Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Prosumers Participation in Markets: A Scalar-Parameterized Function Bidding Approach

Abdullah Alawad, Muhammad Aneeq uz Zaman, Khaled Alshehri, Tamer Başar

Abstract

In uniform-price markets, suppliers compete to supply a resource to consumers, resulting in a single market price determined by their competition. For sufficient flexibility, producers and consumers prefer to commit to a function as their strategies, indicating their preferred quantity at any given market price. Producers and consumers may wish to act as both, i.e., prosumers. In this paper, we examine the behavior of profit-maximizing prosumers in a uniform-price market for resource allocation with the objective of maximizing the social welfare. We propose a scalar-parameterized function bidding mechanism for the prosumers, in which we establish the existence and uniqueness of Nash equilibrium. Furthermore, we provide an efficient way to compute the Nash equilibrium through the computation of the market allocation at the Nash equilibrium. Finally, we present a case study to illustrate the welfare loss under different variations of market parameters, such as the market's supply capacity and inelastic demand.

Prosumers Participation in Markets: A Scalar-Parameterized Function Bidding Approach

Abstract

In uniform-price markets, suppliers compete to supply a resource to consumers, resulting in a single market price determined by their competition. For sufficient flexibility, producers and consumers prefer to commit to a function as their strategies, indicating their preferred quantity at any given market price. Producers and consumers may wish to act as both, i.e., prosumers. In this paper, we examine the behavior of profit-maximizing prosumers in a uniform-price market for resource allocation with the objective of maximizing the social welfare. We propose a scalar-parameterized function bidding mechanism for the prosumers, in which we establish the existence and uniqueness of Nash equilibrium. Furthermore, we provide an efficient way to compute the Nash equilibrium through the computation of the market allocation at the Nash equilibrium. Finally, we present a case study to illustrate the welfare loss under different variations of market parameters, such as the market's supply capacity and inelastic demand.
Paper Structure (13 sections, 4 theorems, 38 equations, 2 figures)

This paper contains 13 sections, 4 theorems, 38 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Bidding strategy: towards scalar-parameterized functions
  3. Prosumer markets: peer-to-peer and other typologies
  4. Mechanism design objectives and prosumer nature
  5. Bidding Mechanism and Market Model
  6. Perfect Competition and Competitive Equilibrium
  7. Strategic Prosumers and Nash Equilibrium
  8. Case Study
  9. Conclusion and Future Directions
  10. Proof of Theorem 1
  11. Proof of Lemma 1
  12. Proof of Lemma 2
  13. Proof of Theorem 2

Key Result

Theorem 1

Suppose Assumption assumption1 holds. Then, there exists a unique competitive equilibrium, i.e., a scalar $\mu$ given by eq10 and a vector $\bm{\theta}^*$, satisfying: Also, the allocation profile $\bm{q}^*$ is efficient where $\bm{q}^*$ is defined by $q_i^* =Q(\theta_i^{*},\mu)$.

Figures (2)

  • Figure 1: Welfare loss with increasing supply capacity and fixed inelastic demand. (Top) Nash equilibrium exists and the welfare loss does not grow unbounded. (Bottom) Nash equilibrium may not exist and the welfare loss grows unbounded.
  • Figure 2: Welfare loss with decreasing inelastic demand and fixed supply capacity. (Top) Nash equilibrium exists and the welfare loss does not grow unbounded. (Bottom) Nash equilibrium may not exist and the welfare loss grows unbounded.

Theorems & Definitions (4)

  • Theorem 1
  • Lemma 1
  • Lemma 2
  • Theorem 2