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Rep
ort Going green: Agent-
based modeling of the diffusion of dynamic
electricity tariffs
Anna Kowalska-Pyzalska1 Katarzyna Maciejowska1
Karol Suszczyński2,3 Katarzyna Sznajd-Weron4
Rafał Weron1
1Institute of Organization and Management, Wrocław University of Technology, Poland
2Institute of Theoretical Physics, University of Wrocław, Poland
3Institute of Physics, Wrocław University of Technology, Poland
4UNESCO Chair of Interdisciplinary Studies, University of Wrocław, Poland
Hugo Steinhaus Center Wrocław University of Technology
Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland http://www.im.pwr.wroc.pl/~hugo/
Turning green: Agent-based modeling of the adoption of dynamicelectricity tariffs
Anna Kowalska-Pyzalskaa, Katarzyna Maciejowskaa, Karol Suszczynskib, KatarzynaSznajd-Weronc,d, Rafał Werona
aInstitute of Organization and Management, Wrocław University of Technology, 50-370 Wrocław, PolandbInstitute of Theoretical Physics, University of Wrocław, 50-204 Wrocław, PolandcInstitute of Physics, Wrocław University of Technology, 50-370 Wrocław, Poland
dUNESCO Chair of Interdisciplinary Studies, University of Wrocław, 50-204 Wrocław, Poland
Abstract
Using an agent-based modeling approach we study the temporal dynamics of consumer opinionsregarding switching to dynamic electricity tariffs and the actual decisions to switch. We assumethat the decision to switch is based on the unanimity of τ past opinions. The resulting modelexplains why there is such a big discrepancy between consumer opinions, as measured by marketsurveys, and the actual participation in pilot programs and the adoption of dynamic tariffs. Weargue that due to the high indifference level in today’s retail electricity markets, customer opinionsare very unstable and change frequently. The conducted simulation study shows that reducingthe indifference level can result in narrowing the intention-behavior gap. A similar effect can beachieved by decreasing the decision time that a consumer takes to make a decision.
Keywords: Dynamic pricing, Demand response, Consumer decisions, Intention-behavior gap,Innovation diffusion, Agent-based model.JEL: C63, O33, Q48, Q55
1. Introduction
Today’s energy markets face many challenges. Among them the imbalance between the grow-ing demand for electricity on one hand and the depleting supply of fuels on the other. On top ofthat, the power system faces an increasing presence of distributed renewable generation and hasto cope with the old and often inefficient technical infrastructure and the changing expectationsof the societies (Allcott, 2011; EC, 2007, 2012). Demand side management and demand responsetools (DSM/DR) nowadays attract the attention of the main market players: politicians, systemoperators, electricity retailers and consumers. A wide range of DSM/DR instruments is being
Email addresses: [email protected] (Anna Kowalska-Pyzalska),[email protected] (Katarzyna Maciejowska), [email protected] (KarolSuszczynski), [email protected] (Katarzyna Sznajd-Weron), [email protected](Rafał Weron)
Preprint submitted to ... November 4, 2013
considered, starting from education (encouraging efficient usage of energy), through time-basedpricing (time-of-use rates, critical peak pricing, real-time pricing) to incentive-based DR (directload control, emergency demand response programs, capacity market programs), see e.g. Darbyand McKenna (2012), Faruqui and Sergici (2010), Gerpott and Mahmudova (2010) and Strbac(2008).
From this plenitude of DSM/DR tools we focus in this paper on time-based pricing, often re-ferred to as dynamic pricing. The main difference between dynamic pricing and flat, conventionaltariffs is the dependence of the price consumers pay for electricity on the actual balance betweensupply and demand in the wholesale market. With such a tariff the consumer may experienceseveral changes in price levels during the day due to the fluctuations of the exchange establishedspot price (Faruqui and George, 2005; Thorsens et al., 2012). Dynamic tariffs have been inventedto flatten the curve and to shift the demand from on-peak to off-peak hours. On one hand, theshift of load implies a change in consumer habits and daily routines. On the other, it may be alsoconnected with the reduction of the overall energy consumption. Dynamic tariffs are often sup-ported by the so-called enabling technologies, like smart meters, in-home displays, smart plugs,smart appliances and home area networks (FORSA, 2010; Gerpott and Paukert, 2013; Jongejan etal., 2010; Paetz et al., 2012; Star et al., 2010). These technologies make the control of the energyconsumption easier for the customers. In particular, the appliances are automatically turned on oroff, according to the changing electricity price and time ranges.
Dynamic tariffs can bring benefits to consumers (potential savings, satisfaction to be ecologi-cal) and to electricity retailers and distribution system operators (lower investment and operationalcosts). However, as many pilot programs and surveys conducted in the recent years have shown, itis quite difficult to get people really involved and to convince them to actually switch to dynamictariffs (Allcott, 2011; Duetschke and Paetz, 2013; OFGEM, 2011; Ozaki, 2011; Star et al., 2010).This situation is due, in the first place, to the general indifference of residential consumers with re-gard to energy, and electricity tariffs in particular. Secondly, the savings that are attainable in manycases are not impressive enough to encourage more people to enroll in the dynamic pricing pro-grams. Finally, switching to the new tariff is often connected with some discomfort, because of theneed to reschedule energy consumption according to price signals from the wholesale power mar-ket (ATKearney, 2012; Faruqui and Sergici, 2010; Thorsens et al., 2012). For these reasons largefluctuations in consumer opinions about electricity tariffs can be observed: one day they are infavor and the next they are against due to their general indifferent attitude to the pricing programs(they do not care, they are disengaged, they do not find it interesting and worth their attention).Consumer opinions and final decisions are also influenced by the social impact of their neighbors(people prefer to have the same opinion as the majority of the group) and the external influenceor field (e.g. advertising of new pricing programs by some electricity retailers). As a result theintentions to reduce energy consumption do not always translate into decisions or actions. The lit-erature calls this discrepancy between opinions and decisions the intention-behavior gap (Godin etal., 2005; Fennis et al., 2011; Ozaki, 2011; Sheeran, 2002), the value-action gap (Gadenne et al.,2011), the KAP-gap (acknowledge-attitudes-practice gap; Rogers, 2003), the attitude-behaviorgap or the belief-behavior gap (Kollmuss and Agyeman, 2002).
