Abstract In this paper, we investigate the impacts of userbehaviour—user loyalty in particular—on pricing strategiesof Internet Service Providers (ISPs) for a profitable yet sus-tainable Internet access marketplace. We carry out an ex-tensive empirical analysis of customer loyalty issues of ISPmarkets including our own survey in the Hungarian ISP mar-ket. Based on the empirical results, we propose a realisticuser loyalty model, the price difference dependent loyaltymodel. Next, we apply the loyalty model in game-theoreticalframework where optimal Internet access pricing strategiesare expressed. Our game-theoretic framework includes bothshort-term and long-term interaction cases (single-shot andrepeated games, respectively) and is capable of dealing withuncertain as well as dynamic scenarios (Bayesian and Stack-elberg games, respectively). Finally, we present the impactsof user loyalty on the prices and profits of ISPs in differentscenarios based on simulation results.
Keywords User behaviour modelling · Internet pricing ·Game-theoretic modelling and analysis
This paper is an extended version of the paper “Revisiting Internetaccess pricing for loyal customers: the long-term interaction case”,presented at the Next Generation Internet conference, Aveiro,Portugal, July 1–3, 2009.
T.A. Trinh (�) · L. Gyarmati · G. SallaiNetwork Economics Group, Department of Telecommunicationand Media Informatics, Budapest University of Technology andEconomics, Budapest, Hungarye-mail: [email protected]: http://netecon_group.tmit.bme.hu
In recent years, there has been an increasing interest in thesocio-economic aspects of network systems. As an exam-ple, initiatives like the Euro-NF [10] and NSF FIND [22]promote economic incentives as a first-order concern in fu-ture network design. Decision-makers trying to work out aplausible solution for the recently surfaced net neutralitydebate would greatly benefit from an in-depth understand-ing of economic processes inside the user-ISP hierarchy.In addition, we have also witnessed a significant change innetworking paradigms: from network-centric to user-centricnetworking [7]. In terms of “Quality”, while technical QoSparameters are still important, user perception and expecta-tions, in other words Quality of Experience (QoE), now in-creasingly attract the attention of manufacturers, operatorsand researchers alike. As a result, it is our belief that under-standing the impact of end-users’ behaviour on the opera-tion as well as the business of the current Internet is crucialfor designing a successful Next Generation Internet. Fromthe ISP business perspective, an itching issue to understandthe impact of user behaviour—user loyalty in particular—on interaction and competition of Internet Service Providers(ISPs) for a profitable yet sustainable Internet access mar-ketplace. Although there exist notable efforts in the area ofmodeling interactions between ISPs [3, 15, 26] that intro-duce and analyze complex models for the interaction of ISPsat different levels of hierarchy, they mostly assume a verysimple user behavior model when investigating the marketfor local ISPs: end-users choose the cheapest provider as-suming that the quality of the certain services is the same.This assumption may be plausible in certain scenarios, butit could be misleading if there are loyal customer segmentspresent in the market. A vivid example of customer loyaltyin practice is the loyalty contract between service providers
and customers. The customers are charged with differentprice if they sign a contract and this difference depends onthe length of the contract! Economists are well aware of thenotion of consumer or brand loyalty, which is very much ex-isting in realistic markets. Practically speaking, a customeris loyal to a brand, when she purchases the product of thatbrand, even if there are cheaper substitutions on the market.Brand loyalty is rooted in both satisfaction towards a givenbrand and customers being reluctant to try substitute prod-ucts. There exist work dealing with classification of buyersinto loyalty groups [27], and a recent study develops andempirically tests a model of antecedents of consumer loy-alty towards ISPs [5]. In [18] authors use a game-theoreticframework to prove that if loyalty is an additional productof market share and penetration, customer retention strate-gies seem to be consequently more efficient for market lead-ers. Another study [9] analyzes a duopolistic price settinggame in which firms have loyal consumer segments, but can-not distinguish them from price sensitive consumers. Theydemonstrate that consumer loyalty plays an important rolein establishing the existence and identity of a price leader.Reference [13] presents a duopolistic price setting game,where loyal and also disloyal customers are on the market.The companies set their prices based on the number of theirloyal customers, therefore the Nash equilibrium of the gamechanges resulting higher utilities.
In this paper, we provide a game-theoretic frameworkto investigate the impacts of user behaviour—user loy-alty in particular—on pricing strategies of Internet ServiceProviders (ISPs) for a profitable yet sustainable Internet ac-cess marketplace. We carry out—by our own—a survey oncustomer loyalty on the Hungarian ISP market, our resultsare combined with other surveys on European markets tosubstantiate our case. It is suggested by our survey, amongothers, that customer loyalty is strongly correlated with theprice difference of ISPs. Based on the empirical results, wepropose a realistic user loyalty model, the price differencedependent loyalty model. Next, we apply the loyalty modelin game-theoretical framework where optimal Internet ac-cess pricing strategies are expressed. Our game-theoreticframework includes both short-term and long-term inter-action cases [28] (single-shot and repeated games, respec-tively) and is capable of dealing with uncertain as well as dy-namic scenarios (Bayesian and Stackelberg games, respec-tively). Finally, we present the impacts of user loyalty onthe prices and profits of ISPs in different scenarios based onsimulation results.
The paper is structured as follows. First, in Sect. 2, afterreviewing European ISP loyalty trends we provide a com-prehensive empirical analysis of ISP customer loyalty inHungarian Internet access market based on a survey, car-ried out by ourselves. We present the basic notions of game-theory in Sect. 3. Section 4 presents a loyalty model of ISP
customers and proposes equilibrium strategies for ISPs on astatic market based on game-theoretical analysis. DynamicISP market, where a new ISP enters the market is coveredin Sect. 5, the ISPs’ set their prices based on their a pri-ori beliefs about the future prices. In addition, we proposeequilibrium strategies and a method of calculating the equi-librium prices. Section 6 presents simulation results wherewe quantify the effect of uncertain a priori knowledge onmarket shares, prices, and profits. We discuss the alternativecustomer loyalty models and applicability of the proposedpricing strategies in Sect. 7. Finally, Sect. 8 concludes thepaper.
