A mechanism to promote social behaviour in household load balancing
AA mechanism to promote social behaviour in household load balancing
Nathan A. Brooks , ∗ , Simon T. Powers , and James M. Borg School of Computing and Mathematics, Keele University, Staffordshire, UK, ST5 5BG School of Computing, Edinburgh Napier University, Edinburgh, UK, EH10 5DT Institute of Liberal Arts and Sciences, Keele University, Staffordshire, UK, ST5 5BG ∗ [email protected] Abstract
Reducing the peak energy consumption of households is es-sential for the effective use of renewable energy sources, inorder to ensure that as much household demand as possi-ble can be met by renewable sources. This entails spreadingout the use of high-powered appliances such as dishwashersand washing machines throughout the day. Traditional ap-proaches to this problem have relied on differential pricingset by a centralised utility company. But this mechanism hasnot been effective in promoting widespread shifting of ap-pliance usage. Here we consider an alternative decentralisedmechanism, where agents receive an initial allocation of time-slots to use their appliances and can then exchange these withother agents. If agents are willing to be more flexible in theexchanges they accept, then overall satisfaction, in terms ofthe percentage of agents time-slot preferences that are satis-fied, will increase. This requires a mechanism that can in-centivise agents to be more flexible. Building on previouswork, we show that a mechanism incorporating social capital- the tracking of favours given and received - can incentiviseagents to act flexibly and give favours by accepting exchangesthat do not immediately benefit them. We demonstrate thata mechanism that tracks favours increases the overall satis-faction of agents, and crucially allows social agents that givefavours to outcompete selfish agents that do not under payoff-biased social learning. Thus, even completely self-interestedagents are expected to learn to produce socially beneficialoutcomes.
Introduction
The UK government has committed to a legally binding tar-get to reduce greenhouse gas emissions by 80% by 2050.This requires a shift to renewable energy sources, such assolar panels and wind turbines. However, integrating renew-able energy sources into a centralised and monolithic ‘na-tional grid’ is difficult because their output inherently de-pends on weather conditions. As such, they cannot simplybe ‘switched on and off’ to meet demand in the way thatcoal, gas, and nuclear power stations can be to match sup-ply and demand. Governments and energy providers haverecognised that this problem of load balancing – matchingsupply and demand – is easier to solve on a local scale. Con-sequently, they are supporting the development of ‘commu-nity energy systems’, where a community (e.g. a town or a small island) owns and manages its own renewable energysources (Walker and Devine-Wright, 2008).The shift towards community energy systems means thatcommunities now become involved in some of the tasks thatwere previously handled by a centralised national grid. Inparticular, they now become involved in the balancing ofsupply and demand. A key problem here is how to re-duce peak demand, i.e. the maximal amount of electricitythat is demanded at any one moment in time. If a commu-nity’s peak demand is too high, then it is unlikely that itwill be able to be met by the community’s renewable energysources, and so the community is likely to have to resort tobuying in electricity from non-renewable sources.The traditional approach to reducing peak demand is dif-ferential pricing set by a central utility company. Simplyput, households are incentivised to run their appliances attimes of low demand through lower pricing at these times(Stern et al., 1986; Dutta and Mitra, 2017). Traditionally,this has involved utility companies offering cheaper elec-tricity overnight. Could a community energy system use thesame mechanism? Potentially, however, variable pricing in-herently discriminates against more vulnerable householdson lower incomes (Simmons and Rowlands, 2007). Thenthere is the question of how prices should be set and whoshould set them? People are unlikely to take part in sucha scheme unless they perceive that they are being treatedfairly.To address these issues, we consider an alternative mech-anism for load balancing in a community energy system,which is not based on pricing set by some centralised au-thority. We assume that each household will have preferredtime-slots for when they would like to run high-powered ap-pliances such as washing machines, dishwashers and electricheating. The aim is then to allocate actual time-slots to eachhousehold for when they run their appliances. On the onehand, this is a classic multi-objective optimisation problemof reducing peak consumption (the maximum amount of en-ergy demanded in a time-slot) while satisfying each house-holds’ preferences as far as possible. On the other hand,issues of fairness are central. If households are to be moti- a r X i v : . [ c s . M A ] J un ated to use the mechanism then they will need to perceivethe