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Environmental Modelling & Software 26 (2011) 482e491

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Environmental Modelling & Software

journal homepage: www.elsevier .com/locate/envsoft

An adaptive agent-based modeling approach for analyzing the influence oftransaction costs on emissions trading markets

Bing Zhang, Yongliang Zhang, Jun Bi*

State Key Laboratory of Pollution Control and Resource Reuse, School of Environment, Nanjing University, 22 Hankou Road, Nanjing 210093, PR China

a r t i c l e i n f o

Article history:Received 23 April 2010Received in revised form16 October 2010Accepted 17 October 2010Available online 4 December 2010

Keywords:Emissions tradingTransaction costsAgent-based modelMarket efficiency

* Corresponding author. Tel.: þ86 25 83592841; faE-mail address: jbi@nju.edu.cn (J. Bi).

1364-8152/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.envsoft.2010.10.011

a b s t r a c t

Transaction costs are considered an essential factor that can adversely affect the performance of emis-sions trading markets. However, most studies are based on a static analyzing framework, making itdifficult to simulate real economic situations, in which the dynamic behavior and interaction betweenfirms in an emission trading system are fairly complicated and appear irrational to some extent. Based onan agent-based modeling approach, an artificial sulfur dioxide (SO2) emission trading market is devel-oped to identify the dynamic influence of transaction costs on market efficiency. The simulation resultsbased on empirical data from Jiangsu Province in China reveal that transaction costs have a negligibleeffect on the market price. However, transaction costs can block a small amount of trading as well asdecrease total emission trading amount and market efficiency. Therefore, the policy design of emissiontrading in China should treat transaction costs carefully.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Increasing worldwide criticism has pressured China to reduceits air pollution to acceptable level. In its 11th Five-Year Plan, theState Environmental Protection Agency has set the target forreducing SO2 discharge to 10% (22.95 million tons) through noveldesulphurization technologies and environmental regulationinstruments. There are several policy options available for SO2reduction. Implementing cost-effective policies is crucial for Chinato meet air quality standards. Emissions trading that utilizesmarket-based mechanisms is considered to be an effective instru-ment in reducing emissions with the lowest possible economiccost.

The key feature of emission trading is that it allows regulatedenterprises to transfer emission allowances that can lead to thedistribution of emission reduction in enterprises, which equalizethe marginal cost of emission reduction among enterprises andreduce the total emission control costs (Burtraw et al., 2005). Thistype of incentive mechanism is commonly used in the US, Europe,and other counties (Tietenberg, 2006). Article 17 of the 1997 KyotoProtocol describes an international emission trading systemfor greenhouse gases (GHGs) as one of the four cooperative

x: þ86 25 83595207.

All rights reserved.

mechanisms to achieve GHGs targets by 2008e2012, has alsosparked global interest (Soleille, 2006; Weber and Matthews,2007).

Emissions trading policies and practices have achieved signif-icant success in reducing emission control costs in the US, Europe,Canada, Singapore, and other countries. However, many factorscan adversely affect the performance of permit markets, concen-tration in the output market, non-profit-maximizing behavior(e.g., sales or staff maximization), the preexisting regulationenvironment, and the degree of monitoring and enforcementinvolved. Transaction costs (when broadly defined) can be a majorhindrance to cost-effective emission trading systems (Stavins,1995; Tietenberg, 2006; Zhang et al., 2010). Several authors havecommented on the potential importance of transaction costsin tradable permit markets and posited that transaction costs(e.g., finding a trading partner) might reduce cost-effectiveness(Montero, 1997; Woerdman, 2001).

A transaction cost is an expense incurred during an economicexchange. Mullins and Baron classify transaction costs into directcosts (e.g., money spent to initiate and complete a trade) andopportunity costs (e.g., loss of time and resources through delayand managerial attention) (Mullins and Baron, 1997). Furubotnand Richter (1997) classify transaction costs into fixed costs andvariable costs; only the latter depends on the number or volumeof transactions. Stavins defines transaction costs as the differencebetween buying and selling prices in a given market. Transactioncosts are generally ubiquitous in market economies because

Table 1State variables and scales.

Variable Unit Description

pe rmb/kWh The price of electricityp rmb/kg The price of emissions permitAi kg The allowance of firm iei kg Total emission producedai kg/ton Sulfur dioxide yield parameter of firm iq % Sulfur dioxide removal rateqi ton The amount of coal usedri kg Pollution reduced by firm i himselfxi kg Emission traded by firm igi(qi) kWh Electricity production functionGi e Electricity production parameterpc rmb/ton Price of coal and adjustment costsRi rmb The benefit of electricity generation excluding

emissions reduction costsp rmb The benefit of firmspd rmb/kg Emissions discharge fee/taxf rmb/kg Emission reduction costs parameterk e The base of emission reduction costs functionk e The exponent of electricity generation

functiona rmb Fixed transaction costsb rmb/kg Trading tax

B. Zhang et al. / Environmental Modelling & Software 26 (2011) 482e491 483

parties to transfer (e.g., property rights such as tradable permits)must find one another, communicate, and exchange information(Stavins, 1995). Transaction costs in the emission trading marketstypically consist of search, negotiation, approval, monitoring,enforcement, and insurance costs (Dudek and Wiener, 1996).

