Towards a Consumer-Centric Grid: A Behavioral Perspective
Walid Saad1, Arnold Glass2 , Narayan Mandayam3, and H. Vincent Poor4
1

Wireless@VT, Bradley Deparmtent of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA, USA, Email: walids@vt.edu
2
Department of Psychology, Rutgers University, New Brunswick, NJ, USA, Email: aglass@rci.rutgers.edu
3
Electrical and Computer Engineering Department, Rutgers University, New Brunswick, NJ, USA, Email: narayan@winlab.rutgers.edu
4
Electrical Engineering Department, Princeton University, Princeton, NJ, USA, E-mail: poor@princeton.edu

arXiv:1511.01065v1 [] 1 Nov 2015

Abstract—Active consumer participation is seen as an integral
part of the emerging smart grid. Examples include demandside 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 decisionmaking within the smart grid is paramount for optimizing
its operation and expediting the deployment of its various
technologies.

I. I NTRODUCTION

The electric power grid has undergone unprecedented
changes over the past few years. The traditional, hierarchical and centralized electric grid has transformed into a
large-scale, decentralized, and “smart” grid [1]–[4]. Such a
smart grid is expected to encompass a mix of devices, as
shown in Fig. 1, that include distributed renewable energy
sources, electric vehicles (EVs), and storage units that can
be actively controlled and operated via a reliable, two-way
communication infrastructure [1]. The effective operation of
such a heterogeneous and decentralized system is expected to
change the way in which energy is produced and delivered to
consumers.
One key byproduct of the smart grid evolution is an
ability to deliver innovative energy management services to
consumers [1]–[4]. Here, energy management refers to the
processes using which energy is generated, managed, and
delivered to consumers in the grid. For instance, demand-side
management (DSM) and demand response mechanisms will
be an integral part of the smart grid. The primary goal of such
programs is to dynamically shape and manage the supply and
demand on the grid in order to maintain a desirable load over
various timescales. Indeed, the design of optimized DSM and
demand response protocols and associated pricing schemes
has led to significant research in this area in recent years [5]–
[37].
This research is supported by the U.S. National Science Foundation under
Grants CNS-1446621, ECCS-1549894, ECCS-1549900, and ECCS-1549881.
Dr. Saad was a corresponding author.

Fig. 1. A future smart grid with a heterogeneous mix of storage units, EVs,
renewable sources, and other consumer-owned equipment.

Moreover, in the smart grid, consumers will be able to
individually own energy production units, such as solar panels,
as well as storage devices in the form of EVs or small batteries. This can potentially transform every smart grid consumer
into an independent energy production and storage source.
Consequently, the possibility of energy trading between such
well-equipped consumers will undoubtedly become a reality
in the next few years. Indeed, many recent works, such as in
[8], [38]–[66], have investigated the various challenges of such
large-scale energy exchange, which include the development
of optimized market mechanisms, the management of the
grid operation, and the optimized exploitation of available
consumer-owned storage and energy production units.
Realizing this vision of a distributed, sustainable, and
consumer-centric smart grid will naturally face many challenges. On the one hand, although DSM programs (and
related ideas) have been theoretically shown to yield important
technological benefits to the grid, their wide-spread deployment still remains insipid [67]–[73]. On the other hand, the
impact of energy trading on the smart grid operation and
the realistic assumption that every consumer can become a
producer of energy is still not well-understood. In addition,
how to maximize the amount of energy that stems from
renewable sources is yet another important challenge. Last but
not least, the design of efficient dynamic pricing mechanisms
that go hand-in-hand with DSM and energy trading schemes
is seen as a critical enabler for most of the foreseen smart
grid features.
To widely deploy such grid features, one important chal-

lenge, among many others, is to properly incentivize consumers to actively participate in emerging grid features.
For example, without effective adoption of DSM schemes
by consumers, power companies will not be able to reap
the technological benefits of such load-shaping mechanisms.
Similarly, the willingness of consumers to own and actively
utilize EVs, storage units, or even renewable sources, is an
essential milestone for the deployment of a truly sustainable,
consumer-centric smart grid. For example, the statistics in [71]
show that installed solar generating capacity has increased
from about 1000 MW in 2010 to more than 6000 MW in 2014.
However, residential capacity has only increased from about
200 MW in 2010 to about 1000 MW in 2014. The reasons for
this small growth are touched upon in [72] – the upfront cost
of $21,000 - $25,000 is more than most homeowners have
to risk on what is still an uncertain venture. Clearly, coupled
with a properly designed and cost-effective ICT infrastructure,
active consumer participation plays an instrumental role in
facilitating the adoption of some of the smart grid technologies
and features.
However, somewhat remarkably, most of the existing research in this area is still based on formal mathematical
constructs, such as game theory or classical optimization,
which presume that consumers are objective, rational entities
that are uninfluenced by real-world behavioral considerations.
While such an assumption will hold in a highly-centralized,
traditional power system, it will remain an important barrier
that has prevented the widespread adoption of the smart grid.
The primary goal of this article is to shed light on the role
of consumer participation in the grid, while exposing the role
of the Nobel-prize winning framework of prospect theory,
in providing a mathematical basis within which to better
understand how consumer behavior and realistic smart grid
considerations impact the operation and efficiency of smart
energy management mechanisms such as DSM, energy trading, and storage management. To this end, we first provide an
overview of important energy management services in which
consumer participation plays an important role. For each such
service, we expose the state of the art and discuss the key
assumptions and limitations. Then, we present the basics of
prospect theory and discuss the motivation for applying this
framework in a smart grid environment. We illustrate the
benefits of prospect theory via two simple examples pertaining
to energy storage management and DSM. We conclude by
providing a future roadmap on how behavioral studies can
play an instrumental role in future smart grid designs.
The rest of this paper is organized as follows: Section II
presents an overview on existing energy management literature. In Section III, we provide a tutorial on the framework of
prospect theory and its motivation. Then, in Section IV, we
discuss two smart grid examples. Finally, Section V draws
some conclusions and future work.