resulting allocation of time-slots to households as be-ing fair (distributive justice, Rescher 1966). Furthermore,households will need to be able to understand why some oftheir time-slot preferences have not been met, and why thepreferences of some other households may have been metinstead. In other words, they need to perceive the allocation procedure as treating them fairly (procedural justice, Hol-landerBlumoff and Tyler 2008).Petruzzi et al. (2013) propose a mechanism inspired bythe building of social capital between agents (households,or software agents representing them). In their mecha-nism, agents are initially allocated time-slots at random, butcan then propose exchanges of time-slots with other agents.Agents have two possible strategies. Selfish agents onlyaccept exchanges that provide them with one of their pre-ferred time-slots. Social agents, on the other hand, acceptnot only these beneficial exchanges but also accept an ex-change request if they owe a favour to another agent (pro-vided the exchange will not cause them to lose one of theirpreferred time-slots).. An agent owes a favour to anotherif the other agent has previously accepted an exchange re-quest from them. Petruzzi et al. (2013) showed that underthis mechanism, a group where every agent was social hadon average more of their time-slot preferences satisfied thana group where every agent was selfish. They construed therecording of favours given and received, and the acting uponthis by social agents, as the accumulation of a form of elec-tronic social capital (Putnam, 1994; Petruzzi et al., 2014).Presumably, this would be intuitive for households to under-stand.However, two important questions arise from this work.First, to what extent is social capital a necessary part ofthe mechanism? Would social agents that always accept ex-changes that do not cause them to lose a preferred time-slotalso reach outcomes with high average satisfaction, with-out the need to track favours given and received? Second,should we expect self-interested agents to adopt the self-ish or the social strategy? We address both of these ques-tions in this paper. To address the first, we re-examine thePetruzzi et al. (2013) model by allowing social capital to beturned off. To address the second, we consider mixed popu-lations of selfish and social agents that change their strategyaccording to payoff-biased social learning (Boyd and Rich-erson, 1985). We find that while a mechanism without socialcapital allows a pure population of social agents to performbetter than a pure population of selfish agents, when agentscan change their strategy through social learning then socialcapital is necessary for social agents to outcompete selfishagents. Our results demonstrate that a time-slot allocationmechanism based on social capital can reduce peak electric-ity consumption, promote social behaviour, and lead to out-comes where the average satisfaction of households is high,even when agents are entirely self-interested. The Energy Exchange Simulation
The Petruzzi et al. (2013) model was built to represent asmart energy network consisting of 96 individual agents.Each day agents request four hour-long time-slots in whichthey require electricity. All requests are for 1KWh of en-ergy, and there can never be more than 16 agents using thesame time-slot, as this is considered the peak capacity of thesystem. Time-slots are initially allocated at random at thestart of the day, so few agents are likely to have their allo-cation match all of their requested time-slots. Because ofthis, after the initial allocation agents can partake in pair-wise exchanges where one agent requests to swap one of itstime-slots with a second agent, and the second agent decideswhether or not to fulfil the request. We define an agent’s sat-isfaction as the proportion of its time-slot preferences thathave been satisfied, and track the mean value of this as ameasure of how well the mechanism is satisfying the agents’preferences.Agents can follow either social or selfish strategies, whichimpacts how they react to incoming requests for exchanges.Selfish agents will only accept exchanges that are in theirimmediate interest. This means that selfish agents need tobe offered a time-slot that they have initially requested anddo not already have in order for them to agree to the ex-change. Social agents also agree to these mutually benefi-cial exchanges. However, they also make decisions basedon social capital, in the form of repaying previous favoursgiven to them by other agents. Specifically, when a socialagent’s request is accepted, they record it as a favour given tothem. When a social agent receives a request from anotheragent who previously gave them a favour, they will acceptthe request if it is not detrimental to their own satisfactionand record that the favour has been repaid. This improvesthe satisfaction of the other agent while earning themselvesmore social capital. This leads to a system of social agentsearning and repaying favours among one another, increasingthe number of accepted exchange requests.Exchanges begin on a day once each agent has receivedtheir initial