Many scholars have allowed for transaction costs within themodel of tradable permit activity (Tschirhart, 1984). Stavinsprovides a theoretical framework to include transaction costs ina model of marketable permits. General transaction cost curvesand continuous marginal control cost curves are used todemonstrate how transaction costs reduce trading levels andincrease abatement costs as well as the relevance of the initialallocation of permits in terms of efficiency (Stavins, 1995).However, this framework is not ideal for measuring how signifi-cant (as opposed to incremental) changes in transaction costsaffect equilibrium price, trading volume, and aggregate controlcosts, especially if emitting sources have discrete control tech-nology choices rather than continuous marginal cost curves.Montero extends the work of Stavins using a numerical modelwith transaction costs and uncertainty to demonstrate theireffects on market performance (i.e., equilibrium price of permitsand trading volume) and aggregate control costs (Montero, 1997).Gu and Li (2006) analyze the influences of transaction costs onthe equilibrium of emission permit markets and find that trans-action costs reduce the volume of emission trading and increaseemission control costs compare with non-transaction costsmarket.

Meanwhile, traditional economic theories and analyses onlyconsider ideal representative participants in static equilibriumstates (Tesfatsion, 2006). Understanding economic processes inmarkets (i.e., interactions among economic agents that standbehind an aggregated index) is essential especially because agentinteractions are heterogeneous and can generate network effects(Bithell and Brasington, 2009; Bonabeau, 2002; Filatova et al.,2010). It is very difficult to analyze the dynamically changingsituations involving heterogeneous subjects when using staticand homogeneous methods (Mizuta and Yamagata, 2001). A newpolicy analysis framework e agent-based model e has beenwidely applied in artificial markets simulation (Guerci et al.,2005; Tesfatsion, 2006; Veit et al., 2009; Walter and Gomide,2008) as well as in emissions trading markets (Genoesea et al.,2007; Mizuta and Yamagata, 2001). Agent-based modelsprovide a powerful analytical approach that enables themodeling of many heterogeneous real world agents (e.g.,households, businesses, and governments) as individual softwareprograms. Their dynamic environmental, political, economic, andsocial behaviors are captured within each software agent,creating a virtual replica of the real world (Peters and Brassel,2000; Tesfatsion, 2006). The agent-based model for analyzingemission trading is considered very useful because of its abilityto capture the complex trading mechanisms of agents,purchasing behavior, and their interdependencies that arebeyond the scope of traditional approaches (Bonabeau, 2002;Tesfatsion, 2006).

This paper establishes a bottom-up analytical framework ofemission trading policy The artificial SO2 emission tradingmarket of power plants in Jiangsu Province in China is developed.This paper also examines the different transaction costs andrelevant performance of emission trading markets. In Section 2,the agent-based model of the Jiangsu SO2 emission tradingmarket is described based on the standard protocol for describingindividual- and agent-based models (Grimm et al., 2006). Thesimulation results and discussion are presented in Section 3.Finally, the conclusions and future research are outlined inSection 4.

2. Agent-based model of the Jiangsu SO2 emission tradingmarket

2.1. Purpose

The agent-based model of the Jiangsu SO2 emission tradingmarket is developed to simulate the emission trading market inpresence of transaction costs and identify the influence of trans-action costs on the cost-effectiveness of the emission tradingmarket.

2.2. State variables and scales

Power plants (considered as the agents in this paper) arerequired to abate SO2 emission below the emission rights and tomaximize their profits. Agents, unlike in traditional economicanalysis, behave based on their own local information. Powerplants rely on information such as the marginal profits (MP)function, SO2 emission rights, market price, and existing environ-mental regulations. Power plants are free to trade permits at anytime and have to meet government standards by exercising pollu-tion control and/or possessing permits for their residual emission.We also assume that nobody exercises market power in emissiontrading market and perfect monitoring and enforcement areavailable for environmental regulators.

We consider ei as the unconstrained emission in units per year, rias the pollution reduction in units per year by firm i, Ai as thequantity of permits in units per year allocated to power plant i, andxi as the amount of emission traded (see Table 1).