II. E NERGY M ANAGEMENT IN
R EVIEW

THE

S MART G RID : A

Owing to the deployment of a smart communication infrastructure and to the presence of new devices, such as storage
units, smart meters, and renewable sources, the smart grid
presents numerous new opportunities for energy production
and distribution that were not possible in a classical grid.
For instance, the possibility of deploying smart meters at
consumer premises, opens the door for enabling consumers to
actively manage their energy. In addition, the ability of a smart
meter to communicate in real-time with a power company’s
control center, provides the latter with various opportunities
to actively control and monitor energy usage. Such new
capabilities undoubtedly change the way in which energy is
generated and distributed to consumers. Clearly, smart energy
management protocols and mechanisms are needed to exploit
the opportunities brought forward by this new smart grid
infrastructure.
Deploying efficient energy management mechanisms in future smart grid systems faces many challenges. The first such
challenge is to actively utilize smart metering and consumerbased energy management systems to shape the overall grid
load over time. Such load shaping is quintessential for an
efficient operation of a large-scale smart grid. Enabling such
demand-side management requires both increased automation
and active participation by the grid consumers. Another important challenge is to properly integrate and exploit storage
devices in the grid. For instance, on the one hand, a power
company can make use of EVs to store energy reserves so
as to regulate the grid operation. In this example, the power
company will be submitting an offer for ancillary services to
an independent system operator (ISO). On the other hand, a
consumer-based storage unit can be used as a means to store
or even sell energy back to the power company (rather than
an ISO). Last but not least, an important energy management
challenge is to properly decide on how to integrate and utilize
consumer-based power sources, such as solar panels, within
an operating smart grid system.
In summary, energy management in the smart grid involves
the planning and operation of energy-related production and
consumption units, particulary when such units are consumerowned. Next, we summarize some of the main research topics
related to energy management in the smart grid.
A. Demand-side Management
Demand-side management and demand response programs
are arguably the most important form of energy management
in the smart grid. DSM can entail a broad range of programs. These programs range from classical direct consumer
load control to peak shaving programs and ancillary service
provisions. Naturally, each such DSM program has its own
challenges. Here, we will summarize some of these programs,
while emphasizing the role of consumers. For example, in
peak shaving or direct load control programs, DSM schemes

typically aim at encouraging consumers to change their energy
consumption habits during peak hours. In particular, such
load control DSM schemes aim at providing consumers with
incentives to shift their unnecessary grid load to various times
during the day, so as to shape the peak hour load on the grid.
For example, a simple DSM scheme can provide monetary
benefits to consumers if they use delay-tolerant equipment,
such as dish washers or washing machines, during the night,
instead of peak hours [5]–[37]. Even if the individual appliance consumption can be small, the participation of consumers
at scale, such as within a neighborhood or city, will significantly impact the smart grid. Moreover, DSM will also extend
to other types of consumer-owned devices, such as storage
units or renewable energy sources whose consumption and
usage might be more significant than standard appliances [5]–
[37]. Last but not least, consumers of DSM need not only be
home users, but they can extend to industry and even small,
local energy providers that work hand-in-hand with the power
company. In such cases, significant gains for both consumers
and power companies can be achieved if DSM is properly
implemented [73].
1) Challenges: The key challenge in DSM is to design
realistic incentive mechanisms that can be used by power
companies and consumers alike to manage their power consumption over time. The essence of demand-side management
revolves around modeling the interactions and decision making processes of various grid players whose goals and actions
are largely interdependent. For example, the change in the
load of a certain consumer can lead to change in the pricing
scheme used by the power company which, in turn, can lead
to a change in the behavior of other consumers. This large
coupling in the behavior and goals of the grid consumers has
led to an abundant literature that applies the mathematical
framework of game theory [74] to analyze and design efficient
DSM schemes.
Game theory is a mathematical framework that enables
one to model the decision making processes of a number
of players whose objectives are largely interdependent. The
merits of a game-theoretic approach for DSM include: 1)
ability to capture the heterogeneity of the devices in the
grid, 2) effective integration of consumer-based decisions,
3) synergy between game-theoretic designs and the design
of incentive mechanisms, and 4) low-complexity learning
mechanisms that can characterize the outcome of a game and
that can be practically implemented in a real-world smart grid.
2) State-of-the-art: There has been a surge in research
activities related to DSM in recent years [5]–[37]. As already
mentioned, the majority of these works adopts a gametheoretic approach to demand-side management.
One of the earliest works in this area is [5] which presents
a DSM model in which the users are able to decide on how
to schedule their appliances over a given time horizon. The
basic idea is simple: each consumer selects a certain schedule
for its appliances, in such a way so as to minimize its overall

cost; given a fixed, yet well-designed pricing scheme from
the company. Using a game-theoretic model, the authors in
[5] characterize the eventual operating system of the grid and
show that, under the assumption that users are rational and
will act strategically, significant reductions in the overall grid
load can be foreseen using such a DSM scheme.
The recent work in [6] extends the model of [5] by including
the power company as a player in the system. In this regard,
following a grid model similar to [5], the authors enable
the power company to strategically decide on its pricing
depending on the total power. The objective is to reduce
the peak-to-average ratio (PAR) of the load demand. Using
numerical simulations, the authors establish the merits of such
a DSM scheme and show that noticeable reduction in the PAR
can be harnessed via dynamic pricing that adapts to the users’
behavior.
Another key contribution on DSM is presented in [7]. In
this work, the goal is not to reduce peak hour consumption,
but rather to match the supply and demand. Depending on
whether there is a deficit or excess of energy, the proposed
game-theoretic market model incentivizes the consumers to
either increase or shed their load so as to match the supply
and maintain normal grid operation. Thus, this work highlights
an interesting use of DSM for regulating the overall grid
operation, rather than just for reducing or shifting load over
time.
The work in [8] studies, using a game-theoretic and optimization framework, the ability of consumers to coordinate
the way in which they defer their grid load, based on the
power company’s pricing scheme. In particular, the authors
observe that, when DSM protocols leave the smart meters to
react independently, in an uncoordinated manner, to pricing
fluctuations, new peak hours may be created thus defeating
the main purpose of a DSM scheme. To this end, the authors
propose a coordination mechanism between a large population
of smart grid consumers. In this mechanism, instead of
directly reacting to the pricing change, smart meters, acting
on behalf of users, aim to adapt the deferment of loads to
the changes in the price. One of the key contributions of this
work is to consider such a coordination over a large number
of consumers. The results, based on realistic, empirical market
models from the UK, show that such a coordinated DSM
approach can reduce peak hour demand while also reducing
carbon emissions.
In [9], an interesting game-theoretic framework was developed to answer an important question: what is the value of
DSM and demand response mechanisms in the smart grid.
Essentially, the system is viewed as a noncooperative, hierarchical game between a number of generation companies and
the consumers. On the one hand, the generation companies
are controlled by the utility operator who can determine
their production level. On the other hand, the consumers are
aggregated into one collective decision maker, who responds
to a pricing signal sent out by the operator, to determine

