In this paper, an electric vehicle (EV) charging competition, among EV aggregators that perform coordinated EV charging, is explored while taking into consideration potential non-ideal actions of the aggregators. In the coordinated EV charging strategy presented in this paper, each aggregator determines EV charging start time and charging energy profiles to minimize overall EV charging energy cost by including consideration of the actions of the neighboring aggregators. The competitive interactions of the aggregators are modeled by developing a two-stage non-cooperative game among the aggregators. The game is then studied under prospect theory to examine the impacts of non-ideal actions of the aggregators in selecting EV charging start times according to subjectively evaluating their opponents' actions. It is shown that the non-cooperative interactions among the aggregators lead to a subgame perfect @math -Nash equilibrium when the game is played with either ideal, or non-ideal, actions of the aggregators. A case study presented demonstrates that the benefits of the coordinated EV charging strategy, in terms of energy cost savings and peak-to-average ratio reductions, are significantly resilient to non-ideal actions of the aggregators.
Empirical evidence from social studies has illustrated that the axiom of rationality of game theory can be violated when users face risk and uncertainty in decision-making @cite_44 . In @cite_28 , discrepancies between rational choice and alternative user behavioral models in an energy market are reviewed. Prospect theory has attracted great attention in various research communities to understand impacts of deviations from rationality @cite_13 @cite_8 @cite_31 . A comprehensive discussion on the potential of prospect theory to understand how decision-making under risk and uncertainty can affect various smart grid applications is given in @cite_40 . In @cite_16 , optimal energy exchange among geographically-distributed consumer-owned energy storage devices is compared under classical game theory and prospect theory. In @cite_9 , the effects of subjective consumer behavior on an energy storage charging-discharging system are investigated using a utility framing method derived from prospect theory. In contrast to previous work, this paper presents precepts of prospect theory to realize potential non-ideal behavior of EV aggregators in a non-cooperative game-theoretic EV charging system.
@cite_8 @cite_28 @cite_9 @cite_44 @cite_40 @cite_31 @cite_16 @cite_13
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In this paper, the problem of optimally charging or discharging customer-owned storage units in a smart grid is studied. In particular, a noncooperative game is formulated between customers equipped with distributed storage units who seek to decide on their optimal charging strategy so as to optimize a utility that reflects both the monetary benefit from the charging discharging operation and the associated penalty from power regulation. In contrast to the traditional game-theoretic models that are often based on rational and objective decisions, we introduce the behavioral framework of prospect theory (PT) so as to explicitly incorporate how the customers estimate their utilities with respect to their real-world considerations of gains and losses. The existence of the mixed-strategy Nash equilibrium is shown for the PT case and the properties of the game are analyzed under both PT and classical game theory. Simulation results show how the individual customer perceptions on their utilities can significantly impact the overall charging and discharging operations. This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low prob- abilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. EXPECTED UTILITY THEORY has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice (24), and widely applied as a descriptive model of economic behavior, e.g. (15, 4). Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory (47, 36), and that most people actually do, most of the time. The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. In the light of these observations we argue that utility theory, as it is commonly interpreted and applied, is not an adequate descriptive model and we propose an alternative account of choice under risk. 2. CRITIQUE Active consumer participation is seen as an integral part of the emerging smart grid. Examples include demand-side management programs, incorporation of consumer-owned energy storage or renewable energy units, and active energy trading. However, despite the foreseen technological benefits of such consumer-centric grid features, to date, their widespread adoption in practice remains modest. To shed light on this challenge, this paper explores the potential of prospect theory, a Nobel-prize winning theory, as a decision-making framework that can help understand how risk and uncertainty can impact the decisions of smart grid consumers. After introducing the basic notions of prospect theory, several examples drawn from a number of smart grid applications are developed. These results show that a better understanding of the role of human decision-making within the smart grid is paramount for optimizing its operation and expediting the deployment of its various technologies. 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. In this paper, the interactions and energy exchange decisions of a number of geographically distributed storage units are studied under decision-making involving end-users. In particular, a noncooperative game is formulated between customer-owned storage units where each storage unit's owner can decide on whether to charge or discharge energy with a given probability so as to maximize a utility that reflects the tradeoff between the monetary transactions from charging discharging and the penalty from power regulation. Unlike existing game-theoretic works which assume that players make their decisions rationally and objectively, we use the new framework of prospect theory (PT) to explicitly incorporate the users' subjective perceptions of their expected utilities. For the two-player game, we show the existence of a proper mixed Nash equilibrium for both the standard game-theoretic case and the case with PT considerations. Simulation results show that incorporating user behavior via PT reveals several important insights into load management as well as economics of energy storage usage. For instance, the results show that deviations from conventional game theory, as predicted by PT, can lead to undesirable grid loads and revenues thus requiring the power company to revisit its pricing schemes and the customers to reassess their energy storage usage choices. Game theoretic models have found widespread use in the analysis and design of radio resource management algorithms for a wide variety of systems such as cellular, ad hoc and sensor networks. The fundamental principle behind such models and much of game theory has been the reliance on expected utility theory (EUT). In this paper, we consider a simple wireless random access game where instead of following the precepts of EUT, the players follow the precepts of Prospect Theory (PT), a theory developed by Kahneman and Tversky to explain real-life decision making that often deviates from the behavior expected under EUT. Specifically, we consider a game where selfish players adjust their transmission probabilities over a collision channel according to rewards received for successful transmission while incurring energy and delay costs. We compare and contrast the Nash equilibria achieved under both EUT and PT and highlight the differences in them.