Revenue of power plant: The profit of power plants in the JiangsuSO2 emission trading market is affected by coal price, electricityprice, transaction costs, existing emission discharge fees and taxes,and other costs. The traditional revenue of a power plant is derivedfrom electricity sales minus the costs of coal and other operatingcosts. The revenue of power plants is then calculated using

Ri ¼ gðqiÞpe � pcqi (1)

where qi is the coal consumed by the power plant, and pe and pcrepresent the prices of electricity and coal, respectively. Assumingthat the technology is still described by a homogenous of thedegree one CobbeDouglas production function, g(q)¼Gqk, we

1 Ep represents the emission discharge when the marginal profits are equal to p.

B. Zhang et al. / Environmental Modelling & Software 26 (2011) 482e491484

isolated the influence of imperfect competition on the electricitymarket, where G is a productivity parameter, 0< k< 1, and k isa constant determined by technology and power capacity.

Emission abatement costs: ci(ri) is assumed to denote the emis-sion abatement costs, where ci0(ri)> 0 and ci00(ri)� 0. Emissionabatement costs are further assumed to be a function of emissionreduction and emission reduction rate. They are derived as follows:

ci ¼ fiaiqiqik1=1�qi (2)

where k and fi are the parameters of the emission abatement costsfunction, and qi is the emission abatement rate. All power plants areassumed to possess the same value of k and different fi. aiqiqi is theemission reduced by power plant i.

Transaction costs: Transaction costs are classified into two partsbased on previous research: (1) fixed costs and (2) costs related togross emission trading. The transaction costs are calculated by

TðxiÞ ¼ aþ bxi (3)

where a is the fixed part of transaction costs, and bx is related to theemission trading quantity. Fixed costs can be considered adminis-trative costs such as additional monitoring costs for trading,approval costs, and other related costs. The government providesthe emission trading center that helps in reducing transactioncosts. However, the building and maintenance of the emissiontrading center produce other costs that, in turn, are transferred totrading firms through “trading tax”.

Emission discharge fee/tax: Power plants in the SO2 emissiontrading market of Jiangsu Province should also pay for emissiondischarge fees/taxes (pd).

2.3. Process overview and scheduling

This research chose the continuous double auction (CDA)emission trading market for further analysis based on the recentpractices of emissions trading in China (Nie and Xu, 2009). CDA isa natural tradingmechanism inwhich both sellers and buyersmakethe buy/sell limit order, including the maximum/minimum priceand the desired/offered amount. When a new order matches thebest waiting order of the opposite type, a trade is made (for thelimit price of the counterpart); otherwise, the neworder is made onhold. Orders may also be cancelled by their submitters (Cliff, 2000;Posada et al., 2005). All participants can learn from previous bid-dings and then adjust the next bideask amount and price. Thedecision-making process of each agent consists of the fourfollowing steps (Fig. 1).

2.3.1. Step one: thinking an orderEach firm considers an order depending on the MP, emission

allowance, market price of the emission permits, and expectedprice of emission permits when they participate in the emissiontrading market for first time or have been waiting to participate insome trading rounds. The first stage is the determination of theemission amount each firm expects to abate and trade in a yearbased on the current market price (p). Assuming that MPA is the MPof a firm at the amount of emission discharge (E) equal to itsallowance (A), there are three choices based on the current emis-sion price of each firm. The firm should be a buyer if its MPA ishigher than the current emission price (Type A), and the firmshould be a seller if its MPA is lower than the current emission price(Type B). However, if a firm has an MPA equal to the currentemission price (Type C), it is neither a seller nor a buyer until theprice changes.

If a firm is considered Type A, it then selects a strategy, deter-mines a bid amount, and calculates theMP to determine a bid price.

The optimal bid price is less than p when the bid amount is Ep� A1

because the actual trading amount is not yet known, and all agentsare risk-neutral. If p is chosen as the bid price, buyers can thendetermine the bid price of p; the bid amount is Ep� A. In the samemanner, sellers can determine the bid price of p; the bid amount isA� Ep.

2.3.2. Step two: making an orderAll agents consider an order but only some of them actually

make it. Each agent has a constant activation probability assumedto be 25% per round. In other words, 25% of the agents are randomlychosen to anticipate a bid in every round (Posada et al., 2005;Walsh et al., 2002).

2.3.3. Step three: accepting an orderThe buyer with the highest bid price is initially matched with

the seller with the lowest asking price as long as both sellers andbuyers exist, and the highest (buying) bid price is not lower thanthe lowest (selling) bid price (Nicolaisen et al., 2001). The purchaseprice is equal to the average of the highest bid price of buyers andthe lowest bid price of sellers. Moreover, if the respective bidamounts of the buyer and the seller do not match, then the bid ofthe buyer is matched with that of the seller for the quantity oftradable permits as the minimum of the two amounts: the biddingamount of the buyer and the asking amount of the seller. Thecarryover amount of buying or selling is then calculated, and thenext pair is matched in the same manner.