the overall consumption level. Using this model, it has been
shown that the use of a demand response mechanism can,
in some cases, be more beneficial to generation companies
than to consumers. This benefit is largely dependent on how
consumers respond to the pricing scheme. Therefore, this work
has yet again shown that the way in which consumers behave
must be properly modeled if one is to reap the benefits of a
technology such as DSM.
Building on those key contributions, a number of equally
interesting DSM schemes have emerged more recently [10]–
[37] expanding on the aforementioned works by developing
more advanced models such as those that integrate additional
players or other energy efficiency metrics.
3) Summary and Remarks: Clearly, existing research has
established the technological benefits of DSM. Indeed, most
of the existing works such as in [5], [6], [8]–[37], have shown
that under fairly realistic scenarios, DSM can yield significant
reduction in peak hour load and can provide an interesting
means for regulating the overall operation of the grid. The
nexus of these existing works remains a game-theoretic model
in which various interactive scenarios between the users and
one or more utility providers are modeled. The outcomes
include a broad range of pricing mechanisms and load-shifting
scheduling algorithms that can be implemented to optimize
various energy efficiency metrics, such as peak hour load,
PAR, and load regulation metrics. Undoubtedly, DSM and
related ideas are likely to become an important component
of the smart grid.
Alas, despite this established gains of DSM, the real-world
implementation of such programs (and related ideas) has
remained below expectations [67]–[73]. One of the underlying
reasons is that, in real life, consumers are not behaving the
way they are supposed to, as assumed by many existing
mathematical models. In this regard, most of these existing
models rely on the assumption that players are rational and
will act objectively when faced with a DSM decision. In other
words, these models presume that, in the real-world, consumer
behavior will follow strictly objective measures of benefits
and losses, when deciding on whether or not to subscribe to a
DSM scheme or when choosing on how to schedule appliance
usage. However, realistically, consumers may deviate from the
rational behavior to various factors. For example, on a cold
winter day, consumers may be reluctant to shift their heating
consumption to a later time of the day, even if such a shift can
be beneficial to the grid or can bring some economic benefit
to the consumers.
Clearly, within the context of DSM, there is an urgent
need to capture such “behavioral” factors when designing the
demand response mechanisms of the future. Without a careful
accounting for the behavioral side, the real-world adoption of
DSM mechanisms will not live up to the expectations.

B. Integration of Storage Units and Consumer-Owned Renewable Sources
Beyond DSM and demand response mechanisms, energy
management in the smart grid must account for the presence
of a variety of new devices that are expected to be deployed in
the near future. Such devices include EVs, storage units, and
renewable energy sources. While renewable energy sources
may be owned by energy providers or consumers, the majority
of EVs and storage units are expected to be consumerowned. The presence of such new components in the power
grid presents an interesting opportunity for deploying evolved
energy trading mechanisms [41], [57]–[63].
In particular, the ability of consumers to store energy or
possibly feed energy back into the grid, via either their storage
units or their owned renewable sources, will pave the way
towards a large-scale exchange of energy within the grid. For
example, on the one hand, consumers with a surplus of energy
may decide to send this energy back into the grid, to improve
grid regulation and reap some possible monetary benefits. On
the other hand, the power company may utilize EVs or other
storage units as a means to store energy reserves or to regulate
the grid frequency [43]–[45], [52]–[56]. Indeed, if properly
managed, the charging and discharging behavior of EVs and
storage units can yield significant technological and economic
benefits for power companies and consumers alike [8], [38]–
[66].
In a nutshell, the effective integration and exploitation of
storage units and consumer-owned renewable sources will
be an essential property of the future smart grid. How to
efficiently exploit such devices to improve the delivery, production, and management of smart grid energy is thus an
important problem that must be addressed.
1) Challenges: The challenges of integrating energy storage and renewable sources are numerous. From a power system point of view, the intermittent nature of renewable sources
will require fundamentally new ways to operate energy production and generation in the grid. How to develop stochastic
optimization algorithms that can adapt to this intermittency
is thus a key challenge. In addition, the foreseen large-scale
deployment of EVs will present an unprecedented increase
in the load on the grid. Here, effective DSM mechanisms, as
those discussed in the previous section, which can manage the
EVs load will be needed. Nonetheless, storage units and EVs
also provide an opportunity for the power grid to store any
excess or mismatch in the generation and demand, so as to
regulate the overall grid operation.
More relevant to this article are the challenges pertaining
to the use of storage units and consumer-owned renewables
within energy trading markets. In particular, it is foreseen
that local markets in which consumers may directly exchange
energy with one another or with the grid can be set up in the
future smart grid. Such markets are enabled by the presence of
storage units, EVs, and consumer-owned generation sources.
Important challenges here include: 1) devising economic

mechanisms that incentivize consumers, power companies,
and energy providers to setup such markets, 2) analyzing
the impact of such localized markets on grid operation,
and 3) integrating such energy trading within existing DSM
mechanisms.
2) State-of-the-art: Integrating storage units and renewable
energy sources has been a topic of significant interest to the
smart grid community in recent years [8], [38]–[66], [75]–
[84]. Beyond the works that focus primarily on the power
system operation side [75]–[84], there has been a number of
interesting works that investigate the usage of storage, EVs,
and renewables, to shape the overall grid load and to establish
energy trading markets [8], [38]–[66].
The earliest work in this area is in [38] in which a gametheoretic framework is developed to analyze how consumers
equipped with storage unit can smartly decide on when
to buy or store energy, in a local smart grid area. The
presented scheme is essentially a modified DSM protocol
which explicitly factors in the presence of storage units. The
market price is assumed to be pre-determined using an auction
mechanism and, thus, the work does not account for dynamic
pricing. Simulation results presented in [8] show that, based
on empirical data from the UK market, the use of storage at
consumer premises along with game-theoretic DSM protocol
can help in reducing the peak demand which also leads to
reduced costs and carbon emissions. The results also analyze
the benefit of storage and how it impacts the social welfare
of the system thus highlighting the possible practical impact
of storage unit integration.
One of the most interesting works that follows in this
direction is presented in [39]. In this contribution, the authors
study a DSM-like scheme in which users can be endowed with
storage units and renewable sources. In contrast to traditional
DSM schemes in which users only decide whether or not to
purchase energy from the grid, the model in [39] enables the
users to decide on whether to purchase, produce, or store
energy in their batteries. By expanding the decision space
of the users, it is shown, using a game-theoretic approach,
that a smart exploration of the storage and energy production
options can reduce the overall aggregate load on the grid
while also providing monetary savings to end-users, under
the assumption of rational decision making. Such a study
thus motivates the penetration of consumer-owned storage and
energy production units.
The effective integration of EVs into a smart grid system is
studied in [40] using a game-theoretic framework that models
the interactions between the grid operator and the EVs. The
primary goal is to analyze how EVs can provide ancillary
services to the grid, once a proper market model between EVs
and the grid is setup. The basic idea is to use a smart pricing
policy to exploit the EVs for regulating the grid frequency.
The idea is to study how EVs (and their owners) can decide
on whether to charge, discharge, or remain idle, in a way to
optimize the grid frequency regulation while benefiting both

