We consider a smart-grid connecting several agents, modeled as stochastic dynamical systems, who may be electricity consumers producers. At each discrete time instant, which may represent a 15 minute interval, each agent may consume generate some quantity of electrical energy. The Independent System Operator (ISO) is given the task of assigning consumptions generations to the agents so as to maximize the sum of the utilities accrued to the agents, subject to the constraint that energy generation equals consumption at each time. This task of coordinating generation and demand has to be accomplished by the ISO without the agents revealing their system states, dynamics, or utility cost functions. We show how and when a simple iterative procedure converges to the optimal solution. The ISO iteratively obtains electricity bids by the agents, and declares the tentative market clearing prices. In response to these prices, the agents submit new bids. On the demand side, the solution yields an optimal demand response for dynamic and stochastic loads. On the generation side, it provides the optimal utilization of stochastically varying renewables such as solar wind, and generation with fossil fuel based generation with dynamic constraints such as ramping rates. Thereby we solve a decentralized stochastic control problem, without agents sharing any information about their system models, states or utility functions.
Viewed from the power system end, there have been many efforts since the deregulation of the electricity sector on a market-based framework to clear the system. @cite_7 have proposed a two-layered approach that internalizes individual constraints of market participants while allowing the ISO to manage the spatial complexity. The approximated MPC algorithm is shown to perform well in many realistic applications. In order to analyze the strategic interactions between the ISO and market participants, game theoretical approaches have been proposed, e.g., @cite_10 uses a Stackelberg game framework for studying economic dispatch with demand response. @cite_1 pose the problem as a noncooperative game, and prove the existence of a Nash equilibrium under some assumtpions.
@cite_1 @cite_10 @cite_7
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In this paper, we raise the question: What is the value that demand response management (DRM) can bring to generation companies and consumers in the smart grid? The question is fundamental for understanding the efficiency and impact of DRM on the future power grid. To answer this question, we first establish a Stackelberg game framework that captures the hierarchical communication architecture of the energy system, and the rational behaviors of the consumers and the market operator. We define the value of demand response based on the Stackelberg equilibrium (SE) solution to the hierarchical two-person game problem, and the standard optimal solution to economic dispatch problem. In order to compute the equilibrium solution, we show that a consistency principle can be used to characterize the SE of the game in which the follower responds to the dual variable of the leader's problem. We use logarithmic utility functions to illustrate the solution concept and show that in some cases, DRM provides conflicting values to the gencos and consumers. This paper proposes an innovative game theoretic framework for a next-generation retail electricity market (“Energy Internet”) with high penetration of distributed residential electricity suppliers (“Energy Cells”). The envisioned Energy Internet is developed for plug-and-play of a large number of distributed renewable energy generation and energy storage. The residential customers, referred as Energy Cells, are not only the electricity consumers but can also be the electricity suppliers by locally operating and managing their own distributed generators, distributed energy storage devices, and dispatchable loads. This paper formulates a set of mathematical models of the retail electricity market participants with a number of local and global constraints. A numerical case study is performed to validate the proposed next-generation retail electricity market framework using game-theoretic methodologies. The numerical simulation results demonstrate the effectiveness of the proposed market clearing scheme with high penetration of distributed residential electricity suppliers. Dynamic spectrum access can significantly improve the spectrum utilization. For wireless service providers, the emergence of dynamic spectrum access brings new opportunities and challenges. The flexible spectrum acquisition gives a particular provider the chance to easily adapt its system capacity to fit end users' demand. However, the competition among several providers for both spectrum and end users complicates the situation. In this paper, we propose a general three-layer spectrum market model for the future dynamic spectrum access system, in which the interaction among spectrum holder, wireless service providers and end users are considered. We study a duopoly situation, where two wireless service providers participate in bandwidth competition in spectrum purchasing and price competition to attract end users, with the aim of maximizing their own profit. We believe we are the first one to explicitly study the relation of these