2.3.4. Step four: learning from previous ordersThe repeated auction constitutes an environment where bidders

can obtain and utilize information from previous auction results.Cliff indicates that the price convergence of zero-intelligencetraders is predictable from an a priori analysis of the statistics of thesystem (Cliff, 1997); thus, more complex bargaining mechanisms orsome “intelligence” is necessary for traders. Agents called zerointelligence plus (ZIP) agents have been developed with simplemachine learning techniques (Cliff and Bruten, 1997). Furtherexperiments have shown that ZIP agents outperform their humancounterparts (Das et al., 2001). Therefore, in this study, agents areendowed with ZIP bideask strategies.

ZIP strategies predict or assume that agents in the emissiontrading market can adjust their profit margin and bid priceaccording to their previous biddings. If there was a transaction inthe last round, and the agent was not the winner or no transactionwas completed, the agent would decrease his/her profit margin inthe current round. Otherwise, the winner would increase his/herprofit margin.

2.4. Design concepts

Emergence: We explicitly modeled the trading behavior of eachpower plant by calculating cost savings, emission trading amounts,and transaction costs to reveal the market performance. Emergentsystem dynamics includes the following: (1) emission tradingamount and market price, (2) MP of the agent, and (3) transactioncosts and cost savings of the emission trading market.

Adaptation: Power plants have two adaptive behaviors: think anoptimal order and learn from previous orders. Power plants decideon their trading amount and bideask price according to the currentmarket price and personal information. They also learn fromprevious orders and adjust their bideask strategies.

no

Agent i

Input data

t=t+1

Make an order last round?

iAMP p>

no

iAMP p<

yes

yes

Make an order ?

Accept an order

Winner?

yes

Asking strategiesAsking price = pAsking amount= i pA E−

Make an order ?

no

yesyes

Accept an order Winner?yes

( ) ( ) ( ) ( )i i it R t q t A tτ = + ( ) ( ) ( ) ( )i i it R t q t A tτ = +

( ) ( ( ) ( ))i i i it t p tβ τΔ = − ( ) ( ( ) ( ))i i i it t p tβ τΔ = −

[ ]0.95,1.0iR ∼

[ ]0.1,0.0iA ∼ −

[ ]1.0,1.05iR ∼

[ ]0.0,0.1iA ∼

( 1) ( ) ( )i i ip t p t t+ = + Δ

yes

no

To be a buyer at last round yes

yes

Biding strategiesBiding price = pBiding amount=

p iE A−

no

no

no

Next round

no

Fig. 1. Flow diagram of the processes of the model.

B. Zhang et al. / Environmental Modelling & Software 26 (2011) 482e491 485

Fitness: Power plants in the emission trading market are profit-maximizing agents. They tend to maximize their profits by buyingpermits when their MPs are higher than the market price and byselling permits when their MPs are lower than the market price.

Prediction: The only prediction power plants use is in evaluatingthe profits or cost savings obtained from emission trading. Powerplants calculate (predict) the profits or cost savings they can obtainat the current market price before selecting the optimal speed.

Table 2Original data from the power plants in Jiangsu Province.