2 Customer loyalty in ISP markets: an empiricalperspective
A number of empirical studies deal with user loyalty in theISP markets. In this section, by reviewing some of their find-ings we try to give a global ISP loyalty picture, the Europeanand in particular the Hungarian situation is presented lateron. The 2005 Walker Loyalty Report for Information Tech-nology shows that 38 percent of US enterprise customerswere truly loyal to their ISPs [29], while 30 percent of thecustomers were high-risk users meaning they have low com-mitment and typically do not intend to stay at their currentproviders. Based on the report, quality, value and price arethe key drivers of loyalty. Choice survey states that 90 per-cent of the respondents had not changed their ISPs in theprevious 12 months including contract-users as well [6]; themost important factor in choosing a service provider wasthe price of the access. The PC Advisor Broadband Survey2008, carried out in the UK, revealed that the vast major-ity of respondents have been with their ISP for ages wellbeyond the minimum subscription period [25]. A survey,made in Taiwan in 2002, investigated customer loyalty to-ward ISPs [4], the key factors of customer loyalty were per-ceived value, service satisfaction and future ISP expectancy.
2.1 Customer loyalty in European ISP markets
A lot of national communication authorities of the EuropeanUnion carry out market research dealing with customer loy-alty toward local ISPs. This section reviews the findings ofthese surveys providing a summary of European ISP loyalty.
UK’s Office of Communications (Ofcom) publishes itsCommunications Market Report in 2008 [23]. Around 60%of households (15 million) have a broadband connection in2007 in the UK, often purchased as part of a bundle. Al-most 90 percent of consumers said they were either ‘very’or ‘fairly’ satisfied both with value for money and with con-nection speed. 27 percent of broadband users have alreadyswitched provider, while, as another type of switch, 45% of
Understanding the impact of loyal user behaviour on Internet access pricing: a game-theoretic framework
narrowband consumers claim they are likely to subscribe tobroadband within 12 months. It is interesting that only 61%of Internet users find easy to switch ISP.
In Ireland, the Commission for Communications Regula-tion made a representative consumer ICT survey which dealtwith broadband Internet access and ISPs in 2008 [8]. 63 per-cent had a choice of broadband service providers, 21 per-cent do not know, and 16 percent had no options choosing aprovider which has an impact on users’ loyalty. The majority(84%) did not change their ISP in the last 12 months, 12 per-cent had a switch which is more frequent than the churn rateof mobile providers and less than fixed line providers. Mostrespondents rated their home Internet service as being fairlygood value for money (56%), while 27 percent rated theirInternet service as being poor value for money, who mayswitch their ISPs more likely.
Anacom, the Portugal communication authority, made itssurvey on the use of broadband in 2006 [1]. As for the con-sumers’ evaluation of broadband Internet access, satisfac-tion was high, only 6.6% were dissatisfied with their ser-vice. Regarding user loyalty, 81 percent of broadband cus-tomers said they do not intend to change operator in the next12 months, this percentage was slightly less in the previousyear (71.1%).
The first interesting finding of the survey, carried out inFinland in 2007 [11], was that only 20 percent of the cus-tomers said they might change their wired Internet accessto a mobile connection if the price levels would be equal.In 2006, this ratio was 30 percent thus the fixed subscribersare more loyal to, more satisfied with their technology thanthey were in the previous year. The survey highlights that16 percent of the subscribers have switched their ISP in 2007mainly because of a better offer from a competitor; the priceof the Internet access was reduced with 5 percent in averagein this one year-long period.
The Malta Communications Authority carried its surveyin 2007 [17]. 84 percent did not switch their ISPs in the lasttwo years, these customers were loyal to their providers.60 percent thought it is not difficult to change their ISP,only 14 percent found it hard to switch. It is surprisingthat 31 percent thought that she does not have enough in-formation about the services and the prices of the serviceproviders. Only 20 percent would switch their current Inter-net subscription if the price of their Internet access would beincreased by 5–10 percent. The main reasons of this loyaltyintention are: the rise of the price is minimal, it is inconve-nience to switch, e-mail address. When choosing an Internetsubscription, 25 percent were not aware of the access but41 percent considered the price as expensive.
Consumer preferences regarding telecommunicationsservices were surveyed representatively in Poland in 2005by the Office of Electronic Communications [24]. 13.4%of respondents with home Internet access were considering
Fig. 1 Percentages of loyal Internet subscribers in Europe (markedvalues are only intentions)
changing their service provider, however, only 76.6% of therespondents had a choice of ISPs.
To conclude the revision of the loyalty intentions on Eu-ropean ISP markets, we present the aggregated results inFig. 1. Europeans are satisfied with their providers as theyusually do not select a new ISP. Different countries havedifferent loyal segments, thus the subscribers’ loyalty de-pends on the countries’ culture. The users tolerate price dif-ference for a certain amount of money, they only changetheir providers if the offer of the other ISP is much cheaper.
2.2 An empirical analysis of subscriber loyalty intentionstowards Internet service providers in Hungary
In this section, we examine user loyalty from two perspec-tives: the service providers and the subscribers’ opinion. Theproviders have exact information about their users’ behav-iour based on selling data while users can judge their ownpreferences and loyal attitudes.
For the first aspect we have contacted major ISPs in Hun-gary to get real world data about user loyalty and their pricesetting strategies. Unfortunately, they refused to give out thiskind of informations because the number of customers andtheir loyalty is a very sensitive company secret, companiescan have disadvantages on the market if they would makethese data public; moreover, the pricing strategy and theprofits of the companies are also private information.
National Communication Authority publish some cumu-lative statistics about the number of subscribers of the ser-vice providers in 2007 along with a churn number, the num-ber of people left the company in the last six months [20].Based on the result we conclude that at most 10 percent ofthe users have switched their ISP; the detailed subscribernumbers and churn ratios, presented in Table 1, predict thatthe users are loyal to their providers.
T.A. Trinh et al.