consumers and the grid operator. On the one hand, using such
a scheme consumers can obtain additional income while, on
the other hand, the grid can achieve the required frequency
regulation command signal.
The impact of energy trading between owners of EVs is
further analyzed in our earlier work in [41]. In this work,
a local market in which EV owners can decide on whether
or not to sell a portion of their stored energy to the smart
grid is studied. Using an auction and a game-theoretic model,
we have shown that, when EV owners act strategically, they
are able to reap significant benefits from selling their surplus
of stored energy to potential buyers in the smart grid. These
benefits are reflected in terms of revenues that can be viewed
as either direct monetary gains or as coupons or other offers
provided from the grid owner to active participants.
The impact of distributed renewable energy sources on
local energy trading markets is analyzed in [42]. The authors
essentially propose the use of an aggregator of distributed
energy resources allowing the smart grid to engage in an open
energy exchange market. The developed mechanism tightly
integrates classical DSM ideas with the use of an active
management scheme at the end-users side to allow a better
utilization of the renewable energy sources. Overall, the results
show that a smart exploration of possibly consumer-owned
energy sources can lead to a sustainable source of energy and
a reduction in the consumers’ energy consumption cost.
Beyond the aforementioned contributions, the exploitation
of storage and renewable sources at consumer premises has
been studied in a broad range of literature [43]–[66]. These
works mainly develop variants of the discussed energy trading
mechanisms and establish clearly that the use of mathematical
optimization frameworks such as game theory to manage the
way in which storage devices, EVs, and consumer-owned
energy sources are integrated in the smart grid can bring
in substantial technological, economic, and environmental
benefits to the smart grid players.
3) Summary and Remarks: The use of energy trading
between consumer-owned devices will indisputably be an
important feature of the smart grid. As demonstrated in the
abundant literature, the associated gains, both from a technical
(energy reduction, sustainable generation) and an economic
(reduced costs on consumers and providers) point of view,
are substantial. Yet, despite these established results, beyond
some small deployments of EVs and renewable energy sources
in Europe and some areas of the United States [85]–[92],
the large-scale introduction of such consumer-owned devices
remains modest.
Similar to the DSM case, one of the primary limitations
of existing models is that they often do not explicitly factor
in realistic risk considerations of both consumers and power
companies. For instance, even though an open, energy trading
market can yield economic and technological benefits, power
companies may remain risk averse and continue to rely on
traditional, largely controlled markets. Similarly, despite the

prospective economic savings and environmental benefits of
owning renewable sources or EVs, consumers may still be
reluctant to change from their current, effective technologies.
Therefore, when analyzing energy trading, one must explicitly factor in such risk considerations and their impact on the
overall operation of smart energy management mechanisms.
III. P ROSPECT T HEORY FOR

THE

S MART G RID

A. Introduction and Motivation
As demonstrated in Section II, the existing literature on
smart energy management in the smart grid has established
significant technological, economic, and environmental benefits for features such as DSM and energy trading. Yet, the
real-world deployment of such mechanisms remains largely
below expectations. One of the hurdles facing the real-world
implementation of the developed DSM and energy management mechanisms, is the lack of a mathematical and empirical
framework that can capture the realistic behavioral patterns of
consumers and power companies.
Indeed, most existing works [5]–[66], [75]–[84] still assume that consumers and power companies are rational and
will abide by the objective decision making rules that are
derived via frameworks such as game theory or optimization.
However, in practice, empirical studies have shown that, in
uncertain and risky situations, human players may not act in
accordance with the rational behavior established by decision
making frameworks such as game theory [93]–[97]. Given
that most foreseen smart grid features are consumer-centric,
the “human” factor will undoubtedly play an instrumental role
in the success or failure of advanced smart grid features. Thus,
uncertainty and risk factors must be properly modeled in any
DSM or energy management scheme. Examples of risk in
the smart grid include the continuous reliance of operators on
traditional markets and the interdependence of the decisions
between consumers. In terms of uncertainty, when dealing
with an energy management scheme, consumers are faced with
uncertain outcomes due to a lack of transparency in explaining
the rules of dynamic pricing or due to the presence of
stochastic elements such as stochastic generation or uncertain
presence or absence of EVs and energy storage units.
Thus, expediting the smart grid adoption requires new
approaches for analyzing the often irrational and nonconforming nature of the energy management decisions of
human players under such risk and uncertainty. Such decisionmaking factors that deviate from the objective, rational behavior assumed in existing works [5], [6], [8]–[66], [75]–
[84] can be analyzed by the Nobel-prize winning framework
prospect theory (PT) [93]–[95], [98]. Originally conceived
for modeling decisions during monetary transactions such
as lottery outcomes, PT has made its way into many applications [93]–[100], due to the universal applicability of
its concepts. In essence, PT provides one with mathematical
tools to understand how decision making, in real life, can
deviate from the tenets of expected utility theory (EUT), a

conventional game-theoretic notion which is guided strictly
by objective notions of gains and losses, player rationality,
conformity to pre-determined decision making rules that are
unaffected by real-life perceptions of benefits and risk.
Illustrative Example: Essentially, PT notions have been
developed to understand how consumers, when faced with
uncertainty of outcome and risky decisions, will behave in
real-life. Suppose that an efficient energy management system
is constructed for individual home owners to both buy and sell
power on the grid and a dynamic pricing DSM mechanism is
available to shift consumption to non-peak periods. Furthermore, suppose that it has been proven that under PT as well as
conventional game theory, stable prices can be found, so that
the smart grid could ultimately result in more efficient power
consumption. Under rational analysis, one might believe when
these conditions were satisfied, offering the opportunity to
buy and sell power to the public would result in widespread
participation and an optimal pricing equilibrium would soon
be reached. However, an important implication of PT is that
these conditions are insufficient to guarantee such a beneficial
result.
One important implication of PT is that the preferred choice
between a pair of uncertain alternatives is not only determined
by the values of the two alternatives but also by how the choice
is stated. Consider the following example, which is unnatural
only in that the alternatives are designed to have equal value,
so that a preference is clearly determined by the statement of
the choice. A power company wishes to entice its consumers
to abandon buying power at a fixed rate and instead join a
system where they buy and sell power at variable rates. Here
are two ways the alternatives may be presented in a letter to
a consumer:
• The Gain Scenario: Your average monthly utility bill is
now $450 a month. Under our new smart system, your
bill will show a debit of $500 a month. In addition you
may choose between:
a) A 50% chance of a credit of $100 if you join the smart
DSM scheme, or
b) A 100% chance of a credit of $50 that will keep your
bill the same.
• The Loss Scenario: Your average monthly utility bill is
now $450 a month. Under our new smart system, your
bill will show a credit of $400 a month. In addition, you
may choose between:
c) A 50% chance of a bill for $100 if you join the smart
DSM scheme, or
d) A 100% chance of a bill for $50 that will keep your
bill the same.
In fact, the Gain and Loss scenarios describe the identical
alternatives in different words. Alternatives a) and c) are
identical and alternatives b) and d) are identical. Nevertheless,
based on theoretical and empirical foundations, PT predicts
that more people will prefer alternative b) to alternative a)

