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Electronic Commerce Research and Applications 11 (2012) 537–547
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Electronic Commerce Research and Applications
journal homepage: www.elsevier .com/locate /ecra
Co-evolution-based mechanism design for sponsored search advertising
Yong Yuan a,b, Daniel Zeng a,c,⇑a State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, Chinab Beijing Engineering Research Center of Intelligent Systems and Technology, Beijing, Chinac Department of Management Information Systems, University of Arizona, Tucson, Arizona, USA
a r t i c l e i n f o a b s t r a c t
Article history:Available online 25 April 2012
Keywords:Sponsored search advertisingMechanism designCo-evolutionary simulationNiche-based evolution
1567-4223/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.elerap.2012.03.002
⇑ Corresponding author at: Department of ManagUniversity of Arizona, Tucson, Arizona, USA.
E-mail addresses: [email protected] (Y. Yua(D. Zeng).
1 http://www.iab.net/insights_research/947883/adre2 http://investor.google.com/financial/tables.htm
phoenix.zhtml?c=188488&p=irol-reportsAnnual.
Sponsored search advertising (SSA), the primary revenue source of Web search engine companies, hasbecome the dominant form of online advertising. Search engine companies, such as Google and Baidu,are naturally interested in SSA mechanism design with the aim to improve the overall effectivenessand profitability of SSA ecosystems. Due to model intractability, however, traditional game theory andmechanism design frameworks provide only limited help as to the design and evaluation of practicalSSA mechanisms. In this paper, we propose a niche-based co-evolutionary simulation approach, aimingat computationally evaluating SSA auction mechanisms based on advertisers’ equilibrium bidding behav-ior generated through co-evolution of their bidding strategies. Using this approach, we evaluate and com-pare key performance measures of several practical SSA auction mechanisms, including the generalizedfirst and second price auction, the Vickrey–Clarke–Groves mechanism, and a novel hybrid mechanismadopted by sogou.com, a major search engine in China.
� 2012 Elsevier B.V. All rights reserved.
1. Introduction
In sponsored search advertising (SSA), online advertisers bid forkeyword-specific advertisements to appear alongside the organicsearch results on Web search result pages. With the promise ofprecise and in-context customer targeting, SSA provides an effec-tive way of monetizing Web search queries. Within a decade, ithas evolved into the dominant form of online advertising and be-comes an industry on its own. In 2010, SSA constituted the largestcategory share (46%) of the $26 billion online advertisementspending in the U.S. markets, far exceeding the share of displayadvertisement, the second largest category, 24%.1 SSA is also theprimary revenue source of Web search engine companies. In recentyears, it accounted for more than 96% and 99.9% of Google andBaidu’s international revenues, respectively.2
The basic economic institution behind most SSA platforms, suchas Google’s AdWords and Baidu’s Phoenix Nest, is keyword-basedposition auction. In this type of auction, advertisers selling similarproducts or services bid for the same keywords on an SSA platform.Once a relevant search query arrives, an auction will be conducted
ll rights reserved.
ement Information Systems,
venuereport#tabs-10.l, and http://ir.baidu.com/
to determine the rank position and the associated payment ofwinning advertisements. When a user clicks on an advertisement,she will be sent to the landing page on the website of the corre-sponding advertiser, who in turn pays the search engine.
From search engine companies’ point of view, SSA auctionmechanism design, i.e., the choice of auction mechanism or formatwith the ranking and pricing schemes at its core, is of paramountimportance. Different auction mechanisms induce different typesof advertiser bidding behavior, which in turn determine advertis-ers’ revenues and search engine companies’ profitability. In thelong run, the stability and sustainability of the SSA ecosystem, toa large degree, hinges on SSA auction mechanism design as well.
A variety of auction mechanisms have emerged during the evo-lution of SSA since its appearance in 1998. The pioneer of SSA,GoTo.com (then Overture, now part of Yahoo!), used the general-ized first-price (GFP) auction, in which advertisers were rankedby and pay their own bids. In 2002, Google started to use the gen-eralized second-price (GSP) auction, which ranks advertisers bytheir bids but charges them, if their advertisements are clickedby Web users, by the next highest bids. Currently, most majorsearch engines around the world have adopted a variant of theGSP mechanism, in which advertisers are ranked by the productof their own bids and search engine-assigned quality scores. Inthe meanwhile, other auction formats have been experimentedand used as well. A prominent example is a hybrid auction formatadopted by sogou.com, China’s third largest search engine. In thisauction, advertisers are ranked by their bids but allowed to selectto pay following either the first or second pricing scheme. In this
538 Y. Yuan, D. Zeng / Electronic Commerce Research and Applications 11 (2012) 537–547
paper, we refer to this auction format as the First–Second-Price(FSP) auction.
In the literature, the Vickrey–Clarke–Groves (VCG) and ladderedauctions have also been studied (Aggarwal et al. 2006). These auc-tion formats offer nice properties such as incentive compatibility,typically aimed at optimizing the profitability of search engines,and at reducing the possibility of advertisers trying to ‘‘game thesystem.’’ As a result, market efficiency can be achieved, i.e., adver-tisers with higher per-click values are more likely to win betteradvertisement slots.
Due to its practical significance, SSA auction mechanism designhas attracted a lot of attention from the research community in re-cent years. Most existing work evaluates auction mechanismsusing frameworks and tools from game theory and, in particular,mechanism design theory. As SSA platforms evolve and associatedauction rules undergo changes in dynamic online business settings,formal mathematical analysis based on mechanism design theoryquickly becomes inadequate in dealing with design and evaluationof practical SSA auction mechanisms. It has become a major chal-lenge for search engines to understand advertisers’ bidding behav-ior and assess the outcome of complex SSA auctions. As a result,these companies can only rely on ad hoc anecdotal evidence or lim-ited scenario-based comparisons to make major decisions concern-ing auction rules, increasing the risk and hindering innovation inthe SSA space.