two competitions in dynamic spectrum market. We formulate the wireless service providers' competition as a non-cooperative two-stage game. We first analyze the static game when full information is available for providers. Under general assumptions about the price and demand functions, a unique pure Nash equilibrium is identified as the outcome of the game, which shows the stability of the market. We further evaluate the market efficiency of the equilibrium in a symmetric case, and show that the gap with the social optimal is bounded within a small constant ratio. When the market information is limited, we provide myopically optimal adjustment algorithms for the providers. With such strategies, short term price updating converges to the Nash equilibrium of the given subgame, while long term bandwidth updating converges to a point close to the Nash equilibrium of the full game. We consider network games with atomic players, which indicates that some players control a positive amount of flow. Instead of studying Nash equilibria as previous work has done, we consider that players with considerable market power will make decisions before the others because they can predict the decisions of players without market power. This description fits the framework of Stackelberg games, where those with market power are leaders and the rest are price-taking followers. As Stackelberg equilibria are difficult to characterize, we prove bounds on the inefficiency of the solutions that arise when the leader uses a heuristic that approximate its optimal strategy. Demand-side management (DSM) has emerged as an important smart grid feature that allows utility companies to maintain desirable grid loads. However, the success of DSM is contingent on active customer participation. Indeed, most existing DSM studies are based on game-theoretic models that assume customers will act rationally and will voluntarily participate in DSM. In contrast, in this paper, the impact of customers’ subjective behavior on each other’s DSM decisions is explicitly accounted for. In particular, a noncooperative game is formulated between grid customers in which each customer can decide on whether to participate in DSM or not. In this game, customers seek to minimize a cost function that reflects their total payment for electricity. Unlike classical game-theoretic DSM studies, which assume that customers are rational in their decision-making, a novel approach is proposed based on the framework of prospect theory (PT) to explicitly incorporate the impact of customer behavior on DSM decisions. To solve the proposed game under both conventional game theory and PT, a new algorithm based on fictitious play is proposed using which the game will reach an @math -mixed Nash equilibrium. Simulation results are provided to assess the impact of customer behavior on DSM. In particular, the overall participation level and grid load can depend significantly on the rationality level of the players and their risk aversion tendencies. Considerable developments in the real-time telemetry of demand-side systems allow independent system operators (ISOs) to use reserves provided by demand response (DR) in ancillary service markets. Currently, many ISOs have designed programs to utilize the reserve provided by DR in electricity markets. This paper presents a stochastic model to schedule reserves provided by DR in the wholesale electricity markets. Demand-side reserve is supplied by demand response providers (DRPs), which have the responsibility of aggregating and managing customer responses. A mixed-integer representation of reserve provided by DRPs and its associated cost function are used in the proposed stochastic model. The proposed stochastic model is formulated as a two-stage stochastic mixed-integer programming (SMIP) problem. The first-stage involves network-constrained unit commitment in the base case and the second-stage investigates security assurance in system scenarios. The proposed model would schedule reserves provided by DRPs and determine commitment states of generating units and their scheduled energy and spinning reserves in the scheduling horizon. The proposed approach is applied to two test systems to illustrate the benefits of implementing demand-side reserve in electricity markets. In this paper, we apply the game theory to study some strategic actions for retailers to fight a price war. We start by modeling a noncooperative pure pricing game among multiple competing retailers who sell a certain branded product under price-dependent stochastic demands. A unique Nash equilibrium is proven to exist under some mild conditions. We demonstrate mathematically the incentives for retailers to start a price war. Based on a strategic framework via the game theory, we illustrate the use of service level to build price walls which can prevent a huge drop in price, as well as profit. Three kinds of price walls are proposed, and the respective strengths and weaknesses have been studied. Analytical conditions, under which a price wall can effectively prevent big drops in both market share and profit, are developed. Aside from the proposed price walls, two other pricing strategies, which can lead to an all-win situation, are examined. This paper presents two different approaches to model expansion planning in electricity markets