Empirical studies of consumer behavior are time consuming, costly and generally of limitedscope. It is hard to imagine a survey involving a few million retail customers, conducted every
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day for a period of, say, two years. Agent-based or artificial society models, on the other hand,allow for multi-run experiments conducted under different market conditions and for differentagent specifications. Agent-based simulations have been also applied to model the demand sideof electricity markets. In most papers, however, the focus has been only on opinions (like inKowalska-Pyzalska et al., 2013) or no distinction between opinions and decisions has been madeat the modeling level. For instance, in the model of Zhang and Nuttall (2011), when facing anumber of options, the one for which a given residential electricity consumer has the greatestintention is his or her preferred option, i.e. it is his or her final decision on which energy supplierto use and whether to choose a smart meter or not. Yet, there are papers that pay attention to thedifference between the willingness-to-pay (WTP) and the actual adoption, but consider the marketof green, renewable energy, not dynamic tariffs (Diaz-Rainey and Tzavara, 2012; Ozaki, 2011).
In this study we focus on the difference between consumer opinions (or attitudes) and decisions(or behaviors) regarding switching to dynamic tariffs. Using an agent-based modeling approach,we show how personal attributes, like conformity and indifference, on one hand, and advertising,mass-media education programs and financial incentives, on the other, impact the decision makingprocess of individual electricity consumers.
The paper is structured as follows. In Section 2 we review the results of pilot programs thathave been run recently in the U.S. and in Europe and whose aim was to evaluate consumer attitudestowards particular demand response tools. In Section 3 we first discuss the innovation diffusionphenomenon as a five-stage process, which includes, among others, the persuasion stage (formingand attitude or opinion) and the decision stage (adoption). Next, we focus on the behavioral aspectsof the transition from opinions to decisions, in particular, in the context of energy conservation.In Section 4 we concentrate on the opinion-to-decision transition algorithm we use in this studyand briefly review the underlying agent-based model of opinion formation, originally introducedin Przybyła et al. (2013) and adopted to the case of electricity consumers in Kowalska-Pyzalskaet al. (2013). In Section 5 we present the results of our simulation study. Finally, in Section 6 wewrap up the results and discuss policy implications.
2. Pilot programs
The rapidly increasing number of distributed generators, like renewable energy sources (RES)or cogeneration, has recently led to a change in the philosophy of power system architecture andoperation and the introduction of smart grids. The latter idea is closely related to DSM/DR tools,which have been known for years, but nowadays attract much more attention. At the same timethe EU long-term strategy and climate policy call for an increase of energy efficiency, an increaseof market penetration by RES and a reduction of CO2 emissions in the coming years. Among EUregulations, Directive 2012/27/EC paves the way for widespread introduction of smart meters thatwould provide feedback to private households on their energy consumption and information aboutenergy efficiency (EC, 2012).
In order to achieve the ambitious goals set by the EU, a durable change in consumer attitudesand behavior is needed. Without consumer willingness to adopt to dynamic tariffs and without theireffort to reduce energy consumption, the efficiency of energy usage will not increase significantly.In the last 10 years a number of pilot programs and surveys in the U.S. and Europe were conducted
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in order to measure and evaluate the reduction of peak demand and energy conservation at theconsumption level (Ehrhardt-Martinez et al., 2010; Faruqui and Sergici, 2010; Jongejan et al.,2010; Sopha et al., 2011; Star et al., 2010). Many of those experiments were run in an attemptto understand consumers’ responsiveness to variation in retail electricity prices (Allcott, 2011;ATKearney, 2012; Faruqui and George, 2005; Grans et al., 2013; Ozaki, 2011; Thorsens et al.,2012).
Switching from a traditional tariff to a dynamic one has been found to reduce peak demand upto 44%, especially when accompanied by enabling technologies (Ehrhardt-Martinez et al., 2010).However, the cost of the enabling technologies is currently higher than potential savings (Gerpottand Paukert, 2013; Jongejan et al., 2010; Paetz et al., 2012). The pilot programs have also revealedanother unwanted feature. Namely, only a small fraction of the program participants decides tosign up for dynamic tariffs after the pilot programs are ended. For instance, the AIU Power SmartPricing Program in Illinois has shown that only 18% of customers, where the pilot program wasrun, were aware of it. Then, only 10% of them understood the program and only 5% were inter-ested in the program. In the end, under 1% of customers enrolled in the program (Star et al., 2010).Similar survey results have been obtained in other pilot programs in North America and WesternEurope, in countries where the societies are rather aware of and sensitive to environmental issues.Most of those surveys have shown that people are generally indifferent to energy conservation.According to a survey conducted in 2010 in the U.K. only 8% of respondents think that energyneeds ‘attention and improvement’ (OFGEM, 2010). The report of ATKearney (2012) shows that60-75% of consumers are not aware of the existence of smart grids and are not willing to shift theirconsumption to off-peak hours. Similar results have been obtained in Germany (FORSA, 2010;Gerpott and Paukert, 2013; Paetz et al., 2012).