From a research perspective, with the end goal of helping theSSA ecosystem maintain its overall effectiveness, profitability,and stability, there is a critical need to develop new research meth-odologies for SSA mechanism design. However, to the best of ourknowledge, research in this area is severely lacking. Our researchis targeted at filling in this important gap. We propose a niche-based co-evolutionary approach, aiming at automatically searchingfor equilibrium bidding behavior of rational advertisers in SSA auc-tions, and in turn evaluating and designing alternative SSA auctionmechanisms. Niche plays a central role in evolutionary divergenceduring the ecological speciation process, and can be used in co-evolutionary simulations to construct the equilibrium continuumof SSA auctions by forming and maintaining stable sub-popula-tions, each converging at a single equilibrium. Compared withthe analytical mechanism design approach, co-evolutionary simu-lation offers the following advantages. First, it evaluates the macro-scope properties of SSA auctions by simulating long-term co-evolu-tion and co-adaptation of advertisers’ micro-scope bidding behav-ior. As such, the simulation process is robust to input mechanisms,and can be adapted to assess various kinds of SSA mechanismswith only minor modifications. Second, co-evolutionary simulationcan be used to optimize advertisers’ bidding strategies via search-ing through the entire strategy space. This can help search enginesbetter understand advertisers’ behavior in a specific SSAmechanism.
This paper makes the following contributions. Methodologi-cally, the reported work is the first attempt to apply the co-evolu-tionary simulation approach to auction mechanism design in SSAcontexts. We also propose a novel niche-based co-evolutionaryalgorithm to help design and evaluate SSA auction mechanisms.Practically, our research can help Web search engines betterunderstand advertisers’ complex bidding dynamics in SSA auc-tions, and computationally evaluate SSA auctions’ performance.From the perspective of competing advertisers, our research andalgorithm can help them discover all kinds of possible equilibriumbidding strategies, and analyze their marketing effectiveness. As aresult, a variety of observed bidding behavior to ‘‘game the system’’(Zhou and Lukose 2006), as well as irrational or even malicious bid-ding behavior (Iyengar et al. 2007), may be recognized and reducedin SSA practice.
The remainder of this paper is organized as follows. Section 2 pro-vides a brief review of the SSA auction mechanism design literature.In Section 3, we discuss performance measures concerning SSA auc-tion mechanisms and the rationale behind co-evolutionary auctionsimulation. We then present in detail our proposed niche-basedco-evolutionary mechanism design. Several typical SSA auctionmechanisms are evaluated through co-evolutionary simulations inSection 4. In Section 5, we summarize our research findings anddiscuss future research possibilities.
2. Literature review
Mechanism design has long been an active topic in auction re-search. Here we are mainly concerned with the mechanism designwork in the SSA context. Two research streams, analytical andcomputational mechanism design, have been developed in the lit-erature. Below we present a brief survey of these two lines ofthoughts.
2.1. Analytical mechanism design
The classical mechanism design framework has been used toformally characterize the key properties of various SSA auctionmechanisms. For instance, the early GFP mechanism has beenproved to be unstable with price cycles in bids (Zhang and Feng2005). In contrast, the prevailing GSP mechanism has a symmetricNash equilibrium (SNE) continuum, and the bids of revenue-max-imizing advertisers will converge to the lowest-price Nash equilib-rium (LPNE) in SNE (Edelman et al. 2007). However, GSP is not atruthful mechanism, and its Nash equilibria (NE) beyond the SNEcontinuum is not yet fully explored. For theoretical analysis,researchers have investigated truthful SSA mechanisms such asthe VCG and laddered auctions (Aggarwal et al. 2006), in whichadvertisers are motivated to truthfully bid their private per-clickvalues. Moreover, an optimal mechanism has been proposed tomaximize search engines’ expected revenue while achievingBayesian incentive compatibility and individual rationality ofadvertisers (Garg and Narahari 2009).
Recent analytical research focuses mainly on mechanism designfor emerging SSA formats. For instance, an execution-contingentVCG mechanism was proposed for SSA platforms operating on fed-erated search engines (Ceppi et al. 2011). Multi-slot SSA auctionshave been studied, in which an advertiser can bid for multipleadvertisement slots simultaneously (Deng et al. 2010). Several ex-tended forms of advertisers’ utility functions, e.g., a linear formwith identical slopes and a single discontinuity, a piece-wise linearform with non-identical slopes and multi-discontinuities, have alsobeen developed to improve the expressiveness of SSA mechanisms(Aggarwal et al. 2009, Duting et al. 2011).
In general, analytical mechanism design has the following lim-itations. First, due to inherent analytical complexity, it is difficult tomathematically evaluate complex SSA mechanisms in dynamic on-line environments. Second, the analytical approach is usuallyhighly sensitive to auction mechanisms. Even a minor modificationto the mechanism can lead to totally different analyses and solu-tions. For instance, if advertisers aim to maximize their revenuesand the rivals’ payments in competitive SSA markets, their bidsin a GSP auction will converge to the highest-price equilibriumin the SNE continuum, instead of the LPNE (Yuan et al. 2011). Third,the standard game-theoretic analysis cannot reveal such dynamicproperties as stability and robustness of equilibrium bidding strat-egies, and thus sheds limited light on which kind of equilibriumoutcome is more likely to be observed in SSA auctions with a spe-cific mechanism over the long run. These limitations have moti-vated research in computational mechanism design.