Number Ai ci Ei qi pe Gqik

Units million kg million rmb million kg thousand tons rmb/kWh kWh

1 3.03 15.00 1.90 600.00 0.3900 1.332 4.92 60.00 2.73 2080.00 0.3900 4.403 5.63 4.00 11.98 1410.00 0.3637 3.454 2.25 2.00 6.20 620.00 0.3517 1.505 1.61 9.00 0.25 268.00 0.3750 0.606 3.63 10.00 9.10 1183.00 0.3900 2.407 23.23 18.86 20.67 3214.00 0.3712 7.948 7.43 100.00 2.37 3263.00 0.3920 6.739 2.45 10.00 14.69 1624.00 0.3900 4.0010 7.82 43.00 15.67 2864.00 0.3600 6.0011 12.58 7.00 87.43 5392.00 0.3277 12.0912 2.54 36.00 0.92 1144.00 0.3900 2.9513 10.91 14.00 24.87 2595.00 0.3874 6.4914 2.49 40.00 3.14 1400.00 0.3800 3.1015 4.75 37.00 3.50 1158.00 0.3900 2.4316 3.43 8.00 4.96 711.00 0.3600 2.0817 4.62 149.69 4.62 3875.84 0.3900 8.7018 4.62 149.69 4.62 3875.84 0.3900 8.7019 2.31 74.84 2.31 1937.92 0.3900 4.3020 3.87 10.00 12.50 1100.00 0.3747 2.7021 4.62 40.00 0.86 890.00 0.3900 2.7022 10.03 3.87 29.89 1860.00 0.3837 5.5423 11.62 22.50 25.43 2121.00 0.3697 5.5724 11.15 120.00 3.67 4003.00 0.3900 10.3725 1.94 16.67 2.97 725.00 0.3747 1.5426 8.45 60.00 4.88 1766.00 0.3900 3.9727 13.73 55.00 9.15 3844.00 0.3931 9.4828 5.60 70.00 1.92 3399.00 0.3900 8.4029 3.70 60.00 1.54 2447.00 0.3900 6.2930 10.65 50.00 15.92 1953.00 0.3800 4.6131 12.36 20.00 39.87 3154.00 0.3637 7.8032 9.24 299.38 9.24 7751.68 0.3900 17.5033 6.49 54.40 20.29 3069.00 0.3807 5.9434 12.22 45.20 17.64 2906.00 0.3900 6.8935 3.01 1.55 6.54 451.00 0.3637 1.0036 4.05 10.00 12.58 1296.00 0.3853 2.7037 9.46 15.00 5.44 1210.00 0.3922 2.7038 6.41 60.00 9.49 2615.00 0.3847 5.6039 15.71 0.78 34.55 2823.00 0.3847 7.3540 11.62 6.00 34.92 4193.00 0.3483 9.8041 5.81 36.00 5.18 1399.00 0.3900 3.4642 9.74 60.00 13.33 3790.00 0.3883 8.0043 7.70 249.48 7.70 6459.73 0.3900 14.6044 1.91 61.79 1.91 1599.83 0.3900 3.6045 6.57 3.00 7.10 470.00 0.3750 1.46

Table 3Initial values of variables.

>Variable Value Reference

pe [0.32,0.40] JSFB (2006), see Table 3Ai e JSEPB (2002), see Table 3ai e Calculated by the data of 2006pc 420 Data from 45 power plantspd 1.26 JSEPB et al. (2007)f e Calculated by the data of 2006k 1.0581363 Calculated by the data of 2006k 0.92011 Calculated by the data of 2006

B. Zhang et al. / Environmental Modelling & Software 26 (2011) 482e491486

Sensing: Power plants are simply assumed to know, withoutuncertainty, the internal (i.e., their revenue and emission abate-ment costs functions) and environmental variables (i.e., marketprice) used to optimize their profits.

Interaction: Power plants in the current emission trading modelinteract indirectly. Power plants’ submitted bideask orders arematched by the trading center to make a deal.

Stochasticity: The profit-maximizing model is completelydeterministic in terms of bideasking amount and price. However,learning and participative models include several stochastic prog-resses. Every power plant chooses to make an order stochastically.The learning stride length can be determined by some uniformlydistributed variable in the ZIP strategies.

Collectives: Our model does not consider the formation ofaggregations among individuals, as in the case of a conspiracy.

Observation: We output data at the end of every trade to test andanalyze our model. These output files can be imported easily toa spreadsheet for analysis and visualization. The “probes” can beused during run time to examine the current values of the variablesunder a wide range of conditions. The platform of the agent-basedmodel includes a graphic display that incorporates the emissiontrading amount, transaction costs, and total emission control costs.This is useful for demonstrating the physical components of themodel.

2.5. Initialization

Here, 45 agents were created in the NetLogo platform based onthe progress and scheduling of the SO2 emission trading market.The location of every agent (power plants) was stochastic, and themodel starts by reading the characteristic value. These character-istics include state variables of agents, such as initial allowance (A)and electricity price (pe). Agents can share global variables such asthe emission discharge fee (pd). The initial values of the variablesand the initialization dates were collected or calculated based onthe 2006 data (Tables 2 and 3).

The production data from power plants cover a period of twoyears. All power plants have the same value of k, giving thefollowing regression equation:

lnðgiÞ ¼ k lnðqiÞ þ ln Gi þ e: (4)

where 3 represents error. The regression results using real datafrom 45 power plants are presented in Table 4. The coefficientof ln q is the value of k in Eq. (4), which gives k¼ 0.92011(Table 4).

In addition, all power plants have the same assumed value of kand a distinct fi. Assuming that aiqiqi is the emission reduced by thepower plant i, the regression equation is expressed as

ln ci ¼ ln fi þ ln Ri þ xi ln kþ ei: (5)

where xi¼ 1/1� qi, and 3 represents error. The regression coef-ficient xi gives the value of ln k using the databases of 45 powerplants. We then have ln k¼ 0.0565 and k¼ 1.0581363 (seeTable 5).

2.6. Input

The values of parameters a and b, aside from the previousvariables, were controlledmanually to test themarket performanceunder different emission discharge fee/tax scenarios. The fixed cost,based on a previous interview, was set to 26,666 rmb, where b isused as an alterable variable in ourmodel for different policy designscenarios. Here, b is set to have values ranging from 0.01 to 0.5rmb/kg.