The difference between stated willingness-to-pay (WTP) or stated willingness-to-adopt (SWA)and the actual adoption has been also investigated in the context of green energy (Diaz-Rainey andTzavara, 2012; Ozaki, 2011; Scarpa and Willis, 2010; Zarnikau, 2003). High rates of willingness-to-pay for green energy have been found in the U.S. (WTP between 40% and 70%) and in mostof the European countries (SWA between 30% and 60%). However, at the same time the actualadoption, i.e. the number of electricity consumers that have actually switched to green tariffs, isrelatively low. In the U.S. the average adoption rates are estimated to be at or below 2% (withthe exception of some best performing regional programs, where rates between 5% and 17% havebeen achieved), whereas in Europe these rates are even lower, see Diaz-Rainey and Tzavara (2012).Baddeley (2011) reports that 52% of Americans claim to support the Kyoto Treaty in principle,but at the same time if they had to pay extra $50 per month they would oppose it. Another surveyin Italy showed that while 70% of respondents are willing to increase energy savings, only 2% arecurrently reducing their use (Pongiglione, 2011). This huge discrepancy between intentions andactions, in particular related to electricity tariffs, will be the focus of the following Section.
3. Intention-behavior gap and electricity tariffs
3.1. Attitudes and behaviorsAttitudes can be understood as a personal belief regarding the consequences of undertaking a
specific behavior as a function of the personal valuation of the consequences (Ajzen and Fishbein,4
2005). In other words, attitudes toward something are favorable or unfavorable evaluative reac-tions – whether exhibited in beliefs, feelings, or inclinations to act (Myers, 2013). In this studywe talk about consumer opinions regarding electricity tariffs. These opinions are understood asconsumers’ attitudes towards dynamic pricing and energy conservation. Formulation of the opin-ion in favor of or against an energy-related issue is influenced by several factors, like personalage, gender, culture, economic and social status, environmental norms and beliefs, social impactof the community (the opinions of the neighbors, family and friends), information, advertisingand incentives provided by mass-media and product sellers (Allcott, 2011; Gadenne et al., 2011;Nolan et al., 2008; Ozaki, 2011; Pongiglione, 2011; Stern, 2000; Zhang and Nuttall, 2011). Beingdependent on so many internal and external factors, the volatility of the opinion may be huge. Theopinion may change easily, even on a daily basis. One day a person can be in favor of energy con-servation, because he or she wants to be seen as pro-environmental or because others are doing it.A few days later the same person can be against, because of the economic barriers (like investmentcosts and limited savings) and discomfort of usage (changing the lifestyle).
On the other side of the decision making process is behavior, understood as an action takenafter making a certain decision. In the context of the adoption of dynamic pricing there can betwo opposing decisions: to switch to the dynamic tariff or to stay with (or go back to) the old,flat tariff. The transition from an opinion to a decision can be described by a typical innovationadoption process. Rogers (2003) identifies five sequential stages of this process:
1. knowledge stage – gain knowledge of an innovation,2. persuasion stage – form an attitude (opinion) towards it,3. decision stage – decide to adopt or reject it,4. implementation stage – implement it,5. confirmation stage – confirm the decision.
As long as only the first three stages are taken into consideration, we may talk about formulationof an opinion. Before the opinion is formulated, the person is influenced by information frommass-media, education, product or idea sellers and the social network. In the context of electricitypricing programs the information about dynamic tariffs and enabling technologies originates fromelectricity suppliers and spreads to consumers through advertising (i.e. a global field) and thesocial network via word of mouth (i.e. local interactions). However, even if an individual isaware of an innovation, he or she may not regard it relevant to his or her situation or potentiallyuseful. Secondly, the information obtained must be sufficient enough to enable formulation ofthe opinion regarding the innovation. Thus, if the new idea is found not relevant to the personalsituation and/or the knowledge obtained is not sufficient to get the person adequately informed,then the spreading stops at the first knowledge stage and the attitude towards the innovation isnot formed. Further, as Rogers (2003) notices, the main outcome of the persuasion stage in theinnovation-decision process is a favorable or unfavorable attitude toward the innovation. In thiscontext, Deffuant et al. (2005) define a preadoption state when an interested individual is readyto adopt, but takes reflection time to be sure of the decision. During this period, social influencesmay change his or her interest and potentially lead to not adopting the innovation. Then, only ifthe fourth stage is achieved, the decision is really made and implemented. There can be two mainoptions: either adoption, understood as a decision to make full use of an innovation, or rejection,
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understood as a decision not to adopt an innovation. Finally, each decision should be confirmed. Itmay happen, that after the decision is made, the individual will not be satisfied with the choice, heor she had made. The individual may suffer from dissonance or internal disequilibrium, which isan uncomfortable state of mind that an individual tries to reduce or eliminate, e.g. by discontinuingthe innovation.