Y. Yuan, D. Zeng / Electronic Commerce Research and Applications 11 (2012) 537–547 539
2.2. Computational mechanism design
Various kinds of computation-intensive techniques, such asexperimental simulation, machine learning, data mining and evo-lutionary search, have been used in computational mechanism de-sign research to better understand advertisers’ bidding behavior inSSA auctions.
In the literature, Feng et al. (2007) compared the steady-stateperformance of four alternative SSA mechanisms, including therank-by-bid, rank-by-revenue, rank-by-click through rate (CTR),and posted-price mechanisms, with systematic computationalsimulations. Balcan et al. (2005) proposed to formulate the prob-lem of design of revenue-maximizing incentive-compatible SSAmechanisms as an algorithmic pricing problem with sample-com-plexity techniques from machine learning theory. Data miningtechniques have been applied to inform empirical mechanism de-sign. For instance, Ciaramita et al. (2008) presented a frameworkfor learning and evaluating the SSA ranking systems based exclu-sively on click-data. Pardoe et al. (2010) proposed a data-drivenadaptive methodology for SSA mechanism design, which incorpo-rates prior general knowledge of bidding behavior to improve theeffectiveness of mechanism design in dynamic and uncertain envi-ronment. Munsey et al. (2010) is the first to use evolutionarysearch in the SSA context, aiming to optimize advertisers’ bids withhistorical data based genetic algorithms.
In this paper, we propose to apply the co-evolutionary simula-tion techniques in SSA mechanism design. This approach offerstwo advantages. First, as an explicit dynamic process, co-evolution-ary simulation can automatically locate the equilibrium continuumof SSA auctions, and characterize the long-term dynamics and sta-bility of specific behavior, strategies and mechanisms evolvingover time. Second, the co-evolution process is largely independentof the auction mechanisms being evaluated, and can evolve theequilibrium outcomes adaptively.
Co-evolutionary mechanism design is not new in computationaleconomics, and has been used successfully to design pricing rulesfor double auctions in a wholesale electricity marketplace (Phelpset al. 2002). In this paper, we make the first attempt to design andevaluate SSA mechanisms by co-evolutionary simulations. We alsocontribute to the methodology by introducing the ‘‘niche’’ tech-nique, which can effectively prevent the co-evolution process fromconverging at a single equilibrium.
3. Co-evolutionary mechanism design for SSA auctions
In this section, we present the detailed methodology and re-lated algorithms of our niche-based co-evolutionary mechanismdesign approach for SSA auctions. Auction mechanism design isconcerned with designing auction mechanisms to meet specificperformance requirements against self-interested bidders. Prop-erly defining performance measures is a prerequisite for evaluatingalternative mechanisms. We begin by presenting a simple SSAmodel and defining these performance measures in Section 3.1.We proceed in Section 3.2 by discussing the rationale behindco-evolutionary simulation, which serves as the base for SSA mech-anism evaluation. In Section 3.3, we present the details of our pro-posed niche-based co-evolutionary mechanism design approachand the related simulation algorithm. We conclude this sectionby analyzing the computational complexity of this algorithm inSection 3.4.
3.1. An SSA model and performance measures
We consider a general SSA model with N revenue-maximizingadvertisers competing for K slots on a specific keyword. The CTR
of the kth highest slot is denoted by xk. We assume higher-placedslots have higher probabilities of being clicked, and thus x1 Px2 P � � �. Each advertiser in slot k 2 [1,N] assigns a click with aprivate value vk representing her maximum willingness to pay.Without loss of generality, we assume v1 P v2 P � � �. The bids andpayments of all advertisers are denoted as b = {b1,b2, . . .} and p ={p1,p2, . . .}, respectively.
Based on this model, we define the following measures used toevaluate the performance of SSA auction mechanisms.
3.1.1. Market efficiency (social welfare)This measure equals in value to the aggregated revenue of the
SSA market participants, including the search engine and advertis-ers (Vijay and Perry 1997). In SSA auctions, an advertiser winningthe kth highest slot assigns a click with value vk and pays pk to thesearch engine when her advertisement is clicked. Advertisers win-ning no slots receive no clicks and thus do not pay. As such, anadvertiser in slot k can expect to make a revenue of (vk � pk)xk,and the total revenue of all advertisers is
PKk¼1ðvk � pkÞxk. Analo-
gously, the revenue received by the search engine equals theaggregated payments of all advertisers, i.e.,
PKk¼1pkxk. Conse-
quently, market efficiency is given by
ME ¼XK
k¼1
ðvk � pkÞxk þXK
k¼1
pkxk ¼XK
k¼1
vkxk
Market efficiency will be maximized (minimized) when adver-tisers are ranked in decreasing (increasing) order by their per-clickvalues. However, a particular SSA auction may not be able to reachthe maximum or minimum market efficiency. Using the niche-based co-evolutionary simulation framework, we can discover alarge number of equilibria in the joint strategy space of advertisersengaging in SSA auctions. Assume we have found H equilibria, andthe market efficiency realized in each equilibrium is denoted asME(i), i 2 [1,H]. Then we can define MEmax, MEmin, and MEavg asthe maximum, minimum and average market efficiency in theresulting equilibrium continuum, or formally
MEmax ¼maxfMEðiÞg; MEmin ¼minfMEðiÞg; and MEavg
¼
XH
i¼1
MEðiÞ
H; where i 2 ½1;H�
3.1.2. Revenue ratioIn SSA auctions, the search engine plays a non-cooperative
game with advertisers to compete for auction surplus, or socialwelfare, equivalently. In order to characterize the revenue proper-ties of SSA mechanisms, we define RRmax, RRmin and RRavg as themaximum, minimum and average proportion of advertisers’ aggre-gated revenues in the total auction surplus among all equilibria,where
RR ¼PK
k¼1ðvk � pkÞxkPKk¼1vkxk
RRmax, RRmin, and RRavg can be defined analogously to marketefficiency. Obviously, search engines prefer SSA auction mecha-nisms with smaller revenue ratio, while advertisers prefer mecha-nisms with larger one.