Table 1 The number of subscribers and switching users at seven mainInternet Service Providers in Hungary at the end of 2007
Name of the ISP Average Number of Switch
subscriber switching percentage
number users
DIGI 22334 725 3.25%
FiberNet 50461 585 1.16%
GTS-DataNet 42156 135 0.32%
Invitel 14568 196 1.35%
Magyar Telekom 228786 21497 9.40%
UPC 240558 16041 6.67%
Enternet 34653 3520 10.16%
We have dealt with the users’ point of view by askingthem a few questions about their personal ISPs and theirloyal intentions. We got in touch with people in differentways: we sent emails to lists, we asked help on Internetforums, and we also used social networks to get more andmore answers.
Based on the received answers we state that the surveywas filled out by a wide community (778 people) whereevery age-group were represented (less than 18 years of age3%, 19–24 years of age 53%, 25–35 years of age 34%,36–45 years of age 6%, more than 46 years of age 4%).The gender and the educational background of the answererswere diversified. The properties of the sample confirm thatthe empirical analysis of the survey is a good illustration ofthe loyalty of the whole community.
To help the interpretation of the outcomes, we describethe Hungarian ISP market and its prices. In August 2008,there were 497 thousands ADSL subscribers, 690 thousandscable subscribers in Hungary [21]. The volume of the pricesof Internet access is hard to judge in case of a foreign coun-try. Therefore, we compared the prices to the average Hun-garian net income in the first half of 2008 [16], in the fol-lowings we present the ratio of the price and the average netincome.
Table 2 shows the statistics of the monthly price of theInternet subscriptions. Most of the surveyed people had anInternet access with moderate price (4–8% of the averagesalary) but there were also a few ones who had really expen-sive Internet access.
User loyalty can be described by different approaches,e.g. based on the number of switches or on the number ofyears to be a customer of an ISP. In terms of the loyaltyhistory of the subscribers, around 60 percent of the ques-tioned people have not change their ISPs in the last five years(Fig. 2), which implies significant loyalty towards ISPs inHungary.
The type of connection always effects the loyalty inten-tions as every communication method has its own speciali-
Table 2 Monthly price of current Internet subscription
Monthly price (relative Frequency Percent Cumulative
to the average percent
net income)
1.5% 21 2.7% 2.7%
4% 249 32.5% 35.2%
8% 426 54.8% 90.9%
12.5% 64 8.4% 99.2%
>12.5% 6 0.8% 100%
Fig. 2 Number of ISP switches in the last five years
ties: wired Internet access does not allow users to switch eas-ily between providers, e.g. technological (change betweencable and ADSL) or deployment issues, contrarily, a mobileISP can be changed easily. We present in Fig. 3 the frequen-cies of how long a user has its current ISP based on the typeof connection. A lot of users have not changed their serviceproviders in the last two or more years, these subscribers canbe considered as loyal users. Note that not all the connectiontypes have a lot of users for long times because they have notbeen available earlier (e.g. mobile Internet, FTTX).
As we mentioned above, Internet providers offer serviceswith contracts in order to keep their subscribers for a longperiod. Only 17 percent of our answerers did not signeda loyalty contract when they bought their Internet access.This ratio is really interesting because 80 percent of the cus-tomers have to be loyal for the duration of the contract. Thecauses of signing a contract verifies that service providersset their prices based on loyalty intentions. Almost half ofthe persons (49.1%) signed an optional contract due to acheaper price. Contrarily, in 29.4 percent of the cases it wascompulsory to sign a contract in order to have the specificsubscription plan. The duration of the contracts is also ansignificant parameter which we show in Fig. 4, people with-out a contract are represented with zero month. The most
Understanding the impact of loyal user behaviour on Internet access pricing: a game-theoretic framework
Fig. 3 User loyalty at differenttype of connection
Fig. 4 Duration of the contract
frequent lengths are one and two years, with these contractsISPs are able to keep customers for a long period.
One of the questions of the survey was a bit provoca-tive, we wanted to know which is the minimal price dif-ference between the users’ current subscription and a sub-scription of another ISP when they would switch their ISPsupposing that the two ISPs offer exactly the same servicesincluding connection speed, help desk, etc. We received sur-prising answers as shown in the bar chart of Fig. 5 and inTable 3, where the exact numbers and percentages are pre-sented. Only around 5 percent of the answers said there donot exist a price difference where they would leave their cur-rent ISPs (last row in the table), these subscribers are reallyloyal to their service providers. At the same time, the re-maining 95 percent would become disloyal and switch theirproviders at a certain price difference. Based on the resultswe argue that modelling user loyalty based on the minimalprice difference to switch is a realistic description of the ISPpricing problem. The first idea what everybody would say is
Fig. 5 Minimal price difference to switch to an other ISP
Table 3 Minimal price difference to switch Internet service provider
Price difference Frequency Percent Cumulative
(relative to the average percent
net income)
0.5% 38 5.0% 5.0%
1% 96 12.5% 17.5%
1.5% 294 38.4% 55.9%
4% 270 35.3% 91.2%
8% 31 4.1% 95.3%
never 36 4.7% 100.0%
to model loyalty based on the price ratios. On the one hand,it represents the relationship between the two prices but onthe other hand, it has not got any information about thesocio-economic aspects. The following short example illus-trates the importance of socio-economic aspects. Consider
T.A. Trinh et al.
Table 4 The connection between the monthly price and the minimalprice difference to switch (number of answers)
Relative Minimal price difference to switch (relative)
monthly 0.5% 1% 1.5% 4% 8% never
price
1.5% 11 3 1 0 1 5
4% 15 64 125 23 1 17
8% 11 26 162 202 14 11
12.5% 0 3 5 40 14 2
>12.5% 1 0 0 4 1 0
two countries, a rich one and a poor one, in each countrythere exist two ISPs providing Internet access for 5$ and for10$, respectively. The price ratios are the same in both coun-tries (0.5) but there will probably be much more switchers inthe poor country, where 5$—the price difference—worths alot more than in the richer country.