2.7. Submodels

2.7.1. Marginal profitsThe optimization problem of the firms is represented as follows:

max p ¼ Gqkpe � pcq� faqqk1=1�q* � pdaqð1� qÞ (6)

subject to : A� aqð1� qÞ ¼ 0 (7)

Table 4Regression results of Eq. (4).

Source SS df MS Number of obs 45Model 23.2669 1 23.2669 F(1, 43) 2029.1

Prob> F 0.0000Residual 0.4931 43 0.0115 R-squared 0.9792

Adj R-squared 0.9788Total 23.7600 44 0.5400 Root MSE 0.10708

ln g Coef. Std. Err. t P> t [95% Conf. Interval]ln q 0.9201 0.0216 45.05 0.0000 0.930523 1.017747_cons 8.1378 0.3126 26.03 0.0000 7.507345 8.768213

B. Zhang et al. / Environmental Modelling & Software 26 (2011) 482e491 487

The Lagrangian expression is given by

L ¼ Gqkpe � pcq� faqqk1=1�q � pdaqð1� qÞ þ lðA� aqð1� qÞÞ

(8)

The necessary first-order conditions determining the maximumat (q*,q*,l*,x*) are

Gkq*k�1pe � pc � faqk1=1�q* � pda

�1� q*

�� l*a

�1� q*

�¼ 0

(9)

�faq*k1=1�q

1þ q ln k

ð1� qÞ2!

þ pdaq* þ l*aq* ¼ 0 (10)

Solving Eq. (10) gives

l* ¼ fk1=1�q

1þ q ln k

ð1� qÞ2!

� pd (11)

where l* is the Lagrangianmultiplier representing theMPs of a unitpermit.

2.7.2. Learning strategiesAn individual ZIP agent (denoted by subscript i) at a given time t

calculates the shout price pi(t) with price li,j using the real-valuedprofit margin of an agent at mi(t). The following equation is derived:

piðtÞ ¼ li;jð1þ miðtÞÞ (12)

This implies that the margin of a seller is raised by increasing miand is lowered by decreasing mi with the following constraint:mi(t)˛ [�1,0]:c t. The aim is for the value of mi for each trader toalter dynamically in response to the action of other traders in themarket (e.g., increasing or decreasing to maintain a competitivematch between the shout price of that trader and the shout pricesof the other traders). Based on the WidroweHoff “delta rule”(Zhanand Zhan, 2008), the following is derived:

Aðt þ 1Þ ¼ AðtÞ þ DðtÞ (13)

where A(t) is the actual output at time t, A(tþ 1) is the actual outputin the next time step, and D(t) is the change in output as

Table 5Regression results of Eq. (5).

Source SS df MS Number of obs 45Model 73.4143 2 36.7072 F(2, 42) 152.61

Prob> F 0Residual 10.1025 42 0.2405 R-squared 0.879

Adj R-squared 0.8733Total 83.5168 44 1.8981 Root MSE 0.49044

ln c Coef. Std. Err. t P> t [95% Conf. Interval]Ln R 1.2232 0.0936 13.07 0.0000 1.0343 1.4121x 0.0565 0.0213 2.66 0.0110 0.0136 0.0994_cons �3.0840 1.4619 �2.11 0.0410 �6.0346 �0.1337

determined by the product of the learning rate coefficient b and thedifference between A(t) and the desired output at time t, which isdenoted by D(t):

DðtÞ ¼ bðDðtÞ � AðtÞÞ (14)

This method can be employed by ZIP traders as a “target price”(denoted by si(t)) can then be calculated for each trader whena trader is required to increase or decrease the profit margin. TheWidroweHoff rule can be applied to take the shout price of thetrader in the next time step (pi(tþ 1)) closer to the target price si(t).Rearranging Eq. (13) is necessary to give an update rule for theprofit margin mi on the transition from time t to tþ 1.

miðt þ 1Þ ¼ ðpiðtÞ þ DiðtÞÞ=li;j � 1 (15)

where Di(t) is the WidroweHoff delta value calculated using theindividual learning rate of the trader bi given by

DiðtÞ ¼ biðsiðtÞ � piðtÞÞ (16)

All that remains is to determine how the target price si(t) shouldbe set. A simplemethod can set the target price equal to the price ofthe last shout (i.e., si(t)¼ q(t)), presenting a significant problem.When the last shout price is very close or equal to the trader’scurrent shout price (i.e., p(t)z q(t)), the value of Di(t) given by Eq.(13) is either very small or zero. Thus, traders who have shoutedprices close to q(t) are likely to make negligible alterations to theirprofit margins. They will shout very similar prices when given thenext opportunity.