3.1.3. Incentive compatibilityAn SSA auction is said to be incentive compatible if all advertis-
ers maximize their revenue when they truthfully bid their privateper-click values (Dash et al. 2003). In co-evolutionary simulation,we consider an SSA mechanism to be incentive compatible ifadvertisers’ bids always converge to their per-click values.
540 Y. Yuan, D. Zeng / Electronic Commerce Research and Applications 11 (2012) 537–547
3.1.4. Output truthfulnessA ranking of advertisers is output truthful if it satisfies vt > vk for
t < k, t,k 2 [1,K] (Bu et al. 2010). We define OT as the proportion ofthe output-truthful equilibria among all equilibria found by co-evolutionary simulations.
3.1.5. Evolutionary stabilityAn SSA auction mechanism is evolutionarily stable if co-evolu-
tionary simulations always converge stably to a unique equilib-rium (Weibull 1995). Note that evolutionarily stable mechanismswill result in predictable bidding behavior and auction outcomes.We use static population variance and evolutionary mobile vari-ance to characterize the co-evolutionary bidding dynamics and sta-bility. The detailed definition of these two measures will be givenin Section 3.3.
3.2. Co-evolutionary auction simulation
Inspired by co-adaptation and co-evolution of biological popu-lations in natural ecosystems, co-evolutionary simulation simulta-neously evolves multiple populations with coupled fitness. Thisapproach has been successfully applied to strategy learning andoptimization in games involving self-interested agents. Co-evolu-tionary simulation is particularly useful in SSA mechanism designfor the following reasons. First, understanding equilibrium biddingstrategies by advertisers plays an essential role in the evaluation ofauction mechanisms. Co-evolutionary simulation has the potentialto identify these stable and equilibrium strategies adaptivelythrough the genetic search in advertisers’ joint strategy space. The-oretically, it has been proved that in strategic environments,including SSA auctions, the co-evolutionary simulation processwill converge at a globally optimal equilibrium with evolutionarystability and dynamic attainability (Apaloo et al. 2005). Second,co-evolutionary simulation has been applied in various kinds ofauction mechanism design contexts with success. For instance,Cliff (2003) used co-evolutionary genetic algorithm to optimizeparameter values for trading agents in online auction e-market-places. Phelps et al. (2002) applied co-evolutionary genetic pro-gramming and developed an auction pricing rule for doubleauctions in a wholesale electricity marketplace. These works pro-vide useful modeling insights to tackle SSA mechanism designchallenges. Third, the co-evolutionary simulation approach is lar-gely insensitive to the auction mechanisms being evaluated. Inves-tigating different kinds of SSA mechanisms only incurs relativelyminor changes in the co-evolutionary simulation algorithm.Fourth, co-evolutionary simulation can serve as a foundation of acomputable and implementable framework for SSA mechanismdesign. This famework may be used as a practical mechanism de-sign and evaluation tool for Web search engines. These advantageshave motivated us to apply co-evolutionary simulation to generateadvertisers’ equilibrium bidding behavior and in turn evaluate di-verse SSA mechanisms.
Due to the non-cooperative nature of SSA auctions, we use thecompetitive co-evolutionary algorithm with host-parasite inter-populational relationship (Frank et al. 1993). In competitive co-evolution, advertisers’ bidding strategies are optimized througharm races resulting from interactions and competitions amongpopulations. Typically, co-evolutionary simulation consists of thefollowing three major steps: evolutionary encoding, fitness evalu-ation, and genetic operations.
3.2.1. Evolutionary encodingEncoding an SSA mechanism involves strategy encoding and
mechanism encoding. We employ the real-coding scheme to en-code the pure strategy space of each advertiser into a strategy pop-
ulation with a finite number of individual strategies. The initialstrategy populations are generated by uniform sampling in adver-tisers’ strategy spaces. An individual strategy is encoded as a chro-mosome with a finite number of gene locuses. The gene on eachgene locus represents a component of an individual strategy, andall possible values for a gene are encoded as alleles. For instance,an individual strategy of the FSP auctions consists of two genelocuses, one containing the bid value and the other containingthe choice to pay by first or second price scheme.
An SSA auction mechanism consists of the auction protocol andmultiple dialogue rules. The former determines the sequence ofadvertisers’ moves, and the latter the rules governing the auctions.These rules in most cases cover bid ranking and payment schemes.In co-evolutionary simulation, the auction protocol is encoded asthe interaction protocol among strategy populations, while thedialogue rules are used to evaluate the fitness of individualstrategies.
3.2.2. Fitness evaluationThe strategy populations of competing advertisers co-evolve
with host-parasite relationships (Frank et al. 1993). Each strategypopulation takes turns to be a host and others are parasites inthe fitness evaluation step. When evaluating the fitness of a hoststrategy, one individual strategy chosen from every other popula-tion will be selected as a parasite and matched with the host strat-egy to play an SSA auction game, as is shown in Fig. 1. Thecumulative revenue earned by the host strategy in all possiblehost-parasite encounters can be considered as its fitness measure.