B. Basics of Prospect Theory
Prospect theory encompasses a broad range of techniques
and tools to account for realistic consumer behavior during
decision making processes [94]–[98], [101], [102]. The basic
underlying idea is that decision makers, in real-life, will have
subjective perceptions of losses, gains, and their competitive
environment. For example, instead of viewing each others’
actions (e.g., load shifting schedules) objectively as in classical game theory, players could have different subjective
assessments about each others behavior, which, in turn can
lead to unexpected, irrational decisions. For example, in DSM,
even though rational behavior dictates that consumers follow
the load shifting mechanisms of the power company, some
consumers may turn on certain appliances at unexpected
times, since they are unsure on whether participation level
is high enough to obtain economic benefits which will hinder
the performance of the DSM scheme. The large spread of
such unconventional actions can thus be disruptive to any
energy management scheme. In such situations, PT provides

Weighted probability (subjective perception)

because a certain gain is preferred to a 50% chance at a
double-gain but will also prefer alternative c) to alternative
d) because a 50% chance of a loss is preferred to a certain,
albeit smaller, loss. This prediction has been confirmed in [93]
and [101].
The point of this example is not just that the level of
participation in smart grid services depends on how it is
presented to the public. The point is that important behavioral
factors outside of the technical specifications of the smart grid
will determine the choices of participants and giving them
the opportunity to perform optimally does not guarantee that
they will. In other words, people cannot be counted on to
always choose optimally among alternatives if merely stating
the alternatives differently influences their choices. This holds
true even if such alternatives, as discussed in Section II, have
immense technological and environmental benefits. Indeed, in
[102], Kahneman suggests that people behave non-optimally
when buying and selling stocks, selling rising stocks too soon
to lock in gains and hanging on to losing stocks too long
to resist locking in a loss. If people behave non-optimally
in the purchase and sale of securities, the default assumption
is that they will perform in the same non-optimal manner in
the purchase and sale of power and commodities, especially
when people are already familiar with the incumbent pricing
and energy management mechanism.
The obvious solution to the problem of human behavior
is to use prospect-theoretic notions to refine existing gametheoretic mechanisms and guide the way in which optimal
strategic decisions are derived as well as to improve the
presentation of information to buyers and sellers in the grid to
encourage optimal behavior in DSM and energy trading. To
provide further insights on the mathematical machinery underlying PT, in the next subsection, we provide an introduction
to the basics of the framework.

1

0.8

0.6

Subjective α=0.4
Subjective α=0.25
Subjective α=0.1
Subjective α=0.7
Objective/rational

0.4

0.2

0
0

0.2

0.4
0.6
Objective probability

0.8

1

Fig. 2. Illustration of the prospect-theoretic weighting effect: how objective
probabilities are viewed subjectively by human participants. The parameter
α determines how far the behavior is from the fully rational case.

solid analytical tools that directly address how these choices
are framed and evaluated, given the subjective observation of
players in the decision-making process.
1) Subjective Actions – The Weighting Effect: The first
important PT notion is the so-called weighting effect. In
particular, in PT [93]–[98], it is observed that in real-life
decision-making, people tend to subjectively weight uncertain
outcomes. In particular, in energy management mechanisms,
the frequency with which a consumer chooses a certain
strategy, say a certain schedule of appliances or a certain
storage pattern, depends on how other consumers make their
own choices. The dependence stems from many factors.
For example, in dynamic pricing schemes, the actual price
announced by a power company depends on the entire load
of the consumers. Therefore, the decision of a consumer, will
subsequently depend on the decision of others. Indeed, when
faced with a given smart grid scenario, consumers may act differently over time due to the interdependence of their actions
and its unpredictability, and, thus, a probabilistic model for
decision making is suitable to capture this uncertainty. Such
uncertainty can stem not only from the individual decisions
of consumers but also from other smart grid factors (e.g.,
uncertainty of renewable energy).
In classical game-theoretic smart grid schemes [5], [6], [8]–
[66], [75]–[84], consumer interdependence is captured via
the notions of expected utility theory in which a consumer
computes an expected value of its achieved gains or losses,
under the observation of an objective probability of choice by
other consumers. In contrast, using the weighting effect, PT
allows one to capture each consumer’s subjective evaluation
on the probabilistic strategies of its opponents. Thus, under
PT, instead of objectively observing the information given by
the other players and computing a classical expected value
for the utility, each consumer perceives a weighted version of
its observation on the other actions. The weighting is used to
express a “distorted” view that a given consumer or player can
have on the actions of others. PT studies have shown that most
people overweight low probability outcomes and underweight
high probability outcomes.
To illustrate the weighting effect, in Fig. 2, we show an

Framing effect example
10
8

EUT raw utility
PT framing utility

6
4
Utility value

example of a weighting function, known as the Prelec function [103], which maps an objective utility into a subjective
utility. The mapping is controlled by a parameter α which
quantifies the level of subjectivity in the observation. For
α = 1, we have the fully rational case, while for α close to
0 we get the fully irrational case. Within a smart grid setting,
such a weighting can have a cascading effect on the way in
which an energy management scheme works. For example,
in a DSM context, a highly irrational consumer will have a
largely distorted view on how other consumers behave. In
turn, this consumer will become more risk averse or more
risk seeking, depending on how the opponents actions impact
the dynamic pricing mechanism. As a result, this consumer
will not follow the actions recommended by classical, rational
mechanisms, but, instead will take an unexpected action
which, in turn, will yield unexpected DSM results.
Indeed, how to model such a weighting effect and how to
integrate it into realistic energy management mechanisms is
an important topic for research. In addition, how to design
weighting functions that are tailored towards the smart grid
and that can work in realistic power system setting is a
key challenge. In Section IV, we will discuss with specific
examples how weighting modifies the results of energy trading
and management protocols.
2) Subjective Perceptions of Utility Functions – The Framing Effect: Another important idea brought forward by PT is
the notion of utility framing. In engineering designs, one often
defines mathematically rigorous objective (utility) functions
that are used to optimize a certain metric of the system. For
example, when dealing with an optimal energy generation
problem, a smart grid system must find the maximum energy
output that can meet or match the demand. In such a case, it
is sound to assume that the function that must be optimized
is based on an objective metric, the energy in this case.
However, when dealing with smart energy management
mechanisms having human players, the idea of an objective
metric for evaluating utility functions might not be a reasonable assumption. For instance, each individual has a different
perception on the economic gains from a certain DSM scheme.
For example, a saving of $10 per month may not seem like a
significant gain for a relatively wealthy consumer. Instead, a
poor consumer might view this amount as a highly significant
reduction. Clearly, the objective measure of $10, can be
viewed differently by different consumers.
In PT, such subjective perceptions of utility functions
are captured via the idea of framing or reference points.
In essence, each individual frames its gains or losses with
respect to a possibly different reference point. Back to the
aforementioned example, the wealthy consumer will frame
the $10 with respect to its initial wealth which could be
close to millions and, thus, this consumer views the $10 as
insignificant. In contrast, the poor consumer might have a
wealth close to 0 and, thus, when framing the $10 with respect
to this reference point, the gains are viewed as significant. One

