2025 Theses Doctoral

Incentives in Market Design: Robust Auction Theory and Applications to Electricity Markets

Anunrojwong, Jirawat

Markets coordinate decisions of and interactions between agents and allocate resources. This coordination requires a deep understanding of the operational details of each particular market: who the participants are, what they have, what they know, and how they can interact.

While some markets form spontaneously, most markets do not. All of the aforementioned markets are human constructs that must be thoughtfully designed and optimized to function effectively and equitably. A common thread throughout this thesis is the critical role of participants' strategic behavior and their interplay with constraints on market structure, available resources, and information access. This thesis explores two themes in markets: robustness, and applications to energy markets and battery operations.

Chapters 1 and 2 comprise the first theme. Traditional market design solutions often assume that the designer knows the environment perfectly, but (i) this knowledge is often neither available nor reliable, and (ii) the optimal mechanism prescribed by the theory is often too complicated or fine-tuned to the details of the environment, to be used in practice. Our work on robust auction design aims to design mechanisms that perform "well" against any "reasonable" shifts in the environment.

One of the fundamental questions in market design is how to optimally sell an item. Developing mechanisms that are robust to incomplete information has remained an open question. In Chapter 1, we formalize and answer this question. We consider a seller optimizing over dominant strategy incentive compatible (DSIC) mechanisms to minimize the worst-case gap between mechanism revenue and the benchmark, where the only thing known about the value distribution of n buyers is the upper bound and the correlation structure. Surprisingly, despite the rich class of DSIC mechanisms, we find the optimal mechanism is a second-price auction (SPA) with random reserve, which remains optimal across a range of distribution classes capturing positive dependence, including i.i.d. and affiliated distributions. This provides an explanation for the widespread use of SPA in practice.

In practice, while we do not have complete knowledge about the environment, we often do have partial knowledge and we aim to incorporate side information into the robust framework. In Chapter 2, we extend the previous work by analyzing the role of support information [a,b] of buyer valuations. We show that if a/b is below a threshold, second-price auctions (SPA) is optimal; if a/b is above another threshold, SPAs are now strictly suboptimal, and a new class of mechanisms we call pooling auctions (POOL) is optimal; if a/b is between the two thresholds, a randomization between SPA and POOL is optimal.

Chapter 3 comprises the second theme, studying the impact of incentives and market power for battery operations in electricity markets. Grid-scale batteries have become much bigger just in the last few years to shift demand from the growing renewables from when the sun shines and the wind blows to when people need energy. Because these privately-owned big batteries maximize profit, they may not be fully aligned with the system goal of minimizing system cost. We propose an analytically tractable model that captures salient features of the highly complex electricity market.

We analyze the resulting battery behavior and generation cost in three operating regimes: (i) no battery, (ii) centralized battery minimizing system cost, and (iii) decentralized battery maximizing profit. We show that a decentralized battery distorts its discharge decisions in three ways. First, there is quantity withholding, i.e., discharging less than centrally optimal. Second, there is a shift in participation from day-ahead to real-time. Third, there is reduction in real-time responsiveness, or discharging less in response to smoothing real-time demand than centrally optimal.

We quantify each of the three forms of distortions in terms of market fundamentals through Price of Anarchy (PoA) and prove that PoA is always between 9/8 and 4/3. We calibrate our model to real data from Los Angeles and Houston and show that the loss from incentive misalignment could be consequential, but still relatively small compared to the gains from having enough battery capacity.