Empirical evidence indicates that the innovation adoption process quite often ends at some ofthe intermediate stages. The initial intentions to adopt the innovation, e.g. reduce energy consump-tion, do not always translate into decisions or actions. The literature calls this discrepancy betweenopinions and decisions the intention-behavior gap (Godin et al., 2005; Fennis et al., 2011; Ozaki,2011; Sheeran, 2002), the value-action gap (Gadenne et al., 2011), the KAP-gap (acknowledge-attitudes-practice gap; Rogers, 2003), the attitude-behavior gap or the belief-behavior gap (Koll-muss and Agyeman, 2002). Such a gap is often observed in health related behaviors (Sheeran etal., 2005), however, it seems that this phenomenon is most pronounced for environmental attitudesand behavior (Dunlap et al., 2000; Gadenne et al., 2011). There are many internal and externalfactors that affect consumer behavior in such situations and it can be really difficult to identifythe exact reasons for why the gap exists. In the case of green energy, for instance, Diaz-Raineyand Tzavara (2012) and Ozaki (2011) argue that the intention-behavior gap can be to some extentexplained by (i) unstable opinions (due to lack of knowledge, confusion generated by the complexstructure of tariffs, lack of guidelines and advice, high consumer indifference), (ii) hesitancy inswitching electricity suppliers and high searching costs, (iii) lack of sufficient supply (offers thatsatisfy consumer needs and expectations) and (iv) the free rider problem.
3.2. Transition from opinions to decisionsFor many years the issues, if and how attitudes influence human behavior and in reverse, if and
how this behavior impacts human attitudes, have been discussed by psychologists, sociologists,economists, marketing and sales experts and politicians. Empirical observations suggest that de-pending on the circumstances, the relationship between attitude statements and behavior can rangefrom no relationship to a strong one (Myers, 2013). For innovations we would like to assume thatthe persuasion stage leads to a behavioral change: adoption or rejection of the innovation, con-sistent with the individual’s attitude. However, in the case of energy conservation and dynamictariffs, attitudes and actions may be disparate (recall the results of the AIU Power Smart PricingProgram, see Star et al., 2010). The formation of a favorable or an unfavorable attitude toward aninnovation does not always lead directly or indirectly to an adoption or rejection.
Referring to a number of surveys regarding attitudes and behavior, Myers (2013) concludesthat one’s attitude will predict one’s behavior, only if three conditions are fulfilled. Firstly, toexamine the attitude’s impact on the behavior, other influences should be minimized. In order toachieve this goal the principle of aggregation can be used. Namely, the effects of an attitude onbehavior become more apparent, when we look at a person’s aggregate or average behavior ratherthan at isolated acts, see also Ajzen and Fishbein (2005). If we want to observe what is the relationbetween opinions and the final decision, for instance whether to choose the new dynamic tariff orstay with the old one, the opinions should be averaged over a certain period of time. Secondly, theattitude should correspond very closely to the predicted behavior. For example, attitudes towardrecycling (but not general attitudes toward environmental issues) predict participation in recycling.
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In our case this means that both – opinions and decisions – have to refer to switching to a dynamictariff or energy conservation, not to environmental issues in general. Finally, the attitude must bepotent, because something reminds us of it or because we acquired it by direct experience. Fordynamic pricing adoption this means that the opinions should be persistent to lead to a decision.Consumers have to be really convinced before making a decision, like in the model of Deffuant etal. (2005). Here, social influence and information gathered from mass-media and energy retailersplays a great role.
Theories in social and health psychology often assume that intentions cause behaviors (Goll-witzer, 1999; Webb and Sheeran, 2006). Among them, the theory of a planned behavior of Ajzenand Fishbein (2005) is a very popular one and useful in the context of understanding the rela-tion between environmental attitudes and energy conservation (Gadenne et al., 2011; Godin et al.,2005; Pickett-Baker and Ozaki, 2008; Rodriguez-Barreiro et al., 2013; Zhang and Nuttall, 2011).According to this theory, attitudes are important to the behavior, but they do not determine be-havior directly. Attitudes influence behavioral intentions, which in turn shape our actions. Whenfacing a number of options, a person prefers the one, for which he or she has the greatest intention.However, even though intentions are believed to be the best predictor of behavior, they account forless than one third of the variance in behavior (Ajzen, 1991; Webb and Sheeran, 2006). Accordingto Gollwitzer (1999), in addition to strong goal intentions, so-called implementation intentions orplans concerning where, when and how one will perform the intended behavior, are required toovercome the intention-behavior gap, see also Fennis et al. (2011).
3.3. Antecedents of behavioral change in case of energy conservationFor a number of years energy consumption behavior has been examined from various perspec-
tives, including microeconomics (rational choice models, pricing, market structure), behavioraleconomics (bounded rationality, decision heuristics), technology adoption (diffusion theories, cog-nitive dissonance, theory of planned behavior), social and environmental psychology (influence ofinformation, pro-environmental attitudes, value-belief-norm) and sociology (organizational behav-ior), see e.g. Baddeley (2011), Pongiglione (2011), Rodriguez-Barreiro et al. (2013) and Stephen-son et al. (2010). Each of these theories and models examines the relation between attitudes anddecisions from a different point of view. However, the literature agrees that consumer environ-mental behavior is strongly connected not only with general environmental beliefs and attitudes,but also with environmental norms, drivers and barriers of environmental behavior, social or com-munity influence and government policy. Some of the most important antecedents of behavioralchange regarding energy conservation and dynamic pricing include:
• General environmental beliefs and attitudes. The presence of the intention-behavior gapindicates that there is no direct relationship between environmental beliefs, attitudes andbehavior. Although pro-environmental values are supposed to impact pro-environmentalbehavior, they do not necessarily do that (Gadenne et al., 2011; Pickett-Baker and Ozaki,2008). If the attitudes are too general (e.g. if they refer to environmental protection in gen-eral, but not precisely to energy conservation), they are not likely to influence the reductionin electricity consumption.
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• Environmental norms. The influence of norms on the attitudes and behavior is emphasizedin the value-belief-norm theory of Stern (2000). According to this theory, normative beliefshave a positive effect on the intention to adopt environmental behavior. As Ozaki (2011)argues, recycling is a good example how an environmental issue can become a normativebehavior. The more consumers are convinced that waste segregation is good for the envi-ronment and start doing it, the higher is the probability that such a behavior will become anorm and that other people will adopt this practice.