2
0
−2
−4
PT value is:
Concave in gains
Convex in losses

−6
−8
−10
−10

−8

−6

−4

−2

0
2
Raw utility

4

6

8

10

Fig. 3. Illustration of the prospect-theoretic framing effect: how objective
utilities are viewed subjectively by human participants. The utility function
value changes depending on a certain reference point that highlights the
individual perceptions of gains and losses.

popular way to capture such framing effects is by observing
that losses loom larger than gains, and, thus, PT provides one
transformation that maps objective utility functions into socalled subjective value functions - concave in gains, convex
in losses - over the possible outcomes. These gains and losses
are measured with respect to a reference point that need not
be 0 and that may be different between players. An illustrative
example is shown in Fig. 3 for one typical PT value function
from [93] assuming a zero reference point for gains/losses.
Naturally, as consumers change the way in which they
compute their utilities, their overall decision making processes
will deviate from the conventional, rational thought. Indeed,
when applying PT ideas to game-theoretic settings such as
in [98], it is shown that the objective results do not hold.
For example, in some cases, it is shown that the choice
of a reference point can impact whether or not a certain
game has an equilibrium solution or not. Clearly, when one
decision maker changes the way in which it evaluates its
objective function, the overall operation of any optimization
mechanisms will be significantly affected.
In the smart grid, we can envision many situations in
which to incorporate the framing effects. These situations
need not be purely economical. For example, during winter,
consumers may perceive less prospective gain from turning
off high-capacity loads (such as heaters) at night than during
day time. How this “frame of reference” transforms the
utility will fundamentally change the outcome of an energy
management mechanism that is based on classical objective
notions. Moreover, in the smart grid, such reference points
and framing effects may change over time, space, and even
demographics. Clearly, properly designing and developing
framing notions in smart grid DSMs is an important direction
that must be investigated to better understand its impact on
energy management and trading mechanisms.
Having defined the two key effects of PT, in the next sec-

EUT Player1
EUT Player2
PT Player1
PT Player2

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

0.02

0.04
0.06
Unit selling price b ($/kWh)

0.08

0.1

Fig. 4. Impact of the weighting effect on consumer behavior in a two-player
charginge/discharging setting.

tion, we discuss, in detail, two energy management scenarios
to highlight, as an example, the impact of weighting on smart
grid protocols.
IV. P ROSPECT-T HEORETIC S MART G RID A PPLICATIONS
A. Example 1: Charging and Discharging of ConsumerOwned Energy Storage
To show the impact of prospect-theoretic considerations in
smart grid design, we first study a model in which consumers
are equipped with storage units and must decide on how to
manage the charging and discharging of their storage units,
depending on the network state and the pricing incentives.
This model is based on our recent work in [104].
In particular, we consider a grid consisting of multiple
consumers who own storage units. For illustration purposes,
we assume the case in which only two consumers are “active
participants” while all other consumers constitute a passive
load on the grid. Each consumer has a storage unit which
holds a certain initial amount of energy stored. The power
company offers these active consumers the option to either
charge their storage unit and, thus, act as a load on the grid,
or, instead to actively feed back and sell energy to the grid.
Note that, any action taken by either of the two consumers
affects both the power system as it impacts the overall needed
generation as well as the prices set by the utility company. The
choices of both consumers are also coupled, since the choice
of acting as load or source, will impact the overall generation
and distribution of energy in the grid.
In this setting, we assume that the consumers need to make
a choice between charging or discharging while optimizing a
utility function that captures two properties: a) the economic
and technical benefits of storing or selling energy and b) the
power system regulatory penalties. Indeed, although the power
company allows the two active consumers to individually manage their storage units, it still requires the generation to remain
within desired operating conditions which are measured based
on an initial point.

Power company revenues from two consumers ($)

Probability of buying (acting as load)

1

3.5
EUT
PT α=0.25
PT α=0.45
PT α=0.65

3

2.5

2

1.5

1

0.5
0

0.02

0.04
0.06
Unit selling price b ($/kWh)

0.08

0.1

Fig. 5. Impact of the weighting effect on the revenues of the power company.

We formulate and investigate this setting using a PT-based,
classical noncooperative game and we study the equilibrium
solution of the game. The equilibrium is essentially a point of
the system in which neither of the two consumers can improve
its utility by changing the frequency with which it chooses to
charge or discharge its storage unit. We analyze the results
under both classical EUT and PT considerations. For PT, we
first consider the weighting effect: each consumer views a
subjective observation on the charging/discharging behavior of
its opponent in accordance with a Prelec weighting function
such as in Fig. 2.
We use a numerical example to show the impact of PT
considerations on the operation of the system. We consider
a standard 4-bus power system with 2 active consumers.
The loads and surpluses of active consumer 1 are, respectively, 20 kWh and 10 kWh, while those of consumer 2
are, respectively, 15 kWh and 5 kWh. Fig. 4 shows the
impact of the unit selling price b that is used by the two
consumers when discharging energy to the grid. This price
is assumed to be equal for both consumers. Clearly, as b
increases, both consumers have more incentive to sell than
to buy, as the gains start outweighing the regulation penalty.
More interestingly, Fig. 4 shows that, for both consumers,
PT behavior significantly differs from the rational EUT case.
For consumer 2, below 0.07$ per kWh, the probability of
buying energy at the PT equilibrium is much higher than
under EUT. This implies that for low gains and high risks, the
consumer follows a conservative, risk-averse strategy under
PT and is less interested in reaping the gains of selling energy
compared to EUT. However, as the unit selling price crosses
the threshold, the probability that consumer 2 acts as load
under PT becomes much smaller than EUT. Thus, once the
selling benefits are significant (risks decrease), PT predicts
that consumer 2 will start selling more aggressively than
in EUT. Analogous behavior is seen for consumer 1 with
threshold 0.045$ per kWh.
Fig. 5 shows the total power company revenues, collected
from the two consumers when they charge their storage unit,
as the unit selling price increases. Fig. 5 shows that, as b in-

EUT
PT (γ=2)
PT (γ=1.5)
PT (γ=1)

0

30

EUT
PT (α = 0.25)

The expected utility ($)

Total average grid load from the two consumers (kWh)

2

35

25
20
15

−4
−6
−8
−10

10

−12
−2.5

5
0
0.03

−2

0.04

0.05

0.06

0.07

0.08

Unit price c ($/kWh)

Fig. 6. Expected grid load when the consumers actively participate with their
storage devices under rational EUT and irrational PT behavior.

