This paper investigates the incorporation of fairness considerations, as defined in the behavioral economics literature, into game-theoretic formulations of dynamic pricing algorithms in electricity markets. Traditionally, these markets are modeled using Stackelberg equilibria between electricity producers (companies) and consumers, where the producer acts as the leader by setting the electricity price, and consumers respond by adjusting their load. This conventional order of play inherently limits the producer's ability to arbitrarily increase prices, as the load is price-dependent and the producer commits to supplying a minimum load prior to the interaction. Recent analyses, however, indicate that the order of play may reverse in practical scenarios where players converge to equilibrium through learning dynamics. In this reversed hierarchy, fairness constraints become pivotal in preventing the producer from opportunistically escalating prices without bound. Employing a time-of-use pricing framework established in existing literature, we perform a numerical analysis of the equilibria associated with both orders of play, with particular emphasis on the role of the introduced fairness considerations.

This paper studies a quantization problem between an encoder and a decoder with misaligned objectives, where the quantization indices are transmitted over a noisy channel. Building on the prior results on the non-strategic counterpart of this problem, we characterize the encoding and decoding strategies and expected encoder and decoder distortions at the Stackelberg equilibrium, where the encoder is the leader, and the decoder is the follower. On the design side, we extend the gradient-descent-based solution framework developed for the noiseless setting to this noisy communication scenario, combined with uniformly randomized index mapping. We finally present numerical simulation results to demonstrate the efficacy of the proposed approach. The Matlab codes associated with the design and evaluation of the proposed algorithm are provided at: https://github.com/strategic-quantization/channel-optimized-strategic-quantizer.

This paper is concerned with the quantization setting where the encoder and the decoder have misaligned objectives. While the unconstrained variation of this problem has been well-studied under the theme of information design problems in Economics, the problem becomes more appealing and relevant to engineering applications with a constraint on the cardinality of the message space. We first motivate the problem via a toy example demonstrating the intricacies of the strategic variation of the quantization problem, explicitly showing that the quantization resolution can change the nature of optimal encoding policy and the iterative optimization of the decoder and the encoder mappings may not converge to a local optimum solution, in sharp contrast with the classical quantization problem that admits the Lloyd-Max method as a local optimum solution. As a remedy, we develop a gradient-descent based solution. We analyze the poor local optimal optima issues associated with the optimization method and show that even for well-behaving sources, such as Gaussian, there are multiple local minima, depending on the distortion measures chosen, in sharp contrast with the classical quantization. We finally present numerical results obtained via the proposed algorithm that suggest their validity and demonstrate features of the strategic version of the quantization problem that differentiate it from its classical counterpart.

This paper is concerned with the quantization setting where the encoder and the decoder have misaligned objectives. We first motivate the problem via a toy example which demonstrates the intricacies of the strategic quantization problem, specifically shows that iterative optimization of the decoder and the encoder mappings may not converge to a local optimum. As a remedy, we propose a dynamic programming based optimal optimization method, inspired by the early works in the quantization theory. We then extend our approach to variable-rate (entropy-coded) quantization. We finally present numerical results obtained via the proposed algorithms.