allocation and decided which of these time-slotsthey wish to keep. They then anonymously advertise slotsthat they have been allocated but do not want to an ‘ad-vertising board’. Several exchange rounds then take placeduring the day, where the number of rounds is a parameterof the model that sets the maximum number of exchangesan agent can engage in per day. In each exchange round,agents can request a time-slot from the board, so long asthey have not already received a request from another agentduring that round. Agents accept or refuse requests basedon their strategy as described above. Only social capital, i.e.social agents’ memory of favours, remains between days.We expand on the original Petruzzi et al. (2013) modelby introducing social learning, allowing agents to changefrom selfish to social or vice versa (note that both socialand selfish agents undergo ‘social’ learning, which we re-er to simply as ‘learning’ from now on to avoid confusion).This works as follows. At the end of each day, a percent-age of the agents are randomly selected to undergo learn-ing. Each agent performing learning observes a randomlyselected second agent. If the observed agent has a higher sat-isfaction than the agent in question, then the first agent willcopy the strategy of the observed agent with a probabilityproportionate to the difference between the two agents’ sat-isfactions. Learning is thus payoff-biased (Boyd and Rich-erson, 1985), with strategies giving higher individual satis-faction more likely to spread in the population. Agents thatmove from a social strategy to the selfish strategy retain theiraccumulated social capital. Pseudocode for the simulationprocedure is given in Algorithm 1 .We also consider, as a counterpoint to social capital, sim-ulations where social capital is not recorded by agents, re-sulting in social agents accepting any non-detrimental ex-change. We refer to the social agents under this mechanismas social without social capital . All simulation results areaveraged over 50 runs for each variation of the simulationparameters. The parameters that we vary are the number ofexchange rounds per day, and the number of agents undergo-ing social learning at the end of each day (the learning rate).We hold the other parameters constant across simulationswith the values given in Table 1. Parameter Value
Population size 96Number of days 500Time-slots per day 24Slots selected by each agent 4Maximum agents per time-slot 16Simulation runs 50Table 1: Constant parameter values.Results from an illustrative run of the Energy ExchangeSimulation can be seen in Figure 1, showing how agent sat-isfaction changes over time.
Results and Analysis
To answer the research questions raised in the introduction,our analysis of the simulation proceeds as follows. We firstconsider populations where every agent uses the same strat-egy, and there is no learning. This allows us to determinewhether a pure population of social agents using the mech-anism without social capital can do as well as a pure popu-lation of agents that do track social capital. We then go onto consider mixed populations where both selfish and socialagents are present and can switch their strategies throughlearning. This allows us to determine the conditions underwhich social agents can outcompete selfish agents, and the Source code is available at https://github.com/NathanABrooks/ResourceExchangeArena
Algorithm 1
The Energy Exchange Simulation. d ← current day e ← current exchange round A ← set of a agents L ← number of agents a undergoing learning for d = 1 to MAX DAYS do for each a ∈ A do a .receive random allocation() end for for e = 1 to MAX EXCHANGES do V ← set of v adverts for each a ∈ A do v ← a .determine unwanted time slots() V .list advert( v ) end for for each a ∈ A do if a .received request() == true then go to next agent end if if a .satisfaction() == 1 then go to next agent else r ← a .identify beneficial exchange( V ) a .request exchange( r ) end if end for for each a ∈ A do if a .received request() == true then a .accept exchange if approved() end if end for for each a ∈ A do if a .made exchange() and a .agent type == So-cial then a .update social capital() end if end for end for d l ← while d l < L do a ← random agent that hasn’t considered chang-ing strategy today a ← random agent to observe if a .satisfaction() < a .satisfaction() then x ← random value between 0 and 1 if ( a .satisfaction() - a .satisfaction()) > x then a .copy strategy( a ) end if end if d l ← d l + 1 end while end for
00 200 300 400 50000.20.40.60.81 Random (No exchange)Optimum (No exchange)SelfishSocial
Average consumer satisfaction at the end of each day
Day A v e r age c on s u m e r s a t i s f a c t i on Figure 1: Average satisfaction per day for a typical run ofthe simulation. The run shown here includes social capi-tal, uses a learning rate of 50%, and 100 exchange roundsper day. The optimum result is calculated as the proportionof requested time-slots that exist within the simulation andcould therefore be allocated to an agent who requested them.extent to which this is affected by whether social capital istracked.