creases, the total revenues decrease, as the consumers begin to
sell more and buy less. Note that, here, the power company’s
revenues pertain to only those revenues that are collected
from the two consumers. This does not include any additional
sources of revenues that the power company might collect
(e.g., taking a percentage on the profits of the consumers).
Clearly, deviations from EUT can have major impacts on
energy management in a smart grid setting. Consider the case
in which the Prelec rationality factor is set to α = 0.25. When
b is below 0.06$ per kWh, under PT, the total revenue is
much higher than predicted by EUT. In contrast, if consumers
set prices greater than 0.06$ per kWh, PT predicts that the
revenues will be much smaller than in EUT. It is thus more
beneficial for the company to regulate the consumers’ unit
selling price to be below 0.06$ per kWh. Fig. 5 also shows
that when the company adopts EUT to regulate the consumers’
selling price, it can lose revenues due to real-life consumer
behavior. Fig. 5 also shows that, as α increases, the consumers
behave more in line with EUT. However, even for a relatively
high value, α = 0.65, the company revenues resulting from
PT still yield non-negligible deviations from EUT.
We further analyze how consumer behavior impacts grid
operation by showing the average expected load on the grid
in Fig. 6, as the company varies its minimum price 1 . Fig. 6
shows that the expected load on the system will significantly
change between PT and EUT. For PT, when the unit price is
small, consumers are less interested in selling their stored energy. However, as the price crosses a threshold, the consumers
will start selling more aggressively, rendering the average load
smaller than expected. Fig. 6 provides guidelines for realistic
DSM with storage. For example, assume the company wants to
increase its price to drive consumers to sell more and reduce
their load to about 10 kWh. Based on classical EUT-based
schemes, the company has to increase the price to 0.078$
per kWh. In real life, because consumers behave subjectively
under risk, the power company can increase its unit price to
1 This pertains to the rates that the power company will use to directly
charge its consumers.

−2

−1.5

−1

−0.5
0
0.5
1
The reference point u0

1.5

2

2.5

Fig. 7. The total utility under both EUT and PT as the reference point u0
varies.

only 0.06$ per kWh and obtain the desired load reduction.
Also, if the power company wants to reduce its price to sustain
a load of 23 kWh from the two consumers, based on EUT, it
must offer a price of 0.035$ per kWh. In contrast, PT shows
that 0.047$ per kWh will achieve the same impact yet yield
more profits.
Next, we consider the same example in the presence of
framing effects, based on our work in [105]. Here, we assume
that both consumers frame their utility with respect to a given
reference point that reflects how these consumers evaluate
the economic gains or losses from charging or discharging
their storage unit. For incorporating framing, we adopted the
classical model of [98] in which, under framing, the utility
function becomes concave in gains and convex in losses,
as losses loom larger than gains. To assess the impact of
framing, in simulations, the reference point is chosen to
coincide with the case in which consumers discharge/sell
energy at the same price that is announced by the power
company. In Fig. 7, we show the total expected utility (sum
for both consumers) under both EUT and PT, as the reference
point varies. In this figure, we choose the same reference
point for both consumers and we use typical values for γ
which is a parameter that represents the loss aversion, i.e.,
how a consumer values its losses versus its gains. First, we
can see that, the expected PT utility will decrease when the
reference point value increases. In essence, the reference point
is subtracted from the EUT utility to determine the exact
values of gains and losses. For a high reference point (i.e.,
electricity price), PT consumers will value their stored energy
more than in cases in which the reference point is smaller.
Thus, using a same selling/discharging price under EUT and
PT, the payoff obtained by consumers under PT is smaller
than under EUT, due to the fact that, in PT, the reference
point reduces the gains from selling energy. Second, this figure
also shows that, the framing aversion parameter, i.e., γ, would
have different impacts on the PT utility. In particular, when
γ increases from 1 to 2, the losses viewed by PT consumers
will increase. Thus, with an increasing γ, a PT consumer will
start valuing its gains less than in the EUT case, which leads
to increasing its conservative, charging strategy. Additional
results on framing can be found in [105].

In summary, ignoring consumer behavior in storage-based
energy management can lead to unexpected results as shown
here for a basic setting. These results can be undesirable
from both an economic and technological perspective. Therefore, building on the presented model, one can design more
elaborate and realistic storage management mechanisms that
account for PT-based notions of subjective perceptions. In
addition, the power company can utilize these results to
properly shape its pricing schemes.
B. Example 2: Demand-side Management under ProspectTheoretic Considerations

2 The reader interested in the mathematical formulation is referred to our
work in [106].

Fig. 8. The expected nonparticipating load for the 6 consumer game under
both EUT and PT over 24 hours, when consumers have different values of
α.
The nonparticipating load profile at 19:00
34
The expected nonparticipating load (kWh)

Another important application for PT is classical demandside management models. Here, we consider a grid in which
consumers are given the opportunity to decide on whether or
not to participate in DSM. The DSM scheme considered is
one in which the participating consumer would shift its load
over time, in order to reduce the overall peak hour load. The
actual DSM process is in line with classical game-theoretic
settings such as those in [5].
However, in our model, it is assumed that consumers have
also a choice of not participating in the DSM at all. In
addition, consumers can choose the time starting which they
will begin their participation. The decisions of the consumers
are driven by the goal of minimizing the overall electricity bill
while maintaining their desired load to operate their required
appliances2 . One important feature of the considered model is
that every load shift by a given consumer will automatically
impact the way in which prices are set by the power company.
Thus, this interdependence in decision making will naturally
warrant a game-theoretic approach to modeling the decision
making.
In essence, we have a model in which every consumer can
decide on the time at which it starts to participate in DSM.
Alternatively, the consumer may decide not to participate
at all. We can then analyze the frequency with which a
consumer will participate or not and we analyze the impact
of this participation on the grid by deriving equilibrium
conditions [106]. This analysis is done for both the rational
and irrational case. For PT, we consider mainly a weighting
effect.
To gain more insights on the impact of weighting on DSM
participation, we consider a numerical validation using a realistic load profile in [107] which represents consumers’ initial
demands during Spring 2013, from the Miami International
Airport. In these numerical examples, each consumer can
choose a starting time to participate in DSM from the time
period between 18:00 and 20:00. Alternatively, the consumer
can decide not to participate.
In Fig. 8, we show the expected nonparticipating load
profile using different values for the Prelec rationality parameters α. In this example, each consumer has a different

EUT
PT
Actual demand

32
30
28
26
24
22
20
18
0.1

0.2

0.3

0.4

0.5

α

0.6

0.7

0.8

0.9

Fig. 9. The impact of the rationality parameter α on the expected nonparticipating load of all consumers at 19:00.