In our survey, both the price of the current subscriptionand the minimal price difference had to be selected from alist of possible values thus the results are discrete probabil-ity variables. Correlation analysis is only useful in case ofcontinuous variables, therefore we used crosstabs to investi-gate the possible connections between the monthly price ofthe current Internet subscription and the minimal price dif-ference. In Table 4 we present the crosstab where every cellstores the number of occurrences of the specific pair.
In addition, we examine the connection between the num-ber of years to be a customer of the current ISP and the min-imal price differences (Fig. 6). Regardless of the years, thereare similar price differences where the customers will switchtheir ISPs.
To conclude this section, we summarize its key observa-tions:
– User loyalty has an impact on price setting strategies ofInternet Service Providers. On the Internet access mar-ket the majority of the users have loyal intentions towardstheir service providers regardless of the countries.
– Subscriber loyalty depends on the price difference of thecurrent and the possible future service providers, userswould become disloyal if the price difference is largeenough.
– Numerous factors have an impact on users’ loyalty, someof them were presented above. However, not all the fac-tors can be examined or measured, thus Internet ServiceProviders do not have exact information about the cus-tomers of their competitors, they have only beliefs aboutit. The users select their access providers based mostly ontheir impression not on exact parameters. Therefore, theprice competition between ISPs has uncertain parameters,resulting non-deterministic decisions.
Fig. 6 Relation of the user loyalty and minimal price
3 Basic notions of game theory
Game theory provides efficient methods to handle multi-person decisions, this section reviews basic notions of gametheory that we use in this paper. For a detailed introductionto game theory we refer to [12]. We will only deal with ratio-nal decisions, namely every person wants to select her bestpossible choice which maximize her utility.
A non-cooperative game, where players do not cooper-ate with each others, can be formalized as follows: N ={1,2, . . . , n} is the set of players, where 1, . . . , n are the in-dividuals who are playing, Si is the strategy set of player i,who selects her strategy si ∈ Si from the set. Every playerhas her own payoff function, which gives the utility of thepossible cases; if S = S1 × S2 × · · · × Sn then the payofffunction of player i is fi : S → R which can be ordered, thusa player can select the best possible strategy from her strat-egy set. s = (s1, s2, . . . , sn) ∈ S is a strategy profile where siis the strategy of player i while s−i denotes the strategies ofplayers except player i.
Nash equilibrium describes a strategy profile which hasgood properties, namely none of the players can have morepayoff if only one of them changes her strategy. Formally,the s∗ ∈ S strategy profile is a Nash equilibrium point, iffi(s
∗i , s∗−i ) ≥ fi(si , s
∗−i )∀si ∈ Si, ∀i = 1, . . . , n. Games canbe partitioned based on several aspects:
Strategy: A player plays with pure strategy if she selectsonly a single strategy with one probability. Contrary, if aplayer selects more strategies with positive possibilities sheplays with a mixed strategy. If every player plays pure strat-egy then a Nash equilibrium is pure equilibrium, otherwiseit is a mixed strategy Nash equilibrium.
Understanding the impact of loyal user behaviour on Internet access pricing: a game-theoretic framework
Number of rounds: If the players play only once we callthe game as a single-shot game, otherwise if they play mul-tiple rounds it is a repeated game.
Information: An important partitioning of games is basedon the amount of information. If every player knows all theinformation necessary for the decision and this knowledgeis common, the game is a complete information game. Incontrast, in an incomplete information or Bayesian gamenot all the players have the same knowledge.
4 Impact of loyal user behaviour on pricingcompetition in static ISP markets
In this section, we investigate the impact of customer loy-alty issues in a static ISP market where there is a fix numberof competing ISPs, no new entrants are allowed. First, wepresent our user loyalty model where the price difference isused examine the stability criteria of ISP price setting gamewith game-theoretic tools. After that we present a criteriawhen the ISPs can play their equilibrium as long-term (re-peated) strategies.
4.1 Game theoretic model of price difference dependentloyalty
First, we investigate a price setting game where only twoservice providers exist. Customers are split into two parti-tions upon their loyalty: l1 customers are loyal to ISP1, whileISP2 has l2 loyal users. d denotes the price difference mean-ing that if the price of user’s ISP is more than the other ISP’sprice plus d then the user will be a switcher, she leaves herISP for the other one. The demand function is modelled asa constant function until a border price (α), if at least oneof the ISPs set a price less than α the demand is l1 + l2 butabove α none of the users buy Internet access. The serviceproviders set their prices simultaneously then the users se-lect their access providers. The payoff function of the ISPscan be expressed as
�i =⎧⎨
⎩
(li + lj )pi if pi < pj and |pi − pj | > d
lipi if |pi − pj | < d
0 if pi > pj and |pi − pj | > d
(1)
Figure 7 illustrates the payoff function (1) in two dif-ferent scenarios. We present the payoff of ISP1 at dif-ferent prices (p1) while the price of ISP2 is fixed. Fig-ure 7(a) presents the payoff function if the border price isnot smaller than the price of ISP2 plus the price difference,while Fig. 7(b) shows the payoff if the border price is lower.
The formal definition of the game is the following, wewill refer it as G1:
Players: the Internet Service Providers, N = 2, ISPi has liloyal customers
Fig. 7 Illustration of the payoff function
Strategies: the price of the Internet access, the decision ofISPi is pi , pi ∈ [0, α], players can have only pure strate-gies, they play only once, thus it is a single-shot game
Payoff functions: the payoff of the ISPs is described in (1)
Proposition 1 Consider G1, the ISP price setting game withprice difference dependent loyalty. (α,α) is the only purestrategy Nash equilibrium of the game, if l1
l1+l2≤ d
αand
l2l1+l2
≤ dα
. At the Nash equilibrium point the payoffs of theplayers are �1 = l1α and �2 = l2α.