Single Strategy Populations
To establish a baseline for the performance of each of theavailable strategies explored here (selfish, and social withand without social capital), each is first run in isolation ofthe others, i.e. as a pure population of the strategy. Average(mean) satisfaction heatmaps for these simulations, acrossall parameters, can be seen in Figure 2. Optimal perfor-mance in these simulations would result in an average sat-isfaction of approximately 0.91 (as seen in Figure 1). FromFigure 2 we can see that social populations with social cap-ital achieve this optimal performance over the vast major-ity of parameters settings. Selfish populations, on the otherhand, consistently fall short of optimal satisfaction, but doshow improvement as the number of rounds of exchangeson a day increases. No improvement is seen as the numberof days the simulation is run for is increased, which followsfrom the fact that the only state carried over between daysis social capital, with selfish agents do not use. Social pop-ulations without the social capital mechanism similarly ex-hibit no improvement as the number of days increases for thesame reason. But crucially, they reach optimal performanceon the first day, if afforded enough exchanges. The inclu-sion of social capital means that agents require more daysto reach (near) optimal performance, with this only beingachieved after 100 days of social capital accumulation.Overall, it is clear from Figure 2 that satisfaction is de-pendent on the number of exchanges available to agents,and that social agents are able to break of out sub-optimal states more easily than selfish agents. This is through socialagents accepting exchanges that are neutral to their satisfac-tion but that increase the satisfaction of another agent. How-ever, the tracking and consideration of social capital slowsthis process down compared to the mechanism without so-cial capital. This is because with tracking of social capital,social agents will only accept neutral exchanges if they owea favour to the other agent, and so they behave like selfishagents until they begin to owe favours from previous days.
Mixed Populations without Social Capital
Results for populations which combine selfish and socialagents, but without access to social capital (resulting insocial agents always accepting non-detrimental exchanges)can be seen in Figure 3. In these simulations, populationsstart with an equal number of social and selfish agents, withlearning taking place at the end of each day, affecting theoverall ratio of social to selfish agents. Different learningrates are also tested; 0%, resulting in all agents retainingthe strategy they were initialised with, 50%, permitting halfof the agents (at random) to undergo learning, and 100%,resulting in all agents engaging in learning per day. Fig-ure 3 (Bottom Row) shows the change in strategy distri-bution across all parameters and learning rates. Within themaximum number of days available in these simulations nei-ther the social nor selfish strategy is eradicated from the pop-ulation (which is possible with the payoff-biased learningin Algorithm 1). In fact, it is often the case that close toa 50:50 distribution of strategies is retained, indicating nosignificant change due to learning. We do find that the so-cial strategy begins to dominate the population when 50 ex-changes per day are allowed, the simulation has run for overhalf the maximum number of days, and learning is imple-mented. But when the learning rate is set to 50%, and thenumber of exchanges exceeds 150, we see the populationdistributions beginning to swing in the favour of the selfishstrategy. Increasing the learning rate to 100% does stop theselfish strategy gaining prominence under these conditionsbut does not even get close to eradicating the selfish strat-egy.Given the (near) optimal performance demonstrated bysocial agents (without social capital) observed in Figure 2,where the social strategy existed in isolation, it is clear fromFigure 3 (Middle Row) that the inclusion of the selfish strat-egy has a detrimental effect of the satisfaction of socialagents, whilst improving the satisfaction of selfish agents(Figure 3 (Top Row)). The only time the social strategyachieves an advantage over the selfish strategy is when ex-changes are set at 50 per day – this result appears to be morea result of 50 exchanges not being sufficient to allow theselfish strategy to achieve its best performance, whilst be-ing sufficient for the social strategy to do so. The negativeconsequences of the continued use of the selfish strategy tooverall satisfaction of the populations, compared to when so-igure 2: Average satisfaction of single strategy populations. For all plots the y -axis shows the simulated day satisfactionwas measured on, and the x -axis shows the number of exchanges an agent is permitted to engage in per day. (Left) Averagesatisfaction for populations of selfish agents. (Middle) Average satisfaction for populations of social agents without socialcapital. (Right) Average satisfaction for populations of social agents with social capital.cial strategies are applied in isolation, are clearly apparent.Whilst the social strategy is necessary for selfish agents toimprove their satisfaction, through exploitation of the socialagents’ willingness to exchange, it is to the detriment of theoverall satisfaction of the population. It is therefore in theinterests of the populations to remove the selfish strategy. Ineffect, without social capital selfish agents are able to par-asitise social agents to the detriment of the population as awhole. Mixed Populations with Social Capital