under imperfect competitive conditions. Both approaches consider a market in which firms compete in quantity as in the Nash-Cournot game. However, the two models differ from each other in how each firm makes its expansion-planning decisions. In the first model, the key assumption that permits its formulation as a Mixed Linear Complementarity Problem (LCP) is that firms not only decide their output in a Cournot manner but also their new generating capacity. In contrast, in the second model, there is a leader firm that anticipates the reaction of the follower firms as in the Stackelberg game. The latter model is formulated as a Mathematical Program with Equilibrium Constraints (MPEC), wherein the leader firm decides its optimal new capacity subject to a set of market equilibrium constraints. Both models have been implemented in GAMS. A simple example is also presented to illustrate their comparison and application. This paper summarizes the results from an exploratory analysis of residential customer response to a critical peak pricing (CPP) experiment in California, in which 15 times per year participating customers received high price signals dispatched by a local electricity distribution company. The high prices were about three times the on-peak price for the otherwise applicable time-of-use rate. Using hourly load data collected during the 15-month experiment, we find statistically significant load reduction for participants both with and without automated end-use control technologies. During 5-h critical peak periods, participants without control technology used up to 13 less energy than they did during normal peak periods. Participants equipped with programmable communicating thermostats used 25 and 41 less for 5 and 2h critical events, respectively. Thus, this paper offers convincing evidence that the residential sector can provide substantial contributions to retail demand response, which is considered a potential tool for mitigating market power, stabilizing wholesale market prices, managing system reliability, and maintaining system resource adequacy. The dynamic spectrum market (DSM) is a key economic vehicle for realizing the opportunistic spectrum access that will mitigate the anticipated spectrum-scarcity problem. DSM allows legacy spectrum owners to lease their channels to unlicensed spectrum consumers (or secondary users) in order to increase their revenue and improve spectrum utilization. In DSM, determining the optimal spectrum leasing price is an important yet challenging problem that requires a comprehensive understanding of market participants' interests and interactions. In this paper, we study spectrum pricing competition in a duopoly DSM, where two wireless service providers (WSPs) lease spectrum access rights, and secondary users (SUs) purchase the spectrum use to maximize their utility. We identify two essential, but previously overlooked, properties of DSM: 1) heterogeneous spectrum resources at WSPs and 2) spectrum sharing among SUs. We demonstrate the impact of spectrum heterogeneity via an in-depth measurement study using a software-defined radio (SDR) testbed. We then study the impacts of spectrum heterogeneity on WSPs' optimal pricing and SUs' WSP selection strategies using a systematic three-step approach. First, we study how spectrum sharing among SUs subscribed to the same WSP affects the SUs' achievable utility. Then, we derive the SUs' optimal WSP selection strategy that maximizes their payoff, given the heterogeneous spectrum propagation characteristics and prices. We analyze how individual SU preferences affect market evolution and prove the market convergence to a mean-field limit, even though SUs make local decisions. Finally, given the market evolution, we formulate the WSPs' pricing strategies in a duopoly DSM as a noncooperative game and identify its Nash equilibrium points. We find that the equilibrium price and its uniqueness depend on the SUs' geographical density and spectrum propagation characteristics. Our analytical framework reveals the impact of spectrum heterogeneity in a real-world DSM, and can be used as a guideline for the WSPs' pricing strategies. Frequent call markets have been proposed as a market design solution to the latency arms race perpetuated by high-frequency traders in continuous markets, but the path to widespread adoption of such markets is unclear. If such trading mechanisms were available, would anyone want to use them? This is ultimately a question of market choice, thus we model it as a game of strategic market selection, where agents choose to participate in either a frequent call market or a continuous double auction. Our market environment is populated by fast and slow traders, who reenter to trade at different rates. We employ empirical game-theoretic methods to determine the market types and trading strategies selected in equilibrium. We also analyze best-response patterns to characterize the frequent call market’s basin of attraction. Our findings show that in equilibrium, welfare of slow traders is generally higher in the call market. We also find strong evidence of a predator-prey relation between fast and slow traders: the fast traders chase agents into either market, and slow traders under pursuit seek the protection of the frequent call market. The classic Vickrey-Clarke-Groves (VCG) mechanism ensures incentive compatibility, i.e., that truth-telling of all agents is a dominant strategy, for a static one-shot game. However, in a dynamic environment that unfolds over time, the agents' intertemporal payoffs depend on the expected future controls and payments, and a direct extension of the VCG mechanism is not sufficient to guarantee incentive compatibility. In fact, it does not appear to be feasible to construct mechanisms that ensure the dominance of dynamic truth-telling for agents comprised of general stochastic dynamic systems. The contribution of this paper is to show that such a dynamic stochastic extension does exist for the special case of Linear-Quadratic-Gaussian (LQG) agents with a careful construction of a sequence of layered payments over time. We propose a layered version of a modified VCG mechanism for payments that decouples the intertemporal effect of current bids on future payoffs, and prove that truth-telling of dynamic states forms a dominant strategy if system parameters are known and agents are rational. An important example of a problem needing such optimal dynamic coordination of stochastic agents arises in power systems where an Independent System Operator (ISO) has to ensure balance of generation and consumption at all time instants, while ensuring social optimality (maximization of the sum of the utilities of all agents). Addressing strategic behavior is critical as the price-taking assumption on market participants may not hold in an electricity market. Agents, can lie or otherwise game the bidding system. The challenge is to determine a bidding scheme between all agents and the ISO that maximizes social welfare, while taking into account the stochastic dynamic models of agents, since renewable energy resources such as solar wind are stochastic and dynamic in nature, as are consumptions by loads which are influenced by factors such as local temperatures and thermal inertias of facilities. In this paper, we study the Nash dynamics of strategic interplays of n buyers in a matching market setup by a seller, the market maker. Taking the standard market equilibrium approach, upon receiving submitted bid vectors from the buyers, the market maker will decide on a price vector to clear the market in such a way that each buyer is allocated an item for which he desires the most (a.k.a., a market equilibrium solution). While such equilibrium outcomes are not unique, the market maker chooses one (maxeq) that optimizes its own objective --- revenue maximization. The buyers in turn change bids to their best interests in order to obtain higher utilities in the next round's market equilibrium solution. This is an (n+1)-person game where buyers place strategic bids to gain the most from the market maker's equilibrium mechanism. The incentives of buyers in deciding their bids and the market maker's choice of using the maxeq mechanism create a wave of Nash dynamics involved in the market. We characterize Nash equilibria in the dynamics in terms of the relationship between maxeq and mineq (i.e., minimum revenue equilibrium), and develop convergence results for Nash dynamics from the maxeq policy to a mineq solution, resulting an outcome equivalent to the truthful VCG mechanism. Our results imply revenue equivalence between maxeq and mineq, and address the question that why short-term revenue maximization is a poor long run strategy, in a deterministic and dynamic setting. Empirical game-theoretic analysis (EGTA) has recently been applied successfully to analyze the behavior of large numbers of competing traders in a continuous double auction market. Multiagent simulation methods like EGTA are useful for studying complex strategic environments like a stock market, where it is not feasible to solve analytically for the rational behavior of each agent. A weakness of simulation-based methods in strategic settings, however, is that it is typically impossible to prove that the strategy profile assigned to the simulated agents is stable, as in a Nash equilibrium. I propose using reinforcement learning to analyze the regret of supposed Nash-equilibrium strategy profiles found by EGTA. I have developed a new library of reinforcement learning tools, which I have integrated into an extended version of the market simulator from our prior work. I provide evidence for the effectiveness of our library methods, both on a suite of benchmark problems from the literature, and on non-equilibrium strategy profiles in our market environment. Finally, I use our new reinforcement learning tools to provide evidence that the equilibria found by EGTA in our recent continuous double auction study are likely to have only negligible regret, even with respect to an extended strategy space. This paper proposes a cooperative demand response scheme for price-anticipating buildings in smart grid. The cooperative demand response scheme is formulated as a constrained social optimization problem. We develop a cooperative strategy and obtain a Pareto-optimal solution from the constrained social optimization problem. Comparing with the Nash equilibrium obtained from the one-stage demand management game, the Pareto-optimal solution reduces the electricity costs to all the building managers. We further align this Pareto-optimal solution with the subgame perfect Nash equilibrium of a