Proof None of the players would set a price higher thanα because otherwise their payoff would be zero. In whichcases is it worth to undercut the other ISP’s price more thand to get the whole market? If ISP2 sets a price p2 ISP1 grabsall users if she sets a price lower than p2 − d . If ISP1 wouldnot compete its maximal price can be p2 + d without los-ing its loyal customer base. On the [0, α − d] ISP1 wouldcompete if (l1 + l2)(p2 − d) > l1(p2 + d) which impliesp2 > d + 2l1d
l2. On the [α − d,α] interval ISP1 can grab the
users of the other ISP if p2 > d + l1αl1+l2
holds, while the max-imal upper price is α. If ISP2 sets p2 = α ISP1 competes if
l2l1+l2
> dα
holds. This game has only one pure Nash equilib-rium at (α,α), as long as none of the ISPs have incentive tocompete at α. The requirement of the equilibrium is that allof the ISPs have best response at α, meaning l2
l1+l2≤ d
αand
l1l1+l2
≤ dα
hold. At other prices does not exist any equilib-rium because on the one hand the price difference have tobe greater the d to grab, on the other hand the price differ-ence has to be less or equal to d in order to hold users. �
The proposition means that if the market’s price differ-ence is large enough then the access providers do not haveto compete with each other, they can sell Internet access onthe highest possible price (α) resulting maximal profits. Thegame can be generalized to N players where the Nash equi-librium is also a Pareto efficient as none of the ISPs can havelarger payoff without harming the others.
T.A. Trinh et al.
4.2 Repeated game
Internet Service Providers are playing usually their price set-ting game repeatedly, e.g. they set a new price every months.We investigate our price difference dependent loyalty modelas a repeated game to analyse it as a long-term pricing strat-egy. There is two ISPs in the market, ISP1 has l1 loyal cus-tomers while ISP2 has l2. We model the repeated game us-ing discounted payoffs where the price is discounted at eachstep with discount factor � ≤ 1. � express the weight of thefuture in ISP’s decision, e.g. if � = 0 only current payoffis considered. d denotes the minimal price difference wherea loyal user will switch its service provider. We computethe condition of sub-game perfect equilibrium, where everysub-game (round) of the game is a Nash equilibrium, for thefollowing strategy: an ISP cooperates, sets α as price, untilthe other ISP sets lower price than her price with at least d ,otherwise she always sets d as her price to preserve her loyalcustomers. We suppose that an ISP can loose her loyal cus-tomer only for that specific round of the game, in the nextround she will have her loyal users again, e.g. ISP1 will havel1 loyal user at the beginning of every round. An ISP’s profitis �
coorpi = liα in case of cooperation and �not
i = lid if shedoes not cooperate. The formal definition of G2 game is thefollowing:
Players: the ISPs, N = 2, ISPi has li loyal customersStrategies: pi ∈ [0, α] the price of the Internet access atISPi , players play multiple rounds as a repeated game, thediscount factor of ISPi is �i
Payoff functions: the payoff of the ISPs is shown in (1)
Proposition 2 The strategy profile “Set α as a price untilthe other player deviates than play d as a price” is a sub-game perfect equilibrium for the repeated game G2, where�i is the discount factor of ISPi , if �i >
(l1+l2)(α−d)−liα(l1+l2)(α−d)−2lid
.
According the condition, if the ISPs weight the future in-comes at least with � then the strategy is optimal in long-term resulting maximal payoffs.
Proof As the prices and payoff functions are continuous weprove the sub-game perfect equilibrium property using theone-step deviation property. Namely, the game is sub-gameperfect if none of the ISPs has incentive to change only onestheir strategy because otherwise her discounted payoff willbe less. if �
coorpi (k,∞) > �dev
i (k) + �noti (k + 1,∞) the
strategy is sub-game perfect. Without loss of generality letus suppose that ISP2 deviates at step k then the discountedpayoffs are
∞∑
i=k
�i�coorp2 > �k�dev
2 +∞∑
i=k+1
�i�not2 (2)
The price of ISP2 can be at most α − d at the deviation stepin order to get all the users but after that she can only setd + d = 2d as her maximal price to keep her own users.
The algebraic calculations yields that � >πdev
2 −�coorp2
πdev2 −�not
2is the
minimal discount factor where this game is sub-game per-fect. Using this the proposition’s lower bound constraints ofminimal discount factors can be expressed. �
5 Impact of loyal user behaviour on pricingcompetition in dynamic ISP markets
The ISPs usually do not have complete knowledge abouttheir competitors, they only have belief. The ISPs set theiraccess prices based on their a priori information which willbe adjusted based on the observed behaviour of the com-petitors. ISPs have to price Internet access not only on sta-tic markets, pricing strategies are even more crucial on dy-namic markets if strategic decisions have to be made. Wecall a decision strategic if it has a significant long-term ef-fect on the company. In this section we analyze dynamicISP markets, where a new ISP enters a market. In [14] wehave analysed dynamic ISP markets as a decision problem,proposing strategy for the entering ISP. We used a simpleISP model in which the ISPs don’t care about the long-termeffect of their decisions. In this section, the ISPs have tomake a strategic decision in order to maximize their profitsin the long run. In particular, after an ISP enters the mar-ket it will gain subscribers from the incumbent ISPs basedon their prices. We model the entry situation using a Stack-elberg leader-follower game, where the incumbent ISPs arethe leaders and the entrant ISP is the follower of the game, aswe had in [14]. The Stackelberg game describes the proper-ties of a situation, where the participants are differentiated,e.g. the incumbents make set their prices before the entrant.In particular, the incumbent companies set their prices basedon their utility functions considering time factors, e.g. basedon the discount factors of the ISPs. As a short example con-sider that ISP1 always wants to maximize its current profit,thus ISP1 will get high access prices from its loyal customersbut will loose lots of its customers. Contrarily, ISP2 sets itsprices in order to have maximal profit in a year which resultsin cheap subscription prices when the new ISP enters themarket. This strategy implies that the number of ISP2’s cus-tomers remains almost the same as before resulting highercumulative profit in long-term.
In the followings, we provide a game-theoretic analy-sis of ISPs’ strategic decisions the dynamic market men-tioned above. The customers buy Internet access if the ac-cess price is at most α. The local ISP market consists ofN = 1, . . . , n company, ISPi has li loyal customers, thusthe total number of the customers is
∑i li . If a subscriber
changes her ISP then she selects the cheapest available price.