3.2.3. Genetic operationsEach advertiser’s strategy population evolves through genetic
operations. We use fitness proportionate selection, stochasticcrossover, and mutation operators to evolve individual strategies.More specifically, selection is performed using the elitist roulettewheel scheme, which first migrates the fittest individuals in parentpopulations directly to offspring populations, and then performsthe roulette wheel selections repeatedly until the offspring popula-tions are generated. Moreover, each individual strategy stochasti-cally crossovers with other strategies, and will be replaced byanother strategy with a certain mutation rate.
3.3. Niche-based co-evolutionary mechanism design
Generally speaking, due to the genetic drift effect, the standardco-evolutionary algorithm will converge uniformly at one equilib-rium (which possesses evolutionary stability and dynamic attain-ability properties) but miss all other alternative equilibria. MostSSA auction mechanisms, however, are associated with an infiniteequilibrium continuum. To address this problem, we have devel-oped a new co-evolutionary algorithm that incorporates theisolated niche technique. Using this approach, stable sub-popula-tions are formed and maintained, and multiple equilibria evolvesimultaneously.
Inspired by observed geographical isolation of species in nature,the isolated niche technique separates a population into severalindependently evolving niches, among which gene communica-tions are not allowed (Rundle and Nosil 2005). As such, the effectof genetic drift is confined within each niche and global conver-gence will be avoided. Isolated niches can effectively maintainpopulation diversity and increase the search efficiency for multiplesolutions. This technique has been successfully used to solve themulti-modal function optimization and multi-issue bilateral nego-tiation problems (Li and Kang 2003, Yuan and Liang 2007).
The basic idea of the niche-based co-evolutionary SSA mecha-nism design is as follows. We search for all possible equilibrium
Fig. 1. Fitness evaluation in co-evolutionary simulation.
Table 1Parameters setting the co-evolutionary simulation.
Auction parameters Algorithm parameters
Parameter Value Parameter Value
Advertiser number N = 5(3) Maximum generation MaxG = 500Slot number K = 3(2) Population Size S = 20Per-click values {0.9,0.7,0.5,0.3,0.1} Niche number c = 1(50)
({0.9,0.6,0.3}) Crossover rate crs = 0.6CTRs {0.8,0.6,0.4} Mutation rate mut = 0.02
({0.8,0.5}) Maximum encounters Maxtest = 20Population variance hSPV = 0.05Mobile variance hEMV = 0.001Maximum niche score hmax = 20Minimum niche score hmin = 1
Y. Yuan, D. Zeng / Electronic Commerce Research and Applications 11 (2012) 537–547 541
bidding behavior in advertisers’ joint strategy space, which typi-cally can be represented by an N-dimensional bid space RN. Forsimulation simplicity, we normalize an advertiser’s bid range tobe within 0 and 1. The joint strategy space is then reduced to[0,1]N 2 RN. In order to form niches in advertisers’ populations,we define a search precision parameter c P 1, and divide the strat-egy space of each advertiser into c intervals. Under this partition-ing scheme, advertisers’ joint strategy space is divided into cN
subspaces, each representing a niche in the co-evolving popula-tions.3 We generate N co-evolving sub-populations, each belongingto an advertiser’s strategy population, to search for the optimal strat-egy profile within a niche. There are S individual strategies in eachsub-population, and each individual strategy is a bid. Standard ge-netic operators are used to search the un-explored strategy space in-side a niche, and no genetic communication (e.g., gene migration) isallowed among niches.
To determine evolutionary stability inside a niche within eachgeneration, we propose two new measures, the static population
3 Obviously, if we set c = 1, the niche-based co-evolution falls back to the standardco-evolution, which searches advertisers’ joint strategy space for a globally optimalequilibrium.
variance (SPV) and the evolutionary mobile variance (EMV). Morespecifically, SPV is the variance of all individual strategies in a spe-cific population, while EMV is the variance of the average bids dur-ing a number of generations in co-evolution. A strategy populationwill stably converge if these two indicators converge to zero. Com-putationally, in case when these two indicators drop below thepreset thresholds, hspv and hemv, respectively, for all populationsin a niche, we will consider the resulting populations as in an equi-librium state. The simulation bookkeeping module then savesadvertisers’ equilibrium bids and increments the score of this nicheby one. The score of the niche is defined as the number of times anequilibrium is reached within this niche so far in the simulationruns.
The niches will be dynamically merged and divided to acceler-ate the co-evolution process. We define two scoring thresholds,hmax and hmin. If the score of a niche exceeds hmax, we divide it intotwo sub-niches, and generate sub-populations for the new niches.In case when the score of a niche is below hmin, we merge this nichewith neighboring niches, and generate new sub-populations for themerged niche. These operations help increase the adaptability andspeed of the co-evolution process.
The detailed co-evolutionary simulation algorithm followingthe ideas discussed above is as follows.
542 Y. Yuan, D. Zeng / Electronic Commerce Research and Applications 11 (2012) 537–547
Algorithm 1. Niche-based co-evolutionary simulation for SSAmechanism design.
