mediator that processes the complex relationships between multiple bidders' bids and values, enabling accurate estimation without requiring direct observation of all bidders' private value distributions.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Reliability

If knowledge of other bidders' value distributions is required, then complete information is available, but computational complexity and data requirements increase significantly

Engineering Contradiction:

Improvebid value computation reliabilityVSAvoiddata requirements

Core Design Contradiction:

ReliabilityVSQuantity of substance

Solution Approach 1:

The patent extracts the essential information needed for bid value estimation from the complex web of all bidders' value distributions. By using the differential equation framework with the observed bid distribution and joint bid distribution, the method isolates and computes bid values without requiring access to or processing of all other bidders' complete value distribution data, thus reducing data requirements while maintaining reliability.

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent segments the bid value estimation problem into independent components for each bidder. The differential equation can be solved for each bidder's bid value independently using their own value distribution and the joint bid distribution, rather than requiring simultaneous solution of a system of equations involving all bidders' value distributions, thereby reducing overall computational complexity.

Inventive Principle:

Principle #1Segmentation

3Measurement precision

If historical auction data is utilized, then bid value estimation accuracy improves, but data processing and computation time increase

Engineering Contradiction:

Improvebid value estimation accuracyVSAvoidcomputation time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent replaces direct mechanical data processing (processing all historical data points individually) with a mathematical model based on differential equations. By fitting the differential equation model to aggregate statistics from historical data (such as the observed bid distribution and joint bid distribution), the method achieves high estimation accuracy without the computational burden of processing every individual historical bid record, thus reducing computation time.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentUS8548882B2Determination of a bid value associated with a selected bidder

Publication Date: 2013.10.01 ENT SERVICES DEV CORP LP

AI summary

A method and associated system comprise obtaining historical auction data, determining, from the historical auction data, a first parameter that is a function of a joint bid distribution and a density function related to the joint bid distribution, selecting a bidder, obtaining a value distribution for the selected bidder, and solving an equation. The equation may include the first parameter and the selected bidder's value distribution, and not the value distribution of other bidders. The equation computes a bid value associated with the selected bidder for a given bid.