As in Figure 2, populations using the social strategy whilstkeeping track of social capital exhibit a slower progressiontoward optimal satisfaction, as they only start accepting neu-tral exchanges as social capital accumulates over the days.This is also the case when the selfish strategy is included ina combined population (Figure 4). However, unlike mixedpopulations where social capital is not tracked (see Figure3), populations tracking and using social capital are able toachieve optimal (or near optimal) satisfaction when affordedenough exchanges, and the simulation is ran for over 100days. As the learning rate is increased to 50% the numberof exchanges required to achieve near optimal average satis-faction scores amongst social agents drops, though it is inter-esting to note that increasing the learning rate again to 100%does cause a drop in satisfaction when fewer exchanges perday are permitted.Social capital thus has the effect of slowing down optimi-sation, but with the benefit of hindering the ability of selfishagents to gain any traction in the population. We can see thatwhen learning is set to 0% selfish agents, despite making uphalf of the population, struggle achieve the same kinds ofsatisfaction scores as previously seen when social capital isnot available (compare Figure 3 (Left) to Figure 4 (Left)).As these selfish agents cannot accumulate social capital, de- sired time-slots held by other agents are harder to obtain thanwhen social capital is not tracked. This enables social agentsto build up exchange networks using social capital that can-not be invaded by selfish agents. When learning is intro-duced, the inclusion of social capital effectively eradicatesthe selfish strategy from the population. As social agentsare on average more satisfied than selfish ones, with this ef-fect becoming more apparent as the simulation goes on formore days or more exchanges are permitted, selfish agentsincreasingly switch strategies. Conversely, with no opportu-nity for selfish agents to parasitise the population there is lit-tle gradient for social agents to switch to the selfish strategy.We can see in Figure 4 (Bottom) that inclusion of learningand social capital results in the entire population adoptingthe social strategy. Increasing learning to 100% does slowthe removal of the selfish strategy down, as it introduces thepossibility of social agents switching to the selfish strategyin cases where some selfish agents have achieved high sat-isfaction by luck alone (i.e. being randomly allocated all oftheir preferred time slots), but generally learning combinedwith social capital has the effects of removing the selfishstrategy form the population, leading to near optimal satis-faction scores when provided with enough exchanges andenough simulated days.
The Population-level Effect of Social Capital
Despite the introduction of social capital removing the self-ish strategy, and achieving near optimal satisfaction acrossa number of parameter settings, it is still the case the over-all population satisfactions (averaged over both selfish andsocial agents) are similar when comparing populations withand without social capital (Figure 5). Due to social cap-ital slowing down the rate at which social agents undergoexchanges, when only a low number of exchanges per dayare available, or the simulations are stopped after a fewigure 3: Average satisfaction of selfish and social agents in mixed populations without social capital. For all plots the y -axisshows the simulated day satisfaction was measured on, and the x -axis shows the number of exchanges an agent is permittedto engage in per day. (Top Row) Average satisfaction of selfish agents. (Middle Row) Average satisfaction of social agents.(Bottom Row) Proportion of population using the social strategy; green indicates a greater proportion of social agents; purpleindicates a greater proportion of selfish agents.days, populations without social capital actually outperformpopulations with social capital, despite selfish agents beinglargely present in populations without social capital. Oncelearning is introduced, the number of exchanges per dayare increased, and the simulation is permitted to run for ex-tended amount of time, we do begin to see social capital pop-ulations outperforming those without social capital, thoughonly by a small margin. Taking just the raw satisfaction re-sults for the 500 th day, we do see a significant difference be-tween the satisfaction of social capital and non social capitalpopulations over most parameter settings. Using a Mann-Whitney U test, we observe p -values where p < . overmost parameter settings (see Table 2), the exceptions beingwhen learning is 50% and exchanges are set to 1, and whenlearning is 100% and exchanges are low (1 or 50). Theseresults indicate that by the 500 th day of the simulation, so-cial capital populations where learning is enabled (at 50% orabove) are significantly more satisfied than non social capi-tal populations. Mann-Whitney U: p < . Exchanges Learning 0% 50% 100%1 True False False50 True True False100 True True True150 True True True200 True True TrueTable 2: Mann-Whitney U test p -values when comparingsatisfaction of agents in populations with and without socialcapital. Test conducted for 500 th day only. p < .