The target price, si(t), can be determined in many ways. Thisresearch generated the target price using a stochastic function ofthe shout price q(t), as shown in Eq. (17):

siðtÞ ¼ RiðtÞqðtÞ þ AiðtÞ (17)

where Ri is a randomly generated coefficient that sets the target pricerelative to the price q(t) of the last shout price, and Ai(t) is a (small)random absolute price alteration (or perturbation). Ri> 1.0 andAi> 0.0 if the intention is to increase the shout price of the dealer;0.0< Ri< 1.0 and Ai< 0.0 if the intention is to decrease it. Ri isassumed tobeuniformlydistributedover the range [1.0,1.05] for priceincreases and over [0.95,1.0] for price decreases, giving relative risesor falls of up to 5%. We also assumed that Ai is uniformly distributedover [0.0,0.1] for increases and [�0.1,0.0] for decreases. The learningrate value of each trader, bi, is randomly generatedwhen the trader isinitialized, using values uniformly distributed over [0.1,0.5].

3. Simulation results

3.1. Market efficiency of a perfectly competitive market

We first examined the performance of a completely competitiveemission trading market while the transaction costs are zero andthe total emission control costs are under the “command andcontrol” scenario (i.e., when emission trading is not allowed) toevaluate the proposed artificial market model and policy perfor-mance. The optimization problem of the firm in a completelycompetitive emission trading market is calculated using thefollowing equations:

max p ¼ Gqkpe � pcq� faqqk1=1�q*�pdaqð1� qÞ � px (18)

subject to : Aþ x� aqð1� qÞ ¼ 0 (19)

0 � q � 1 (20)

Fig. 2. Price under different transaction cost scenarios.

Table 6Regression results of the average market price by transaction costs.

Source SS df MS Number of obs 50F(1, 48) 3.7

Model 0.0714 1 0.0714 Prob> F 0.0603Residual 0.9256 48 0.0193 R-squared 0.0716

B. Zhang et al. / Environmental Modelling & Software 26 (2011) 482e491488

0 � q � qmax (21)

X45i¼1

xi ¼ 0 (22)

The equilibrium price in the Jiangsu SO2 emission tradingmarket is 4.20 rmb/kg, and the marginal control costs are equatedacross all agents. The total emission control costs decrease to4.24Eþ 09 rmb when the market achieved equilibrium, therebysaving 5.50Eþ 08 rmb or 11.45% of the total emission control costsunder the “command and control” scenario.

Adj R-squared 0.0522Total 0.9970 49 0.0203 Root MSE 0.1389

Price Coef. Std. Err. t P> t [95% Conf. Interval]b 0.2618 0.1361 1.9200 0.0600 �0.0118 0.5354_cons 3.1966 0.0399 105.2500 0.0000 4.1164 4.2768

3.2. Results of the agent-based model

This research set different transaction costs scenarios that thetrading taxwas converted from 0.01 rmb/kg to 0.5 rmb/kg, based on

othermarkets. The evolution of market price under different tradingtaxes is shown in Fig. 2. Themarket prices in ourmodel convergedonthe equilibrium price quickly. The ZIP agents in our model alsoconverged to the equilibrium price quickly; this result is different

Fig. 3. Total emission trading amount under different trading tax scenarios.

B. Zhang et al. / Environmental Modelling & Software 26 (2011) 482e491 489

from thefindings of other studies (Posada and López-Paredes, 2008).The main reason is that only 25% of the agents are chosen to maketheir orders. Agents who have been waiting for some rounds woulddecide on thebideask strategies according to the “thinking anorder”rules. Thus, the market converged to the equilibrium price quickly.

Transaction costs in completely competitive emission tradingmarkets will decrease the equilibrium price (Stavins, 1995). Themarket price in our artificial market is dynamic. We examined thetrend of average market price under different transaction costs.The regression results show that the market prices in this researchdo not reveal a significant difference (Table 6).

The increase in trading tax will also depresse the activity oftransactions and heighten the total emission control costs whilecomparing to the completely competitive market. The existence oftrading tax not only increase the cost of emission trading but alsoblock the trading with small amount. Fig. 3 reveals the totalemission trading amount under different trading tax scenarios. Thetotal emission trading amount decreased when the trading taxincreased. When trading tax was 0.5 rmb/kg, the total emissiontrading amount was 68.5 thousand tons of SO2, that is, 75% of the

4.3

4.35

4.4

4.45

4.5

rmb/

kg

0 10 20

marginal profit

Fig. 4. Distribution of marginal

total emission trading amount at a trading tax of 0.01 rmb/kg.Moreover, the emission trading market could not achieve equilib-rium in which all marginal abatement profits (costs) of firms wereequal to the market price even if the market was run in the longterm.

Fig. 4 illustrates the distribution of the MPs of the power plantsafter the long-term running of the emission trading market. Thepower plants stopped trading if the MPs were higher than p� b forsellers and lower than pþ b for buyers.