• Environmental drivers and barriers. Environmental drivers include procedural knowledgeand understanding (which is necessary to turn beliefs into concrete actions, see Gyberg andPalm, 2009; Pongiglione, 2011; Stern, 2000), consumer feelings of guilt or moral obligation,sense of social responsibility, ease of adoption and personal relevance. On the other hand,the strongest environmental barriers include large initial investment costs, expected longpay-back time, insufficient information, lack of professional help and advice, lack of time(Gadenne et al., 2011; Sidiras and Koukios, 2004).
• Social influence. Many studies have shown that normative social influence has a positiveeffect on the intention to engage in environmental behaviors, like the acceptance of greenenergy or energy conservation behavior (see e.g. Allcott, 2011; Ayres et al., 2013; Gangaleet al., 2013; Jager, 2006; McMichael and Shipworth, 2013; Ozaki, 2011; Pickett-Baker andOzaki, 2008; Schultz et al., 2007; Sidiras and Koukios, 2004). As Nolan et al. (2008) ar-gue, in the context of energy conservation social norms have a greater impact than othernon-normative motivations like protection of the environment, benefiting the society or evensaving money. Moreover, they reveal an inconsistency between stated motivation and ac-tual behavior. ‘Because others are doing it’ was judged to be the least important reasonat the self-reported motivation stage. But the highest correlation with actual energy con-servation behavior had the respondents’ belief whether or not their neighbors were doingit. Further, as Rogers (2003) mentions, all innovations carry some degree of uncertaintyfor an individual, who is typically unsure of the new idea’s functioning and thus seeks so-cial reinforcement from others of his or her attitude toward the innovation. The individualwants to know whether his or her thinking is on the right track in the opinion of peers. Atthe persuasion stage and at the decision stage, an individual seeks innovation evaluation in-formation, messages that reduce uncertainty about an innovation’s expected consequences.This type of information is usually gathered by individuals from nearby peers, whose sub-jective opinions on the innovation (based on their personal experience with adoption of thenew idea) are more accessible and convincing to them (Bollinger and Gilingham, 2012; Fehrand Fischbacheri, 2002).
• Government policies and subsidies. Financial incentives, grants, discounts, subsidies, etc.,can be helpful in changing consumer behavior, but they are not enough. They should goalong with some of the other factors: pro-environmental attitudes, social influence and lackof environmental barriers.
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4. The model
4.1. Bridging the gap – from opinions to decisionsTo summarize the discussion of Section 3 we may conclude that an individual’s decision re-
garding an innovation is not an instantaneous act but rather a complex process that occurs overtime. At least two separate mechanisms, which affect the process, should be distinguished: changeof opinions (or attitudes) and decision making. In Kowalska-Pyzalska et al. (2013) we have fo-cused on the first mechanism and proposed an agent-based model of opinion dynamics, whereelectricity consumers face the problem of switching to innovative dynamic tariff programs (andpotentially back to the original flat tariffs). Here we propose an extension of the model whichbridges the gap between opinions and decisions, and addresses the second mechanism – the adop-tion of dynamic pricing.
As previously, we consider a social system represented by a square grid (i.e. a lattice, a chess-board) L× L. Each site of the grid is occupied by an agent (a household) characterized by opinionS i = ±1. Following Nyczka and Sznajd-Weron (2013) and Przybyła et al. (2013), we call theseagents spinsons (= ‘spin’ + ‘person’) to reflect their dichotomous nature originating in spin modelsof statistical physics and humanly features and interpretation. If S i = −1 the spinson prefers theold flat tariff, if S i = +1 it prefers the new dynamic tariff. Because we are studying the diffusionof innovation, i.e. diffusion of the new dynamic tariff, we assume that initially all spinsons haveopinion S i = −1, i.e. all pay for consumed electricity according to the flat tariff.
In subsequent time steps a spinson’s opinion can change according to a set of rules put forwardby Kowalska-Pyzalska et al. (2013), see also Przybyła et al. (2013) and Section 4.2. Based on itsopinion the spinson makes a decision to adopt (Di = +1) or reject (Di = −1) the innovation (i.e.the dynamic tariff). The assumption that an opinion (intention, attitude) influences the decision isconsistent with the majority of theories that explain consumer’s acceptance of new technologies,see Section 3 for a discussion and references. Unfortunately, to the best of our knowledge, oneestablished theory on how exactly a decision is made still does not exist. It is known, however,that substantial time – usually measured in months – elapses between the time when the consumerbecomes aware of the product and when he or she actually purchases it (Greenleaf and Lehmann,1995; Rogers, 2003). Therefore, we assume that a spinson must posses a consistent opinion for acertain period of time τ to make a decision. In other words, at time t a spinson decides to:
• adopt the innovation – switch to the dynamic tariff, if currently using the flat tariff, or staywith the dynamic tariff, i.e. Di(t) = +1 if its opinion was positive over certain period of timeS i(t − τ) = S i(t − τ + 1) = . . . = S i(t) = +1,
• reject the innovation – switch back to the flat tariff, if currently using the dynamic tariff, orstay with the flat tariff, i.e. Di(t) = −1 if its opinion was negative over certain period of timeS i(t − τ) = S i(t − τ + 1) = . . . = S i(t) = −1.