Input: An SSA auction mechanism.Output: The equilibrium continuum of the input auction
mechanism.1 Parameters initialization;2 Set Evolutionary generation T = 0;3 For each advertiser i 2 [1,N] do//niche formation4 Split the strategy space of advertiser i into c intervals5 Create a sub-population with S individual strategies for
advertiser i ineach interval
6 End for//resulting in cN niches in the joint strategy space7 Repeat8 For each niche, do9 For each population Popi 2 Pop of advertiser i do//
fitness evaluation10 For each individual strategy Sj 2 Popi do//Host
strategy11 For Test = 1 to MaxTest do// Generate MaxTest
encounters12 For each population Popk 2 Pop such that k – i
do13 Choose a strategy individual in Popk//
parasite strategy14 End for15 Match the host and parasite strategies, and
play SSA auctions16 Calculate the revenue of the host strategy in
the auction17 End for18 Fitness of Sj= discounted sum of revenues over
MaxTestencounters
19 End for20 End for21 End for22 For each niche n 2 [1,cN], do23 If SPVn < hSPV and EMVn < hEMV do24 Save the average bids in all populations of the
niche as anequilibrium
25 scrn = scrn + 1;//Increase the score of the niche by1;
26 End if27 If T > MaxG/2 do//merge and divide niches28 If scrn < hmin do: merge the niche with neighboring
niche.29 If scrn > hmax do: divide the niche into two new
niches.30 End if31 End for32 For each population Popi 2 Pop do//genetic operations33 Select individuals with elitist tournament scheme
based on fitness34 Apply crossovers and mutations with probabilities
crs and mut35 Produce offspring population36 End for37 Set evolutionary generation T = T + 138 Until (T > MaxG)39 Output all the saved equilibria.
Note that the auction mechanism (as input) in Algorithm 1 isprocessed only in the SSA auction simulation step (Line 15). Typi-cally, an SSA auction mechanism consists of an auction protocoland two dialogue rules, i.e., a ranking rule and a payment rule.The protocol and dialogue rules can be flexibly configured and eas-ily integrated into our algorithm. For instance, switching from theGFP to GSP mechanism can be easily implemented by simplyadjusting each advertiser’s payment from her own bid to the bidof the next highest advertiser. In this sense, our algorithm is largelyinsensitive to the auction mechanisms under investigation.
3.4. Computational complexity analysis
In this section, we present a computational complexity analysisof the niche-based co-evolutionary simulation algorithm devel-oped in the previous section. We decompose this algorithm intofour parts to analyze its computational complexity. First, let’s con-sider niche formation and initial population generation (Lines 3–6).In this part, we need to complete c ⁄ S random sampling operationsto create a sub-population for each niche in an advertiser’s popula-tion, and in total N ⁄ c ⁄ S operations for N advertisers. The timecomplexity is O(Nc) since S is an constant in the algorithm. Second,we focus on fitness evaluation (Lines 8–21). There are altogetherMaxG ⁄ cN ⁄ N ⁄ S ⁄Maxtest encounters for fitness evaluation dur-ing co-evolution. In each encounter, we select N � 1 parasite strat-egies (O(N)), and simulate the SSA auction by ranking advertisersby their bids (O(NlogN)), and finally determine their revenue(O(N)). Therefore, the time complexity of fitness evaluation isO(MaxG ⁄ cN ⁄ N ⁄ S ⁄Maxtest ⁄ N ⁄ logN), or O(cNN2logN). Third,consider niche operations (Lines 22–31). In each niche, calculatingSPV and EMV, as well as merging or dividing niches, need O(NS)time. Thus, the time complexity in this part is O(MaxG ⁄ cN ⁄ NS),or O(cNN), equivalently. Fourth, we concentrate on genetic opera-tions (Lines 32–36). The time complexity for genetic operationsis O(MaxG ⁄ N ⁄ S) or O(N), equivalently. To summarize, the overallcomputational complexity of our algorithm is O(cNN2logN).
At the first glance, the computing time increases exponentiallywith the number of advertisers, which is to be expected of search-ing for equilibria in the high-dimensional joint strategy spaces ofadvertisers. However, in evaluating SSA mechanisms, this expo-nential complexity can be significantly reduced for the followingreasons. First and most importantly, the performance of an SSAmechanism is an inherent property and do not vary with respectto the number of advertisers and niches. For instance, as predictedby theoretical models, the VCG mechanism is incentive compatibleregardless how many advertisers are involved in auctions (Jansenand Mullen 2008). In this case, we can simply evaluate an SSAmechanism by running our algorithm for only one time with a ran-domly selected N and c. As a result, the computational complexitywill be reduced to O(cN) with N as a constant. As such, the algo-rithm complexity depends only on the search precision of SSAequilibrium, controlled by c. Second, as a mechanism evaluationtool, our algorithm does not necessarily need to run in an onlineand real-time environment. Meanwhile, the nature of simulta-neous searches on niches makes parallel implementation possiblethrough mechanisms such as map-reduce. Third, dynamic mergingof non-equilibrium niches in our algorithm can significantly accel-erate the co-evolution process.
4. Analyzing SSA mechanisms
In this section, we analyze four SSA auction mechanisms includ-ing GFP, GSP, VCG, and FSP, with co-evolutionary simulations.These mechanisms with the exception of FSP have been intensively
Fig. 2. Co-evolutionary dynamics of advertisers’ bids.
4 The reason why the top advertiser’s bids do not converge precisely at the LPNEbid is that her bid values have no influence on all advertisers’ revenues.
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studied in the literature. All mechanisms with the exception ofVCG have been used in practice. Nevertheless, the equilibrium con-tinuum of advertisers’ bidding behavior and the performance ofthese mechanisms are not yet fully explored. Our research goal isto investigate the globally stable equilibria and the entire equilib-rium continuum in SSA auctions with each of these four mecha-nisms, and then provide a qualitative and quantitative evaluationand comparison of the key properties of these mechanisms.
We proceed in two steps. First, we investigate the globally sta-ble equilibria in each mechanism using the standard co-evolution-ary algorithm. In standard co-evolution, advertisers’ strategypopulations uniformly converge at an optimal and stable equilib-rium in advertisers’ joint strategy spaces, and this equilibriumcan be considered as the long-term outcome of SSA markets withrevenue-maximizing advertisers. Second, we derive the equilib-rium continuum using the niche-based co-evolutionary algorithm,and evaluate the performance of these auction mechanisms basedon the derived equilibrium continuum. In niche-based co-evolu-tion, local search will be performed within each niche, and resultin all possible equilibria in SSA auctions.