Understanding the impact of loyal user behaviour on Internet access pricing: a game-theoretic framework
The new, entering ISP has not got any subscribers at thebeginning. We assume that the subscribers loyalty is basedon the ISPs’ price difference, for analytical tractability theloyalty function of the customers are linear, meaning ISPi
looses Li = pi−pj
αli customers if ISPj has the lowest price
(pj < pi ). Every service provider plays rationally, namelyselects its profit maximizing strategy. The discount factor isdenoted by 0 ≤ θ ≤ 1, the profit of ISPs is discounted ateach step with θ . We assume, that each ISP has the samediscount factor. ki denotes the number of rounds for ISPi
looks forward. We suppose that the cost of providing In-ternet access for a single customer is c as a unit cost. TheISPs do not know in advance the payoff of future rounds,they only have a priori knowledge. EP
(k)i denotes ISPi ’s
belief about the expected access price in round k, simi-larly El
(k)i is the ISPi ’s expected subscriber number in that
round. The payoff function of the service providers is �i =l∗i (pi − c) + ∑ki
j=1 �j El(k)i (EP
(k)i − c), i = 1, . . . , n + 1,
where l∗i denotes the number of subscribers after the entry.We present equilibrium strategies in two cases, first a new
ISP enters to a monopolistic then to a competitive market. Inboth cases we assume that the expected subscriber numbersequal li and the expected access price P is constant in thefuture based on the mixed strategies of ISP on a competitivemarket. The formal definition of the monopolistic G3 gameis the following:
Players: the ISPs, N = 1, ISP1, the leader, has l1 loyal cus-tomers, ISP2 is the entrant without customers
Strategies: pi ∈ [0, α] the price of the Internet access atISPi , ISPi looks forward ki rounds in order to maximizeits payoff, pure strategies are only allowed
Payoff functions: the payoffs of the ISPs are �1 = (1 −p1−p2
α)l1(p1 − c) + ∑k1
j=1 �j(1 − p1−p2α
)l1(P − c) and
�2 = p1−p2α
l1(p2 − c) + ∑k2j=1 �j p1−p2
αl1(P − c).
Proposition 3 The equilibrium prices of G3, the long-termISP price setting game with price difference dependent loy-alty, are
p∗1 = c + α + c − P
2
k2∑
i=1
�i + c − P
2
k1∑
i=1
�i
p∗2 = c + α
2+ 3(c − P)
4
k2∑
i=1
�i + c − P
4
k1∑
i=1
�i
Remark 1 The equilibrium prices of the ISPs are differentwhich is a consequence of their different market power. Theequilibrium prices consist of three parts, which represent thecurrent round, future rounds of the entrant, and future roundsof the incumbent respectively. On Fig. 8 we illustrate theequilibrium prices as the number of rounds that the entrantISP looks forward changes, while the incumbent do not takefuture in account is its decision (k1 = 0).
Fig. 8 Illustration of equilibrium prices
Proof As the situation is modelled with a Stackelbergleader-follower game, first we express the best responsefunction of ISP2 because the best response function givesthe equilibrium price of ISP2 for every possible price ofISP1. The algebraic calculation yields BR2 = maxp2 �2 =c−P
2
∑k2i=1 �i + p1+c
2 as ISP2’s best response function. ISP1
is the leader of the game, therefore she maximizes its pay-off based on the best response of ISP2: maxp1 �1 = (1 −p1−BR2(p1)
α)l1(p1 −c)+∑k1
j=1 �j(1− p1−BR2(p1)α
)l1(P −c).Solving the maximization we get the equations of the propo-sition as the Nash equilibrium prices. �
We assume that the ISPs have complete informationwhen they select their strategies. However, real ISPs usu-ally do not know the exact values of the parameters, e.g.the scope of other ISP’s payoff, the price of the Internet ac-cess in the next rounds, the number of own subscribers, andthe discount factor of the ISPs can also be variable. Theseuncertainties have an impact on the price setting decisionswhat we quantify in Sect. 6.
We analyse an other game where N = 1, . . . , n incum-bent ISPs exist on the market and a new company enters, theformal definition of G4 is as follows.
Players: the Internet Service Providers, i = 1, . . . , n, ISPi
is an incumbent with li loyal customers while ISPn+1 is theentrant of the game
Strategies: pi ∈ [0, α] the price of the Internet access atISPi , ISPi looks forward ki rounds in order to maximizeits payoff, only pure strategies are allowed
Payoff functions: the payoffs of the ISPs are �i = (1 −pi−pn+1
α)li(pi − c) + ∑ki
j=1 �j(1 − pi−pn+1α
)li(P − c),
i = 1, . . . , n and �n+1 = ∑ni=1
pi−pn+1α
li(pn+1 − c) +∑kn+1
j=1 �j pi−pn+1α
li(P − c).
T.A. Trinh et al.
Remark 2 The first term of the payoff function denotes theprofit of the current round, while the second describes theweighted profit of future rounds. The profit is proportionalto the number of subscribers and the profit of an access.The entrant ISPn+1 has to set the lowest price in order tohave customers, otherwise ISPn+1 can not enter the market.The following proposition expresses the equilibrium pricesof ISPs.
Proposition 4 The equilibrium prices of G4 game, the long-term ISP price setting game with price difference dependentloyalty, are
pi = 1
4li∑n
j=1 lj
[
2α
n∑
j=1
lj
(
li +ki∑
s=1
(c − P)liθs
α
)
+ li
n∑
j=1
lj
(
3c + pj +kn+1∑
s=1
(c − P)θs
)]
pn+1 =∑n
j=1 lj (c + pj − ∑kn+1s=1 (−c + P)θs)
2∑n
j=1 lj
Proof The algebraic calculation yields the proposition basedon the same steps as for Proposition 3. �
The equilibrium prices can be expressed explicitly solv-ing a system of linear equations formulated from the implicitequations. However, the solutions of the system are equilib-rium prices only if all the prices are between 0 and α. Inother cases the optimal prices can be computed creating anorder of the ISPs, e.g. based on their number of customers,the last ISP in the hierarchy is the entrant company. Usingthe ordering the equilibrium prices can be expressed step-by-step using the backward induction paradigm of game the-ory. In particular, first the entrant ISP selects its equilibriumprice in every possible scenarios which can exist based onthe decisions of the other ISPs, after that the next ISP se-lects its price, etc. We present case studies in Sect. 6 wherethe equilibrium prices are computed using this backward in-duction method, moreover we also quantify the profits andmarket shares of the ISPs.