01 =
T rue , p ≥ .
01 =
F alse . Discussion
We have extended the Petruzzi et al. (2013) model to an-swer two research questions. Our first question was, to whatextent is the tracking of social capital a necessary featureigure 4: Average satisfaction of selfish and social agents in mixed populations with social capital. For all plots the y -axisshows the simulated day satisfaction was measured on, and the x -axis shows the number of exchanges an agent is permittedto engage in per day. (Top Row) Average satisfaction of selfish agents. (Middle Row) Average satisfaction of social agents.(Bottom Row) Proportion of population using the social strategy; green indicates a greater proportion of social agents; purpleindicates a greater proportion of selfish agents.Figure 5: Average difference in satisfaction between all agents in populations with and without social capital. In all rows purpleindicates higher satisfaction in populations without social capital, orange indicates higher satisfaction in populations with socialcapital. For all plots the y -axis shows the simulated day satisfaction was measured on, and the x -axis shows the number ofexchanges an agent is permitted to engage in per day.f the exchange mechanism? We demonstrated that if so-cial agents exist in isolation in a pure population, then theyend up more satisfied when social capital is not tracked, forcases where the number of days that the simulation is run foris low. When the number of days is increased, they performsimilar to when social capital is tracked. Thus, in pure popu-lations with no possibility of selfish agents being introducedthen tracking of social capital is not beneficial. Moreover,tracking social capital is detrimental under some conditionssince it requires more days before social agents start accept-ing neutral exchanges, and hence more days before they es-cape from sub-optimal initial allocations.However, in a real system we must allow for the possi-bility that agents may act selfishly, or may learn to do soover time. To account for this, we have considered mixedpopulations where both social and selfish agents are presentand can exchange with each other. In this case, social agentsare able to achieve (near to) optimal satisfaction when so-cial capital is tracked, whereas without social capital they doless well. This effect becomes more pronounced once agentsare permitted to adjust their strategy by payoff-biased learn-ing. This is because without social capital, selfish agents areable to persist in the population under payoff-biased learn-ing. Their persistence is detrimental both to social agentsand to the population as a whole, since by not acceptingneutral exchanges they can prevent the agents escaping fromsub-optimal allocations. Conversely, with social capital self-ish agents are effectively purged from the population underpayoff-biased learning, which has a significant positive ef-fect on the satisfaction of the collective population.The results with payoff-biased (social) learning also an-swer our second research question: should we expect self-interested agents to adopt the selfish or the social strategy?This is because under payoff-biased learning, agents willonly change their strategy if they see another agent is doingbetter than itself under another strategy. Thus, our resultssuggest that self-interested agents should adopt the socialstrategy if social capital is tracked, but without social capitalthere is no pressure for them to do so.Recent research has shown that a diverse range of agent-based mechanisms can be effective at managing communityenergy systems. Allowing agents to form self-organisedclusters working to optimise their collective performancehas shown to be an effective approach with larger populationsizes ( ˇCauˇsevi´c et al., 2017). There are also more complexalgorithms that have the potential to be highly effective atmanaging decentralised heating systems(Kolen et al., 2017;Dengiz and Jochem, 2020). Our work differs in that it is in-herently human