A similar mechanism has been considered by Deffuant et al. (2005) in an extension of a modelinitially targeted at the diffusion of green practices among farmers in the EU (Deffuant et al.,2002). A preadoption state was defined in which an interested individual was ready to adopt, buttook reflection time to be sure of the decision. During this period, social influences may have
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changed his or her interest and potentially led to not adopting the innovation. If the individualremained ‘interested’ during a given number of time steps (τ = 15 in the original paper) he or sheadopted. ‘Interest’ was defined as a three state variable (‘no’, ‘maybe’ or ‘yes’) and its value wasdependent on the global opinion and uncertainty in the society.
4.2. The underlying model of opinion formationOf course an individual’s opinion is generally not constant and changes over time due to auton-
omy that breaks determinism (indifference, independence), social influence and rationality relatedto product features. In this study we use the opinion formation model proposed by Przybyła etal. (2013) and adapted to the case of electricity tariffs by Kowalska-Pyzalska et al. (2013), whichaddresses all three aspects. In particular, at time t the opinion of a spinson depends on three factors:
• Indifference – which introduces indetermination in the system through an autonomous be-havior of the individuals. In the case of indifference the spinson is immune to the influenceof its neighbors and the global field (advertising, mass media). This kind of behavior canarise if two options (e.g. traditional and dynamic electricity tariffs) offer both advantages anddisadvantages and these advantages and disadvantages are not clearly comparable (Boudonand Bourricaud, 2003). With probability p an agent is indifferent and takes a purely randomopinion, independently of the neighboring spinsons and product features.
• Conformity – according to empirical observations social pressure, that results from interac-tions between neighbors, has to be taken into account when considering electricity tariffs(Allcott, 2011; Ayres et al., 2013; Nolan et al., 2008). In our model the nature of these in-teractions is motivated by the psychological observations of the social impact dating back toAsch (1955): if a group of spinson’s neighbors unanimously shares an opinion, the spinsonwill also accept it. We consider 2 × 2 panels of four spinsons, which is a natural choice forthis kind of ‘outflow dynamics’ on 2D lattices (Galam, 2012; Sznajd-Weron, 2005).
• Product features – which are modeled by a global field. The strength of the field h dependson features of the new dynamic electricity tariff: potential savings, (dis)comfort of usage,intensity of advertising, etc. As in Sznajd-Weron and Weron (2003), with probability h thespinson, who has not been influenced by its neighbors, can gain a positive attitude towardsthe new dynamic electricity tariff.
Regarding conformity, note that a different idea has been proposed by Galam (2005), who useda local majority rule with bias instead of unanimity. It turns out that the macroscopic behaviorof the system is qualitatively different and richer if we assume that social influence takes placein the case of unanimity (Nyczka and Sznajd-Weron, 2013). It is also better motivated by socialexperiments.
4.3. Model parametersAs seen from the above description, the expanded model of opinion formation and decision
making is characterized by three parameters:
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1. p ∈ [0, 1] – the level of indifference. Generally p be could be different for each spinson andexpress the fact that customers are not identical and have individual, potentially differentlevels of autonomy. However, in this paper we assume that p is equal for all spinsons and,therefore, can be treated as a certain average value in the society.
2. h ∈ [0, 1] – the strength of the external influence. Similarly as p, the strength of the field hcould be different for each spinson reflecting the fact that product features (such as potentialsavings, (dis)comfort of usage) are not equally important for all customers. But again weassume that it has a constant value for all spinsons and expresses a certain average value forthe society.
3. τ ∈ [0,∞] – the time delay needed to make a decision, so-called decision time (Greenleafand Lehmann, 1995) or reflection time (Deffuant et al., 2005). We use a single value of τ forthe whole population, which should be treated as an average decision time. In this paper wepresent results for τ = 30 and 60.
We study the model running M Monte Carlo simulations. A single experiment consists of TMonte Carlo steps (MCS), which can be interpreted in terms of time intervals, e.g. days. In eachMC step, N = L × L elementary sub-steps are repeated to ensure that on average each spinsonis chosen once in a single MCS (see Landau and Binder, 2005, for an excellent guide to MCsimulations). The simulations were performed on a square lattice 100 × 100 (which correspondsto N = 10000 spinsons) and the results were averaged over M = 1000 experiments.
5. Results
The time evolution of the opinion formation process and the dependence on model parametershave been thoroughly analyzed in Kowalska-Pyzalska et al. (2013). The model has been shown notonly to reproduce the S -shaped curve representing the time change of the number of consumershaving adopted to a new product, but also to describe two other phenomena that are crucial forthe diffusion of innovation – existence of the so-called critical mass (Oliver and Marwell, 1985;Rogers, 2003) and the valley-of-death (Weyant, 2011). Probably the most important conclusionfrom the study of Kowalska-Pyzalska et al. (2013) was that the adoption of dynamic electricitytariffs was virtually impossible due to the high level of indifference in today’s societies. Althoughwe have been dealing only with opinions, our conjecture was stronger – for a high level of indiffer-ence, the fluctuation of an agent’s opinion leads to his/her inability to make a decision and switchto a new dynamic tariff, no matter how strong is the influence of the external field. In this paperwe verify our predictions by expanding our model to incorporate actual decisions. To attain thisgoal we concentrate on quantifying the relationship between opinions and decisions.
In Figures 1 and 2 we plot the dependence between opinions or decisions and the indifferencelevel (0 < p ≤ 1) for four values of the external field (h = 0.05, 0.1, 0.2, 0.4). Note that theresults were averaged over M = 1000 experiments (or trajectories). The decision to switch to thedynamic tariff is made based on the current and (τ− 1) past opinions. To change the decision fromDi(t) = −1 to Di(t) = 1, the opinions must have been in favor of the dynamic tariff, i.e. S i(t) = 1,for at least a month (τ = 30) in Figure 1, and at least two months (τ = 60) in Figure 2.