6 Simulation analysis
As mentioned earlier in the previous section, analytical com-putation of the equilibrium prices on a dynamic market isnot always possible, especially if more than two ISPs exist.Therefore, in this section we present and discuss differentlong-term interactions on ISP markets based on simulationresults. In addition, we quantify the impacts of discount fac-tors, number of rounds to look forward, and expected futureprices on the equilibrium prices, market shares and profits.
We have built an ISP market simulator in MATLAB whichmodels dynamic and static ISP markets [19]. We have com-bined the price difference dependent loyalty game of staticmarkets and the dynamic ISP market game in the simulator.We have implemented the backward induction based algo-rithm in order to handle entry situations, the hierarchy ofthe ISPs is based on their number of subscribers. The ISPsselects their prices based on the proposed payoff functions.The loyalty of the customers are based on the price differ-ences, in particular we use the linear loyalty model. Fur-thermore, on static markets, where the number of ISPs isconstant, ISPs set their prices based on a simple strategy asthey suppose that other ISPs do not change their prices. Weare aware of the limitations of our simulation results arisingfrom some of these assumptions, however the results stillpresent interesting implications.
6.1 Short-term results
If a new ISP enters the local Internet access market thepricing decisions of ISPs have short-term and long-term ef-fects. In this section we deal with the short-term effects aswe present the equilibrium prices, market shares and prof-its based on only a single round, when the new ISP entersthe market. The payoff of the ISPs consists of the payoff ofthe current round and the discounted expected payoffs of thefuture rounds.
First, the impact of incumbent’s discount factor is ana-lysed when a new ISP enters a monopolistic local ISP mar-ket (Fig. 9). The market share of the incumbent ISP is hun-dred percent (l1 = 100), she looks forward k1 = 5 rounds.The access prices can be between 0 and 100, the unit cost ofan access is 20 while the expected future price is 40. The en-trant ISP has a discount factor of 0.8 and she looks forward15 rounds while setting the price. At smaller discount valuesthe possible future incomes are negligible to the income ofthe current round, therefore the incumbent ISP sets a price ashigh as possible, shown on Fig. 9(a), to maximize its profit.Accordingly, the entrant ISP can grab a significant part ofthe market with a small enough price, in some case almostthe half of the users select the entrant ISP (Fig. 9(b)). Asthe expected profit of the future becomes more significant,meaning the discount factor is more than 0.8, the incum-bent ISP tries to hold its subscribers by lowering its price.Because of the lower prices the profit of the ISPs are de-creasing (Fig. 9(c)), but the incumbent ISP has always largerprofit than the entrant ISP.
On Fig. 10 we show the effects of the expected futureInternet access price, still on a monopolistic market, whena new ISP enters. The discount factor of the ISPs are 0.7while the other parameters of the simulation are the sameas before. If the expected future price is small, between0 and 30, the incumbent company sets the highest possi-ble price (Fig. 10(a)) even if she can loose almost half of
Understanding the impact of loyal user behaviour on Internet access pricing: a game-theoretic framework
Fig. 9 The impact of discountfactor on prices, market shares,and profits, when an ISP entersa monopolistic market
her subscribers (Fig. 10(b)) because the expected future in-comes are smaller than the profit of the current round. Asthe expected future price increases the main objective ofthe incumbent ISP becomes keeping subscribers because thefuture incomes are expected to be higher than the currentprofit. Therefore, the incumbent lowers its prices even untilshe offers Internet access free of charge for this round. Fig-ure 10(c) shows that the profit of the incumbent ISP is neg-ative at higher expected future prices, she realises a smallexpense for the expected larger incomes of the future.
6.2 Long-term results
Pricing decisions have also long-term effects, for examplea market situation of next year can be a consequence of acurrently made decision. We analyse long-term scenarios inthis section, where a new ISP enters the local market thenthe ISPs compete with each other for many rounds. In everyround the ISPs look forward for a specific number of roundsin order to maximize their profits.
On Fig. 11 the market shares, prices, and profits of 10rounds are presented after a new ISP entered the market.Initially, incumbent ISP1 has almost 60 percent of the mar-ket, while ISP2 has the remaining part. Each ISPs has 0.8as discount factor but the scope of their decisions are dif-ferent as the incumbents look forward for one and seven
rounds while the entrant ISP is a long-term investor with ascope of 10 rounds. The entrant ISP sets a really low price atthe first round in order to have as many subscribers as pos-sible (Fig. 11(a)), because she expects to have significantincomes in the future. On the other hand, incumbent ISP1
is a short-sighted provider, she maximizes her actual profitwithout thinking on the future incomes. Thus, the prices ofincumbent ISP1 are high until the number of her customeris not too low. As an effect of her behaviour, she looseslots of her customer just after the new ISP enters the mar-ket (Fig. 11(b)). She would have kept her subscribers withlonger scope, as incumbent ISP2 did. Incumbent ISP1 re-alises the fewest income in almost every round (Fig. 11(c)),accordingly short-term decisions result bad market positionsand profits.
Same trends can be seen on Fig. 12 more explicitly. Theincumbent ISPs have same market shares before the new ISPenters the market. Incumbent ISP2 looks forward only oneround while the other ISPs are long-term decision makerswith 15 rounds. Incumbent ISP2 has almost none subscribers(Fig. 12(a)) because of its high prices (Fig. 12(b)), while theother incumbent has more than the half of the market. OnFig. 12(c) we present the profits of the ISPs. It is interestingthat only ISP2 with its short-term decisions has always posi-tive profits. The reason for this is that the other ISPs are well
T.A. Trinh et al.