subjective perception on other consumers and, thus, has a
different rationality parameter. In particular, we choose α =
[0.5 0.5 0.2 0.1 0.1 0.1] for the 6 considered consumers. This
implies that consumer 1 is more rational than consumers 36 while consumers 4-6 are the least rational. In this figure,
we can see that, when some consumers have a very irrational
observation on their opponents, the PT nonparticipating load
between 21:00 and 23:00 will be higher for PT than EUT. This
implies that, in realty, if some consumers deviate significantly
from their rational strategies (for example, a consumer decides
not to assist the power company in load shifting despite the
economic benefit), the power company will not be able to
shift the total load predicted by the rational, objective model.
Thus, this simple, yet insightful example shows that one must
better understand how consumers behave (here reflected by
the rationality parameter) to better design the dynamic pricing
and DSM scheme.
We further analyze the impact of the consumer rationality
on DSM by showing, in Fig. 9, the expected nonparticipating
load at a chosen time of the day which is here selected to

be 19:00 for illustrative purposes. Here, it is assumed that
all consumers have a similar level of rationality. In Fig. 9,
we observe that, under EUT, the expected nonparticipating
load is 65.7% of the total load. In contrast, under PT, the
nonparticipating load is less than EUT when α > 0.56, i.e.,
when consumers are fairly rational. Thus, the power company
can shift more load in practice, compared to an EUT scheme,
if the consumers are all of equal rationality level when α >
0.56. Clearly, there exists a rationality threshold, such that, if
α is greater (smaller) than the threshold, PT consumers will
have lower (higher) nonparticipating loads than EUT cases.
A large value of α, which maps to a small deviation from
EUT, yields an increased competition thus raising the costs
to the consumers. Consequently, the consumers will become
risk seeking and more apt to shift their loads and decrease
their payments. Thus, the increasing PT costs will force the
majority to shift more loads, compared to EUT. In contrast,
a relatively small rationality parameter or a large deviation
from EUT, will lead to highly irrational behavior from the
consumers which will lead to increasingly high competition
and decreasing participation, as consumers become extremely
risk averse and unwilling to participate in the DSM process.
From Fig. 9, we can infer that one of the reasons for
which DSM schemes might have not been adopted widely
in practice is due to a severely irrational behavior observed
from the consumers. Indeed, as per Fig. 9, one can see
that a small deviation from EUT (slight irrationality) may
in fact be beneficial for the power company as it increases
consumers’ participation. In contrast, a significant deviation
from EUT will inevitably lead to highly risk averse behavior
which will prevent most consumers from participating; thus
yielding detrimental results for the grid and preventing the
power company from reaping the benefits of DSM.
Through this simple, yet realistic DSM example, we are
able to see that by only considering the weighting effect of
PT, the results of DSM can significantly change. This is due
to the fact that the PT model allows to better capture the
way in which consumers behave in practice. Consequently,
this motivates a deeper investigation of the role of human
decision making in practical DSM mechanisms.
C. Choice of PT Parameters
In this section, we have brought forward several key results
that show how realistic consumer behavior can impact smart
grid energy management. However, in these models for assessing the rationality (e.g., the parameter α) or risk aversion of
the consumers, we have adopted PT models of risk that were
conceived in the economics literature such as in [93]–[98],
[103]. Naturally, to understand whether those models map
directly into the smart grid, there is a need to run analogous
behavioral experiments, with real-world smart grid consumers,
to generate new empirical models for PT that can be used to
further enhance the results of this section. Such experiments
can be based on both qualitative surveys and on real-world

simulations in which grid consumers (e.g., homeowners or
factories) are solicited to participate in simulated experiments
on grid scenarios that pertain to DSM, storage, or other
consumer-centric features. Such experiments can mimic the
gain and loss scenarios presented in Section III-A. Using such
behavioral experiments, we can refine the choice of the various
PT parameters and we can generate more advanced models
and results.
V. C ONCLUSIONS

AND

F UTURE O UTLOOK

Realizing the vision of a smart, consumer-centric grid is
without any doubt strongly dependent on gathering a better
understanding on the impact and role of consumer behavior
in energy management processes such as demand-side management, demand response, or energy trading. In this article,
we have shown that the use of prospect theory, a powerful
framework from operations research and psychology, can
provide the first step towards better understanding the impact
of consumer behavior on smart grid operation. Indeed, our
preliminary investigations have shown that consumer-related
deviations from conventional, rational game-theoretic energy
management mechanisms can be one of the primary reasons
behind the modest adoption of such mechanisms in practical
smart grid systems.
Nonetheless, in this article, we have only scratched the
surface of this emerging area in smart grid research. Indeed,
the study of consumer behavior in the smart grid requires
significant advances to frameworks such as PT. Many future
directions can be envisioned. For example, our results so far
have solely relied on the analysis of the weighting effect.
However, we anticipate that the use of both framing and
weighting can provide deeper insights into how DSM and
energy management can operate in the smart grid. Indeed, the
fact that smart grid consumers will have time-dependent reference points while measuring their utility functions provides
a very interesting and promising research direction.
In addition, our study thus far has focused primarily on
economic-oriented models, in which the impact on the power
system is restricted to load management. Instead, one can
envision the use of PT-based behavioral model to better
understand how the overall regulation of the power system
operation can be modified due to the uncertainty and risk
introduced by consumer-based decision making. Such studies
can also be extended to explicitly account for communication
and security considerations, both of which can involve enduser decisions.
Another important direction for future work is to explicitly
account for renewable energy sources. In fact, renewable
sources will introduce two types of uncertainty: a) uncertainty
due to consumer decisions, as captured in the models of this
paper and b) uncertainty due to nature and other environmental
factors that affect renewable generation. Here, it is of interest
to apply PT models to capture both types of uncertainty. Some
early works on PT such as in [98] have shown that when

both weighting effects and utility uncertainty are considered,
one can expect significant deviation from conventional rational
results. How such deviations can be applied in a smart grid
context remains an open problem.
Moreover, the recent surge in the application of big data
analytics in various smart grid scenarios will provide an
important avenue to explore the differences between EUT
and PT. These data that are being constantly collected can,
in the future, provide an important source for corroborating
the intuition provided by PT while also providing important
information to derive more realistic PT models.
Last but not least, as mentioned previously, one important
challenge is the lack of any large-scale data on how buyers
and sellers will in reality behave in the still speculative smart
grid market. Though PT provides broad hints about the factors
that may affect choices, the tests of it have been so far
restricted to basic models such as those presented here, which
are still somewhat distant from the context of a large-scale
practical smart grid to be determinative. In other areas, the
experiments confirming PT have overwhelmingly been single
session experiments in which naive participants make choices
in speculative scenarios of no consequence to themselves.
This is different from regular participation in a smart grid
in which their choices have direct financial consequences on
themselves. People have the ability to learn from experience
and this is known to affect their choices in some contexts. For
example, the endowment effect is that amateur collectors will
not sell an item they already own for the price they would be
willing to pay for it [108]. However, professional merchants
do not show an endowment effect [109]. Fortunately, current
internet technology makes it possible to simulate the smart
grid and systematically evaluate consumer behavior in it
under different conditions. Conducting such simulations will
be an important area for future work as the results of such
studies should make it possible to design transaction rules
and human interfaces that constrain behavior into optimal
pathways. Such results will also help corroborate and improve
upon PT models.
In a nutshell, the deployment of smart energy management
mechanisms is an integral and essential part of the smart
grid. However, in order to expedite the introduction of such
features, it has become crucial to properly develop behavioral
models that can factor in explicitly the impact of human
behavior on the overall operation of the future, consumercentric smart grid.
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