4.1. Bidding behavior analysis based on standard co-evolutionaryalgorithm
We use the standard co-evolutionary algorithm (by setting c = 1in Algorithm 1) to search the global strategy space of each SSA mech-anism for the evolutionarily stable equilibrium. Obviously, searchengine companies prefer SSA mechanisms possessing evolutionarystability since auction outcomes can be easily and precisely pre-dicted with advertisers’ bids converging at a specific equilibrium.
The detailed setting of experimental parameters, including auc-tion parameters and algorithm control parameters, are presentedin Table 1. We ran co-evolutionary simulations for all four auctionmechanisms. The detailed experimental results, including the evo-lutionary dynamics and convergence of advertisers’ bids and fit-ness, are shown in Figs. 2–4.
We summarize the findings from Fig. 2 concerning biddingbehavior.
(1) Advertisers’ bids in GFP auctions do not converge. Further-more, even their ranks change frequently during the co-evo-lution (Fig. 2a).
(2) The bids in GSP auctions stably converge to the LPNE(Fig. 2b), which indicates that LPNE is a globally optimalequilibrium in GSP auctions.4 As such, SSA markets with aGSP auction mechanism will stabilize at an outcome in whichall advertisers submit LPNE bids and obtain the maximumrevenue in SNE.
(3) VCG auctions will result in a truthful-bidding equilibrium,since advertisers’ bids converge to their private values-per-click (Fig. 2c).
(4) Interestingly, we observe that in FSP auctions, advertiserschoosing to pay by the first-price scheme become (approxi-mately) extinct during co-evolution (Fig. 2e). This indicatesthat the FSP mechanism will finally evolve to, and in fact isstrategically equivalent to, the GSP mechanism. As a long-run stable outcome of FSP auctions, rational advertisers willlearn to pay by second-price scheme and their bids will con-verge to the LPNE (Fig. 2d).
Fig. 3 indicates that GFP is not evolutionarily stable with theindicators EMV far exceeding the predefined thresholds. In con-trast, other mechanisms possess evolutionary stability.
Finally, we observe from Fig. 4 that advertisers participating inGFP auctions cannot obtain stable revenue, while advertisers inGSP and FSP auctions will get the LPNE revenue and those inVCG auctions will get the truth-telling VCG revenue. Moreover,we observe from the simulation that the LPNE revenue equalsthe truth-telling VCG revenue.
4.2. Mechanism evaluation based on niched co-evolutionary algorithm
We now investigate the equilibrium continuum using theniche-based co-evolutionary algorithm. For illustration purposes,we consider an SSA auction scenario with three advertisers withvalues {0.9,0.6,0.3} competing for two slots with CTRs {0.8,0.5}.The niche parameter c is set to 50. Other parameters are the samewith those in Table 1. As can be seen from experimental results, theunstable GFP mechanism has an empty equilibrium continuum.Meanwhile, the strategically equivalent GSP and FSP mechanisms
Fig. 3. Co-evolutionary stability of advertisers’ bids.
Fig. 4. Advertisers’ fitness in co-evolution.
544 Y. Yuan, D. Zeng / Electronic Commerce Research and Applications 11 (2012) 537–547
have similar equilibrium continuums. Therefore, we present inFig. 5 only the equilibrium continuums of the GSP and VCGmechanisms.
It can be concluded from Fig. 5a that enabled by the niche tech-nique, we have derived two clusters of equilibria in GSP auctions.One cluster, to the left, corresponds to non-output-truthful equilib-ria. The other, to the right, corresponds to output-truthful equilib-ria. Note that using the standard co-evolution, only a singleoptimal equilibrium in the output-truthful cluster can be derived.
From Fig. 5b, we note that advertiser 3 will always be a loser inall equilibria. Advertiser 2 wins the top slot only in cases whenthe competing first advertiser submits a bid less than her privatevalue (0.6). We can also approximately locate the upper boundand lower bound of the equilibrium continuum, namely,{0.9885,0.7068,0.5912} and {0.3125,0.3013,0.0068}, which arethe most preferred equilibria by the search engine company andadvertisers, residing on the rightmost and leftmost sides of the2-dimensional plane, respectively. These two extreme equilibrium
Fig. 5. Equilibrium continuums for GSP and VCG mechanisms.
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bids help compute the performance measure of revenue ratio ofthe GSP mechanism. Analogously, we note from Fig. 5c and d thatVCG is an output truthful auction mechanism with only one equi-librium continuum, in which advertisers are always ranked indecreasing order of their bids.
Based on these equilibrium continuums, we can now evaluatethe key properties of SSA mechanisms. It is worth noting that sinceno equilibrium exists in GFP auctions, we assume that all bids sat-isfying individual rationality (i.e., not exceeding advertisers’ pri-vate values) occur with equal possibility. We use all individuallyrational bids to evaluate the GFP auction mechanism.
The performance measures of the SSA mechanisms under inves-tigation are listed in Table 2. We draw the following conclusions.First, the FSP mechanism performs equally well to the prevailingGSP mechanism. Considering the similarity in advertisers’ biddingbehavior, we can conclude that FSP is essentially equivalent to GSP.In other words, the hybrid FSP mechanism invented by Sogou.com,is in fact not a fundamentally new mechanism from a mechanismdesign perspective.
Second, VCG can maintain the maximum market efficiency in allequilibria (i.e., 1.02), while GFP might lead to the minimum market
Table 2Performance measures of SSA auction mechanisms.