Less emission trading motivation and amount led to thedecrease of market efficiency of the Jiangsu SO2 emission tradingmarket. Transaction costs significantly reduced the emissiontrading market efficiency when we examined the total emissioncontrol costs under different transaction cost scenarios. Fig. 5shows the total emission control costs under different tradingtaxes. The total emission control costs also increased from 4.27 to4.33Eþ 09 rmb when the trading tax increased from 0.01 to0.5 rmb/kg. In contrast, the total cost savings rate declined from10.57% to 9.14%. Thus, transaction costs significantly reduced themarket efficiency of the Jiangsu SO2 emission trading market.

Many researchers assume that transaction costs will reducemarket efficiency. The results of this study also reveal that sucheffect is significant. The trading tax in the Jiangsu SO2 emissiontrading market is around 0.3 rmb/kg which will cause 7.5% marketefficiency reduction. Moreover, the transaction costs may be higherthan predicted in the real emission trading market. The SO2 emis-sion permit trading scheme employed by the Jiangsu Provincerequires power plants to search for trading partners themselves.The two trading parties, after reaching an agreement, should applyfor permission from the Economics and Trade Committee (ETC).The environmental protection bureau will then pursue a detailedauditing after the ETC approves the application. The two tradingparties can then sign the emission trading contract once the envi-ronmental protection bureau finally approves the emission tradingapplication. This process needs a certain period to fix and causeshigh transaction costs. In contrast, the CDA system reduced thetransaction costs significantly in this model. Thus, transaction costis a key factor in reducing market efficiency of emissions trading.

30 40 50x

equilibrium price

abatement profits (b¼ 0.3).

Fig. 5. Total emission control costs and cost saving rate under different trading tax scenarios.

B. Zhang et al. / Environmental Modelling & Software 26 (2011) 482e491490

4. Conclusions

Market-based permit programs for environmental protectionhave the potential in helping states attain the same environmentalquality, which is expected with lower aggregate costs. However,according to several scholars, transaction costs play a key role in thesuccess of an emission trading system (Grubb et al., 1998; Hahn andHester, 1989; Heller, 1999). Due to the transaction costs, assumingthat the post-trading outcome is the least-cost equilibrium wouldbe a mistake. Taking the potential cost savings as the real savings,which is achieved through an emission trading program in lieu ofthe traditional “command and control” approach, would also bea mistake (Bressers and Huitema, 1999; Krutilla, 1999).

This study has described an agent-based simulation frameworkand its application to the SO2 emission trading market imple-mented in the Jiangsu Province to examine the influence of trans-action costs on the cost-effectiveness of emission trading market.The result reveals that transaction costs have negligible influenceon market price; this finding is different from certain analysis-based complete competitive market assumptions (Stavins, 1995).However, transaction costs significantly reduce the emissiontrading amount as well as the market efficiency of the SO2 emissiontrading market in China. This research asserts that the emissiontrading center or the electronic bulletin board performs well andreflects the market conditions aside from reducing the searchingcosts; however, trading tax also reduces market efficiency. Thus,the government should set an acceptable trading tax for the SO2emission trading market in China.

This research applies an agent-based model to illustrate theemission trading market and examines the influence of transactioncosts on market efficiency. The agent-based model simulates thereality and the details of a system, providing a behavioral micro-simulation. Macro-level behavior then emerges from the manyinteracting agents at the micro-level. Analysts using behavioralmicro-simulation are able to evaluate policies (e.g., trading mech-anisms and market rules) and gain greater insight into the func-tions of a system, as well as study their social, economic, and

environmental effects. The usefulness of the agent-based model foranalyzing emission trading lies in its ability to capture the complextrading mechanisms and purchasing behavior of the agents as wellas their interdependencies which are beyond the scope of tradi-tional approaches. Moreover, another important strength ofcomputational modeling is the ability of the modelers to hold allvariables constant (except the one of interest to them).

However, agents should be more intelligent and their actionrules should be more complex in actual emission trading systems.The model of the SO2 emission trading market should be exploredin future research. This study adopted the CDA market mechanismand ZIP agents. However, the learning algorithm should be furtheradapted for agents to maximize joint profits with other agentsbelonging to the same company and to learn from strategies usedby other agents in the SO2 emission trading market. Perfectmonitoring and enforcement were assumed in this research,enabling the emission discharge of all power plants to be lowerthan their available allowance. However, violation and non-compliance in the SO2 emission trading market should also betaken into consideration.

Acknowledgments

This paper was supported by the National Science Foundation ofChina (Grant No. 70903030) and the Science Foundation of JiangsuProvince (Grant No. BK2009250). The authors are grateful to thereviewers and the editor for their helpful comments.

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