It can be noticed that the external field has a significant impact on the opinions and the resultingdecisions only if the indifference level is rather low (p < 0.2). If the indifference level is high,
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0 0.2 0.4 0.6 0.8 10
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s
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h=0.05h=0.1h=0.2h=0.4
0 0.2 0.4 0.6 0.8 10
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h=0.05h=0.1h=0.2h=0.4
Figure 1: Dependence between opinions or decisions and the level of indifference (p) for several values of the externalfield (h) after t = 720 MCS time steps and for decision time τ = 30. The intention-behavior gap is clearly visible inthe upper panels. Bottom panels present the influence of the external field on the opinions (bottom left) and decisions(bottom right). The results were averaged over M = 1000 experiments.
say p > 0.5, the external field does not influence too much the opinions nor the decisions. If thedecision (or reflection) time is longer (τ = 60, as in Fig. 2) the ratio of decisions to switch to thedynamic tariff is even lower, no matter how strong is the external field.
Furthermore, lower left panels in both figures indicate that with high indifference, indepen-dently of the level of the external field, the ratio of spinsons having a positive opinion towards thedynamic tariff converges to 0.5. At the same time, the ratio of decisions is close to 0, see the lowerright panels in Figs. 1 and 2. The decisions are compatible with the opinions, only if the indif-ference level is rather low, say p < 0.4. Otherwise the intention-behavior gap can be observed:even if the opinions (attitudes) toward the dynamic tariff are in majority, they do not translate intodecisions to adopt the innovation. This is more visible for the longer decision time, i.e. for τ = 60.For instance, for indifference p = 0.3, about 75% of spinsons have a positive attitude towards thedynamic tariff, while only under 3% actually decide to adopt the innovation, see the upper rightpanel in Fig. 2. For p > 0.5 the ratio of spinsons that adopt is negligible, despite the ratio ofopinions in excess of 0.5. For the shorter decision time (τ = 30, as in Fig. 1) this effect is lesspronounced, yet also then the intention-behavior gap is clearly visible. This phenomenon is due tothe fact that opinions are unstable. One day a spinson is in favor of dynamic pricing, e.g. becauseof potential financial savings, and the next day it is against it, e.g. because of the discomfort causedby shifting the consumption to off-peak hours and changing the lifestyle.
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0 0.2 0.4 0.6 0.8 10
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0 0.2 0.4 0.6 0.8 10
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0 0.2 0.4 0.6 0.8 10
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0 0.2 0.4 0.6 0.8 10
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h=0.05h=0.1h=0.2h=0.4
Figure 2: Dependence between opinions or decisions and the level of indifference (p) for several values of the externalfield (h) after t = 720 MCS time steps and for decision time τ = 60. The intention-behavior gap is clearly visible inthe upper panels. Bottom panels present the influence of the external field on the opinions (bottom left) and decisions(bottom right). The results were averaged over M = 1000 experiments.
The bottom panels in Figures 1 and 2 also imply that the external field, even a relativelyhigh one (h = 0.4), does not lead to a significant increase in the ratio of decisions in favor ofthe new dynamic tariff. When the level of indifference in the society is high, the social networkand external field have no significant influence on the adoption rate. On the other hand, if theindifference level is low we can observe a somewhat surprising phenomenon – a reverse situation,where the number of spinsons that have adopted is larger than the number of spinsons having apositive attitude towards dynamic pricing. This phenomenon is better visible for shorter reflectiontimes, see the upper panels in Fig. 1 for τ = 30 and compare with the upper panels in Fig. 2for τ = 60. This ‘reverse gap’ can be explained by the fact that for small p the fluctuations (i.e.the noise) in the system are relatively small and advertising (combined with conformity) easilyconvinces spinsons to adopt. The smaller the decision time the faster is the convergence of thesystem to a steady state. This can be seen in the time evolution plots of the adoption rate in Fig.3. For τ = 15 a ‘nearly steady state’ for p ≈ 0.2 is reached after ca. 150 MCS, for τ = 30 afterca. 500 MCS, while for τ = 60 not before 1200 MCS. The opinion fluctuations that take placeafterward are not strong or long-lasting enough for the spinsons to revert back to the old tariff(i.e. to abandon the innovation). Hence, the observed ‘reverse gap’. On the other hand, for largerindifference, say p > 0.5, convergence to the steady state is much slower, see Fig. 4. Despite thevery long simulation time, i.e. 10000 MCS corresponding to 10000
365 ≈ 27.4 years in our model, for
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Figure 3: Decisions as a function of indifference p and time measured in Monte Carlo Steps (MCS) for external fieldh = 0.05 and decision time τ = 15 (upper left), τ = 30 (upper right) and τ = 60 (lower left). Opinions (lowerright) are the driver of adoption decisions, irrespective of τ. Note that opinions stabilize – approach the steady state –relatively quickly. In particular, for high indifference levels the average opinion does not deviate too much from 0.5,no matter how long is the observation time.
τ = 60 – and even for τ = 30 – the system does not reach a true steady state. Nevertheless, thechanges in decisions are so small that from a practical perspective they are negligible. Thereforethe intention-behavior gap does not vanish over time.