facing. A real world implementation of oursystem could easily operate in a socio-technical manner inwhich individuals can take over from the virtual agent rep-resenting them, setting their own preferences for time-slotsand making decisions on whether or not to accept requestedexchanges. Utilising a system based on social capital repre- sented as ‘favours’ would also be easy for the average userto understand facilitating procedural justice.In conclusion, we have demonstrated a decentralisedmechanism for household load balancing that is effectiveat satisfying agents’ preferences. The benefits of a decen-tralised mechanism are that it is inherently scalable as moreagents are introduced (Petruzzi et al., 2013), and helps topromote privacy and trust by not requiring households tosubmit their time-slot preferences to a centralised author-ity. In a real implementation, the exchanges may be per-formed by software agents running on home gateways in-stalled in households. This could involve various levels ofuser engagement with the exchange process. The mech-anism could also be used alongside differential pricing –households could be given a cheaper rate in their allocatedtime-slots. Future work should empirically investigate howusers perceive distributive and procedural justice both withand without tracking social capital (Powers et al., 2019). Acknowledgements
This work has been supported by a fellowship to Simon T.Powers from the Keele University Institute of Liberal Artsand Sciences.
References
Boyd, R. and Richerson, P. J. (1985).
Culture and the Evolu-tionary Process . University of Chicago Press, Chicago.ˇCauˇsevi´c, S., Warnier, M., and Brazier, F. M. (2017). Dy-namic, self-organized clusters as a means to supplyand demand matching in large-scale energy systems.In , pages 568–573. IEEE.Dengiz, T. and Jochem, P. (2020). Decentralized optimiza-tion approaches for using the load flexibility of electricheating devices.
Energy , 193:116651.Dutta, G. and Mitra, K. (2017). A literature review on dy-namic pricing of electricity.
Journal of the OperationalResearch Society , 68(10):1131–1145.HollanderBlumoff, R. and Tyler, T. R. (2008). Proceduraljustice in negotiation: Procedural fairness, outcome ac-ceptance, and integrative potential.
Law & Social In-quiry , 33(2):473–500.Kolen, S., Molitor, C., Wagner, L., and Monti, A. (2017).Two-level agent-based scheduling for a cluster of heat-ing systems.
Sustainable cities and society , 30:273–281.Petruzzi, P. E., Busquets, D., and Pitt, J. (2013). Self organ-ising flexible demand for smart grid. In , pages 21–22. IEEE.etruzzi, P. E., Busquets, D., and Pitt, J. (2014). Experi-ments with social capital in multi-agent systems. InDam, H. K., Pitt, J., Xu, Y., Governatori, G., and Ito,T., editors,
PRIMA 2014: Principles and Practice ofMulti-Agent Systems , Lecture Notes in Computer Sci-ence, pages 18–33, Cham. Springer International Pub-lishing.Powers, S. T., Meanwell, O., and Cai, Z. (2019). Finding fairnegotiation algorithms to reduce peak electricity con-sumption in micro grids. In
Advances in Practical Ap-plications of Survivable Agents and Multi-Agent Sys-tems: The PAAMS Collection , Lecture Notes in Com-puter Science, pages 269–272. Springer InternationalPublishing.Putnam, R. D. (1994). Social capital and public affairs.
Bul-letin of the American Academy of Arts and Sciences ,47(8):5–19.Rescher, N. (1966).
Distributive Justice: A ConstructiveCritique of the Utilitarian Theory of Distribution . TheBobbs-Merrill Company, Inc., Indianapolis.Simmons, S. I. and Rowlands, I. H. (2007). TOU rates andvulnerable households: Electricity consumption behav-ior in a Canadian case study. Technical report, Univer-sity of Waterloo.Stern, P. C., Aronson, E., Darley, J. M., Hill, D. H., Hirst,E., Kempton, W., and Wilbanks, T. J. (1986). The ef-fectiveness of incentives for residential energy conser-vation.
Evaluation Review , 10(2):147–176.Walker, G. and Devine-Wright, P. (2008). Community re-newable energy: What should it mean?