repeated demand management game and develop an incentive-compatible trigger-and-punishment mechanism to avoid the noncooperative behavior of the building managers. Numerical results demonstrate that the cooperative demand response scheme can reduce the electricity costs, the electricity price, and the total energy consumption. We formalize the current practice of strategic mining in multi-cryptocurrency markets as a game, and prove that any better-response learning in such games converges to equilibrium. We then offer a reward design scheme that moves the system configuration from any initial equilibrium to a desired one for any better-response learning of the miners. Our work introduces the first multi-coin strategic attack for adaptive and learning miners, as well as the study of reward design in a multi-agent system of learning agents. Noncooperative game theory provides a normative framework for analyzing strategic interactions. However, for the toolbox to be operational, the solutions it defines will have to be computed. In this paper, we provide a single reduction that 1) demonstrates NP-hardness of determining whether Nash equilibria with certain natural properties exist, and 2) demonstrates the NP-hardness of counting Nash equilibria (or connected sets of Nash equilibria). We also show that 3) determining whether a purestrategy Bayes-Nash equilibrium exists is NP-hard, and that 4) determining whether a pure-strategy Nash equilibrium exists in a stochastic (Markov) game is PSP ACE-hard even if the game is invisible (this remains NP-hard if the game is finite). All of our hardness results hold even if there are only two players and the game is symmetric. We study the demand side management (DSM) problem when customers are equipped with energy storage devices. Two games are discussed: the first is a non-cooperative one played between the residential energy consumers, while the second is a Stackelberg game played between the utility provider and the energy consumers. We introduce a new cost function applicable to the case of users selling back stored energy. The non-cooperative energy consumption game is played between users who schedule their energy use to minimize energy cost. The game is shown to have a unique Nash equilibrium, that is also the global system optimal point. In the Stackelberg game, the utility provider sets the prices to maximize its profit knowing that users will respond by minimizing their cost. We provide existence and uniqueness results for the Stackelberg equilibrium. The Stackelberg game is shown to be the general case of the minimum Peak-to-Average power ratio (PAR) problem. Two algorithms, centralized and distributed, are presented to solve the Stackelberg game. We present results that elucidate the interplay between storage capacity, energy requirements, number of users and system performance measured in total cost and peak-to-average power ratio (PAR). Due to the stochastic nature of wind power, its large-scale integration into the power grid requires techniques to constantly balance the load with the time-varying supply. This can be done via smart scheduling of energy consumption and storage units among end users. In this paper, we propose a game-theoretic algorithm to be implemented in an aggregator in order to coordinate the operation of demand-side resources via pricing in order to tackle the intermittency and fluctuations in wind power generation. The demand-side resources to be considered are both non-shiftable and shiftable load, in particular, electric vehicles that charge or discharge their batteries to provide extra resource management flexibility. After formulating the interactions in an aggregator-consumer system as a game, we analytically prove the existence and uniqueness of the Nash equilibrium in the formulated game model. Simulation results show that our proposed design scheme can benefit both end users (in terms of reducing energy expenses) and the power grid (in terms of integrating wind power). In this paper, the cross-layer design problem of joint multiuser detection and power control is studied, using a game-theoretic approach that focuses on energy efficiency. The uplink of a direct-sequence code-division multiple-access data network is considered, and a noncooperative game is proposed in which users in the network are allowed to choose their uplink receivers as well as their transmit powers to maximize their own utilities. The utility function measures the number of reliable bits transmitted by the user per joule of energy consumed. Focusing on linear receivers, the Nash equilibrium for the proposed game is derived. It is shown that the equilibrium is one where the powers are signal-to-interference-plus-noise ratio-balanced with the minimum mean-square error (MMSE) detector as the receiver. In addition, this framework is used to study power-control games for the matched filter, the decorrelator, and the MMSE detector; and the receivers' performance is compared in terms of the utilities achieved at equilibrium (in bits joule). The optimal cooperative solution is also discussed and compared with the noncooperative approach. Extensions of the results to the case of multiple receive antennas are also presented. In addition, an admission-control scheme based on maximizing the total utility in the network is proposed.