6. Conclusions and policy implications
Using an agent-based modeling approach we have studied the temporal dynamics of consumeropinions regarding switching to dynamic electricity tariffs and the actual decisions to switch. Byexpanding a relatively simple model of opinion dynamics to incorporate adoption decisions asa function of past opinions, we have been able to explain why there is such a big discrepancybetween consumer opinions, as measured by market surveys, and the actual participation rate inpilot programs and the adoption of dynamic tariffs. In an extensive simulation study we have found
14
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Figure 4: Decisions as a function of indifference p and time measured in Monte Carlo Steps (MCS) for external fieldh = 0.05 and decision time τ = 30 (left) or τ = 60 (right). Note that the time cutoff is set to 10000 MCS, whereas inFig. 3 is was set to 720 MCS.
that for moderate and high values of indifference (as measured by p), no matter how intensiveis advertising (i.e. external field h), we obtain the empirically observed intention-behavior gapbetween opinions and decisions. Moreover, the longer is the decision (or reflection) time, the largeris the gap. On the other hand, for low levels of indifference and a sufficient level of advertising, theopinions and decisions are closely related. Interestingly, as shown in Section 5, for a certain rangeof model parameters the adoption rate may even exceed the average opinion level in the society.
Due to a high indifference level in today’s retail electricity markets, customer opinions are veryunstable and change frequently. This may hamper the adoption of new dynamic tariffs, becauseconsumers typically need some sense of certainty before they take an action, especially if the costand consequences of such an action (changes in lifestyle, investments in new equipment, etc.) aresignificant. The conducted simulation study shows that reducing the indifference level can resultin narrowing the intention-behavior gap. On the other hand, a similar effect could be obtained byshortening the decision time. Interestingly, a similar phenomenon has been observed by Galam(2006) with respect to the highly unexpected victory of the ‘no’ to the 2005 French referendumon the European constitution. The long public debate resulted in a switch from initially positiveattitudes to eventually negative decisions.
In light of these results and of the pilot programs conducted in the U.S. and Europe, we canderive an important policy recommendation: as long as the indifference level of the retail con-sumers is not reduced or the decision time to switch to the dynamic tariff is shortened, the effortsto smooth the electricity demand via dynamic tariffs will not bring the expected results. In order toovercome the first part of the problem, utility companies should cooperate with the policy makers,governments and ecological organizations. In particular, the following steps could be taken:
• communicate to consumers the potential benefits of adoption at social and personal levels,
• provide clear and full information to consumers – to reduce the confusion and to increasethe interest in dynamic pricing and other DSM/DR tools,
15
• increase public awareness of the problem.
An alternative or parallel action to narrow the gap between opinions and decisions would be toshorten the decision time. For instance,
• by providing enough incentives that will overcome the cost and discomfort when switchingto a new tariff,
• by making the process of signing the contract easier for the consumer (e.g. via internet),
• finally, by offering consumers an easy return to the old contract, in case the new tariff willnot satisfy their needs.
When customers engage more in the topic or their decision time is shortened, the adoption ofdynamic electricity tariffs will be much more likely. Then in the future, when the indifference leveland/or the decision time are reduced, the external field (i.e. tariff pricing schemes, advertising, etc.)will become the focal point.
Finally, we should make clear that the above mentioned results have been obtained within arelatively simple agent-based model. However, as Deffuant et al. (2003) argue complicated modelsare not necessarily more realistic than simple ones. (...) A close link to the social sciences is not aguarantee of realism either. The current state of the social sciences shows a lot of different schoolsin competition, without any clear recognized paradigm providing generic rules of individual orcollective behavior. (...) To summarize, making complicated models is very easy. Establishingstrong results about their dynamical properties and relating them to evidence from psychology orsociology is the difficult part. We argue that the study of simple approximations is a good strategyfor progress in this direction.
Acknowledgements
This paper has benefited from conversations with the participants of the European Energy Mar-ket conference (EEM13), the European Conference on Complex Systems (ECCS’13), the Confer-ence on Energy Finance (EF2013) and the 2013 Econometrics, Energy and Finance Workshopat Cass Business School. This work was supported by funds from the National Science Centre(NCN, Poland) through grants 2011/01/B/HS4/01077 and 2011/01/B/ST3/00727.
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HSC Research Report Series 2013
For a complete list please visit http://ideas.repec.org/s/wuu/wpaper.html
01 Forecasting of daily electricity spot prices by incorporating intra-day relationships: Evidence form the UK power market by Katarzyna Maciejowska and Rafał Weron
02 Modeling and forecasting of the long-term seasonal component of the EEX and Nord Pool spot prices by Jakub Nowotarski, Jakub Tomczyk and Rafał Weron
03 A review of optimization methods for evaluation of placement of distributed generation into distribution networks by Anna Kowalska-Pyzalska
04 Diffusion of innovation within an agent-based model: Spinsons, independence and advertising by Piotr Przybyła, Katarzyna Sznajd-Weron and Rafał Weron
05 Going green: Agent-based modeling of the diffusion of dynamic electricity tariffs by Anna Kowalska-Pyzalska, Katarzyna Maciejowska, Katarzyna Sznajd-Weron and Rafał Weron
06 Relationship between spot and futures prices in electricity markets: Pitfalls of regression analysis by Michał Zator
07 An empirical comparison of alternate schemes for combining electricity spot price forecasts by Jakub Nowotarski, Eran Raviv, Stefan Trueck and Rafał Weron
08 Revisiting the relationship between spot and futures prices in the Nord Pool electricity market by Rafał Weron and Michał Zator
09 Rewiring the network. What helps an innovation to diffuse? by Katarzyna Sznajd-Weron, Janusz Szwabiński, Rafał Weron and Tomasz Weron
10 Going green: Agent-based modeling of the diffusion of dynamic electricity tariffs by Anna Kowalska-Pyzalska, Katarzyna Maciejowska, Katarzyna Sznajd-Weron, Karol Suszczyński and Rafał Weron
