Periodic Double Auction Equilibrium for Multi-Round Energy Bidding
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Solution Overview
Problem
Existing methods for determining optimal bidding strategies in periodic double auctions (PDAs) for energy markets fail to consider multi-shot scenarios with multiple buyers and sellers, leading to inefficiencies and suboptimal profit generation, and existing numerical solutions lack verification of true Nash equilibria.
Innovation Solution
Modeling PDAs as a finite horizon Markov game to derive Markov Perfect Nash Equilibrium (MPNE) solutions, using a joint policy to determine optimal bidding strategies that minimize procurement costs by spreading demand across multiple auctions, considering both buyers and sellers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If numerical approaches (reinforcement learning) are used to determine equilibrium strategies, then computational feasibility is improved, but verification of true Nash equilibrium cannot be ensured
Solution Approach 1:
The patent replaces numerical approximation methods (reinforcement learning) with an analytical mathematical framework. By formulating the PDA as a Markov game and deriving closed-form equilibrium strategies through backward induction, the system achieves both computational efficiency and exact verification of Nash equilibrium conditions, eliminating the need for iterative training processes.
Solution Approach 2:
The patent transforms the problem from a numerical optimization approach to an analytical parameter-based solution. By expressing equilibrium strategies as explicit functions of game parameters (discount factor, supply curves, demand functions), the system enables direct computation and verification without numerical approximation, resolving the contradiction between computational feasibility and equilibrium verification.
2Device complexity
If single-shot auction models are used, then analytical solutions are easier to derive, but they fail to capture multi-shot strategic planning capabilities
Solution Approach 1:
The patent segments the multi-shot auction into sequential stages using backward induction. By solving the game from the final period back to the initial period, the system derives equilibrium strategies that account for future strategic interactions. This segmentation enables analytical tractability while capturing the full strategic planning capability of multi-shot auctions.
Solution Approach 2:
The patent incorporates preliminary strategic planning by deriving equilibrium strategies that anticipate future auction outcomes. The backward induction process allows players to pre-determine optimal bidding strategies based on expected future conditions, enabling multi-shot strategic planning while maintaining analytical solvability through the structured approach.
3Device complexity
If complete information about supply and demand is assumed, then equilibrium analysis becomes tractable, but it reduces realism in competitive energy markets
Solution Approach 1:
The patent develops a Markov game framework that serves multiple functions: it models complete information scenarios for analytical tractability, accommodates incomplete information through Bayesian extensions, and captures strategic planning in multi-shot settings. This universal framework can analyze various market conditions and information structures within a single unified approach, maintaining both tractability and realism.
Data Source
AI summary
Periodic double auction (PDA) setting is where buyers of the auction have multiple (but finite) opportunities to procure multiple but fixed units of commodity. The goal of each buyer participating in such auctions is to reduce their cost of procurement by planning purchase across multiple rounds of the PDA. Formulating such optimal bidding strategies in multi-agent periodic double auction setting is a challenging problem as such strategies involve planning across current and future auctions. The method and system disclosed herein addresses such setup wherein the composite supply curve is known to all buyers. Specifically, for the complete information setting, the method models the PDA as Markov game and derives Markov perfect Nash equilibrium (MPNE) solution to devise an optimal bidding strategy for the case when each buyer is allowed to make one bid per round of the PDA. The efficacy of the Nash policies obtained is demonstrated with numerical experiments.