Pricing for Information Revelation in Demand Response: A Strategic Communication Approach

TL;DR

Simulations show that a properly designed price for the communication scheme can recover up to 95% of the ideal system utility, whereas a price-unaware choice leads to significant losses in social welfare.

Abstract

Many smart grid frameworks, such as demand response programs, require accurate information about consumers' parameters (e.g., flexibility) at the aggregator side to optimize grid operations. Existing works typically rely on perfect information assumptions or complex incentive-compatible mechanisms; however, in voluntary settings, and in the presence of strategic consumers, possibly implemented by automated intelligent agents, private parameters may be misreported due to strategic incentives. We analyze this communication setting using cheap-talk game theory, delivering four key insights. First, the nontrivial scenario of multiple strategic transmitters (consumers) turns out to be tractable for the case study of interest: we prove that complex strategic interactions among multiple consumers decouple into independent subgames. Second, we demonstrate that a pre-announced retail price can be exploited as a design lever to control the information revealed by the consumers and therefore the overall system efficiency. Third, we derive a closed-form expression for the optimal uniform price that maximizes information revelation. Finally, we characterize the equilibrium structure to identify when communication is informative. Simulations show that a properly designed price for the communication scheme can recover up to 95% of the ideal system utility (i.e., under perfect information reporting), whereas a price-unaware choice leads to significant losses in social welfare.

Figures (5)

• Figure 1: Framework Overview. The interaction proceeds in four steps: (1) The Aggregator sets an ex-ante tariff $p$. (2) Private consumer types $\omega_n$ are drawn from priors $\psi_n$. (3) Consumers strategically reveal information via messages $m_n$ based on their incentive alignment. (4) The Aggregator determines the optimal dispatch $x_n$.
• Figure 2: Convergence of the BRD algorithm for computing equilibrium partitions. The algorithm exhibits convergence across all population sizes, with the convergence rate gradually decreasing as $N$ increases due to the system approaching the constant-bias regime ($\gamma_n \to 1$).
• Figure 3: The role of price in shaping equilibria and welfare. (a) Maximum number of messages $\kappa_{n,\mathrm{max}}$ as a function of price, revealing three regimes: Non-informative (orange hatched), strict bias (unshaded regions), and outward bias (blue dotted) around $p^*$, which enables $\kappa_{n,\mathrm{max}}=\infty$. (b) Recovered welfare (left axis) and expected bias (right axis) versus price. The optimal price $p^*$ minimizes expected bias and maximizes welfare, achieving 95% of the first-best outcome.
• Figure 4: Asymptotic price convergence. Dashed: asymptotic $p_\infty^*$; solid: $p^*$. High curvature converges rapidly; low curvature shows effects up to $N \approx 50$. All achieve $>80\%$ welfare for a sufficiently large $N$.
• Figure 5: Welfare vs. Number of Messages $\kappa$. At $p^*$, welfare increases monotonically to 95% of the first-best; a $1\%$ price deviation ($p^*+\Delta$) limits $\kappa_{\mathrm{max}}$ to $3$, reducing welfare, though 72% recovery is still maintained.

Theorems & Definitions (30)

• Remark 1: The First-Best Benchmark
• Remark 2: Price as an Internal Transfer
• Remark 3: Price as a Design Lever
• Definition 1: Perfect Bayesian Equilibrium
• Remark 4: Credible Communication
• Theorem 1: Strategic Independence for Interior Equilibria
• proof
• Corollary 1: Effective Single Sender Game
• proof
• Proposition 1: Reduction to a Canonical Form