Mechanism Number of equilibria Market efficiency Revenue ratio (%)
MEmax MEmin MEavg RR-max
RRmln RR
GFP 0 1.02 0.54 0.9074 99.98 15.48 62GSP 394,721 1.02 0.93 1.0012 76.04 15.24 49VCG 977,598 1.02 1.02 1.02 99.22 15.46 64FSP 394,835 1.02 0.93 1.0011 76.14 15.5 49
efficiency (i.e., 0.54). GSP and FSP can be considered as a tradeoffon average market efficiency between the optimal VCG and worstGFP mechanisms.
Third, all mechanisms have approximately equal minimum rev-enue ratio, while GFP and VCG may achieve the maximum revenuerate. On average, advertisers will obtain the largest share of auctionsurplus in VCG and a relatively high share in GFP auctions(although not stable). In contrast, search engines will prefer GSPand FSP auctions in which advertiser only obtains no more thanhalf of auction surplus.
Fourth, all VCG equilibria are output truthful, while other mech-anisms will lead to non-output truthful equilibrium bids.
Finally, as to qualitative measures, we can see that only VCGpossesses incentive compatibility, and all mechanisms other thanGFP are evolutionarily stable and may evolve to one equilibrium.
To summarize, VCG proves to be the best mechanism for bothadvertisers and the SSA markets among all the mechanisms stud-ied. However, we experimentally observe that there is no revenueguarantee for the search engine in VCG auctions as advertisers mayget all auction surpluses (RRmax ? 1) by strategic collusions. As agood alternative, search engines in GSP and FSP auctions will have
Output truthfulness (%) Incentive compatibility Evolutionary stability
avg
.54 44.42 No No
.10 79.16 No Yes
.42 100 Yes Yes
.14 79.03 No Yes
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guaranteed revenues in case when advertisers submit the LPNEbids. We strongly believe that this might be one of the factors be-hind the huge practical success of GSP.
4.3. Discussion of experimental results
The experimental results readily support the existing theoreti-cal analyses. For instance, it has been proved by theoretical andempirical analysis that advertisers bidding in GFP auctions willnot form a equilibrium (Zhang and Feng 2005, Edelman andOstrovsky 2007). This prediction has been validated by the co-evolutionary simulation results shown in Fig. 2a. Edelman et al.(2007) theoretically proved that in GSP auctions, advertisers’ bidswill stabilize at a ‘‘locally envy free’’ equilibrium, which is equiva-lent to the LPNE. All players, including search engines and advertis-ers, will get the same payoff in the LPNE as in auctions with theVCG mechanism. This has been observed in Fig. 2b that advertisers’bids stably converge to the LPNE values. Meanwhile, VCG has beenproved to be a incentive compatible mechanism with a truth-tell-ing equilibrium in dominant strategies (Aggarwal et al. 2006). Thiscan be verified in Fig. 2c that advertisers’ bids in the VCG mecha-nism have stably converged to their private values. We can con-clude that co-evolutionary simulation is effective in analyzingadvertisers’ equilibrium bidding behavior in SSA auctions.
Our simulation also offers novel insights about SSA mechanismdesign and evaluation. For instance, we have validated that the FSPmechanism is strategically equivalent to the prevailing GSP mech-anism. Through discovering all possible equilibria in SSA auctions,we have determined the distribution of the equilibrium continuumin the GSP and VCG mechanism, and investigated the key perfor-mance measures of these auction mechanisms. As a key result,we experimentally observe that advertisers can squeeze out allsurplus in SSA auctions with GFP and VCG mechanisms throughstrategic bidding, which has not been explored by the existing the-oretical research and can be considered as one of the major reasonswhy search engines do not use these mechanisms. These simula-tion results can effectively complement and enhance the existinganalytical results, and offer new insights on SSA auctions withmore complex mechanisms.
5. Conclusion and future work
This paper focuses on SSA mechanism design and evaluation. Toaddress the limitations of the analytical mechanism design frame-work, we propose a niche-based co-evolutionary simulation ap-proach for SSA mechanism design, aiming at computationallyanalyzing advertisers’ equilibrium bidding behavior, and derivingthe key performance measures of various kinds of SSA auctionmechanisms.
Our approach has the following managerial implications. Foronline advertisers, our work can help generate the optimal equilib-rium bids. For Web search engine companies, it can help betterunderstand advertisers’ bidding behavior and dynamics throughanalyzing the equilibrium continuum of SSA auctions. It can alsobe used to evaluate key performance of alternative SSA auctionmechanisms.
Our research has two major limitations. First, the proposed ap-proach can only be used to evolve advertisers’ equilibrium biddingbehavior in SSA scenarios where advertisers have complete infor-mation, or reliable estimations about all advertisers’ per-click val-ues and CTRs for all slots. Second, co-evolutionary simulations forSSA auctions with a large number of advertisers will impose majorcomputational overhead.
In the future work, we plan to extend our approach to handleincomplete information settings through maintaining a hybrid
strategy population for each advertiser according to her Bayesianbeliefs of the competitors’ private per-click values. To deal withthe computational overhead, we are working on parallelizing thekey simulation algorithm. We also plan to conduct formal analysisof the co-evolutionary simulation framework through replicatordynamics theory.
Acknowledgments
We gratefully acknowledge funding support from the NationalNatural Science Foundation of China (Grant 71102117, 70890084,71025001, 71071152, 60921061) and the Chinese Academy of Sci-ences (Grant 2F07C01). We would like to thank the Editor-in-Chief,the special issue Editors, and anonymous reviewers for their con-structive comments and suggestions in improving this study.
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