Fig. 10 The impact of expectedfuture access price on prices,market shares, and profits, whenan ISP enters a monopolisticmarket
Fig. 11 The impact of futurerounds on prices, market shares,and profits on a market wherethe incumbents have differentinitial market shares
Understanding the impact of loyal user behaviour on Internet access pricing: a game-theoretic framework
Fig. 12 The impact of futurerounds on market shares, prices,and profits on a market wherethe incumbents have same initialmarket shares
aware of the expected future incomes, but they overestimatethe future price of the Internet access. They suppose that theprice will be around 40 (this is a parameter of the simula-tion) but as we see on Fig. 12(b) they never have a higherprice than 30.
Finally, we illustrate further the impact of the scope of thepricing decisions on market shares. On Fig. 13 we presentthree scenarios where the scope of incumbent ISP2 is 5,10, and 20 rounds respectively, while the other ISPs lookforward for 15 rounds. The incumbent ISPs weight the fu-ture incomes with a discount factor of 0.9 while the entranthas only 0.2 as a discount factor. If the number of roundsis small (Fig. 13(a)) ISP2 lost almost all of her customers,while if she sets prices based on 10 rounds her market shareis the same as the entrant’s (Fig. 13(b)). Furthermore, if ISP2
prices Internet access based on long-term decisions, whereshe looks forward 20 rounds, the entrant ISP’s market sharebecomes marginal (Fig. 13(c)).
7 Discussion
7.1 Applicability of the pricing strategies
The applicability of the proposed ISP pricing strategies istwofold. On the one hand, telecommunication regulatory
authorities can model the impacts of their regulations. Bysimulating different scenarios, they can create incentives forboth incumbents and new-entrants to enhance the competi-tion on the local ISP market. On the other hand, the pre-sented pricing strategies can be used by the ISPs as a guide-line for shaping their own price setting approach in differentscenarios, even with incomplete information. As the localISP markets will be more and more dynamic, an optimalstrategy is crucial to permanently have competitive advan-tage.
The presented game-theoretic framework enables to for-mulate good starting strategies for long-term Internet accesspricing on dynamic markets. However the framework takesthe prime factors only into account. There are several fac-tors not taken into account in the applied game-theoreticmodels which limit the practical applicability of the resultsand stimulate the extension of the framework. We can ex-tent the models by the acceptance of the innovation. As re-gards the customers, we can differentiate groups of innova-tors, early users, early majority, late majority and laggards tobe addressed in time shift. As regards the ISPs, positioned asmarket leaders, visionaries, challengers or gap-players, theirpricing strategy for promoting a new technology, service orapplication can be differentiated. There are similar innova-tion issues, when a technology or a service is substituted bya new one. The access network is suitable for the provision
T.A. Trinh et al.
Fig. 13 Market shares whenISP2 looks forward differentnumber of rounds, theincumbents have same initialmarket shares
of phone calls, Internet access and streaming video (TriplePlay) at the same time. It is reasonable to design multime-dia level access networks, bundle various IP based services(VoIP, IPTV etc.), which emerges additional, more sophisti-cated pricing issues.
7.2 Alternative customer loyalty models in ISP markets
The price difference dependent loyalty game, what we pro-posed in Sect. 3, is only a simple model of the problem,it may not describe all the characteristics of the price set-ting game exactly. First, we present a loyalty model, wherethe loyalty of the subscribers is based on the ratio of theprices, then we propose three novel extensions to handle theprice difference dependency. Each model is constructed tobe used in a repeated price setting game, where the Internetproviders simultaneously set their prices in every round.
7.2.1 Original model
This model effectively describes the price competition be-tween ISPs both in deterministic and in stochastic ways. Weonly review this model shortly, for a detailed description werefer to [2]. The model calculates the number of switch-ers who are changing their service provider at the end ofa round. The number of the switchers is calculated based
on the relative price difference between their current and theother ISPs. The formula provides a ratio which describes therate of the switchers and the total users of the ISPs. Li is theuser migration threshold, which constraints the number ofusers who switch their ISP at a single step. In practice, thisconstraint is due to the fact that termination and creationof contracts are time consuming. Based on the model, fora given ISPi , the number of users it loses to or gains fromother providers in round k is defined as
�U(k)i = U
(k−1)i max
(
min
(minj p(k)j − p
(k)i
minj p(k)j + p
(k)i
,Li
)
,−Li
)
The population change is described by the fraction, theminmax conditions constraint the number of switchers to the[−Li,Li] interval.
Next, we will present our three novel price difference de-pendent loyalty model which expand this original model.
We will use F = minj p(k)j −p
(k)i
minj p(k)j +p
(k)i
as a short for of the origi-
nal model’s function. The change in the number of users ofa given ISP i will be the following in all cases, where G isthe distribution function of the loyalty model:
�U(k)i = U
(k−1)i max (min (G · F,Li) ,−Li)
Understanding the impact of loyal user behaviour on Internet access pricing: a game-theoretic framework
7.2.2 Threshold based price difference dependent loyalty
Our first model is the simplest one which can express theprice difference dependent loyalty behaviour, where d rep-resents the minimal price difference. Like a step function,if the price difference is larger than d all potential switchercan change her ISP, if the difference is smaller or equal to d ,none of the users will change. The distribution function ofthe threshold based model is the following:
The threshold based loyalty model is a good reference butit may not describe accurately the user behaviour. Our nextmodel is the uniformly distributed price difference depen-dent loyalty where all users switch if the price difference islarger than the d threshold value while a fraction of the userschange if the price difference is smaller than the threshold.This function involves uncertain user decisions better. Thedistribution function of this loyalty model is:
The Internet Service Providers usually have large number ofcustomers thus the users’ price difference dependent loyaltydistribution function can be modeled as a normal distribu-tion based on the Central Limit Theorem. The mean of thefunction is d which was the threshold price difference. Thedistribution function of the normally distributed price differ-ence dependent loyalty model is the cumulative distributionfunction of the normal distribution:
G = 1
2
(
1 + �
( |minpj − pi | − d
σ√
2
))
We note that any kind of cumulative distribution functioncan be used to model the loyalty of the population.
7.3 Simulation results
We apply the above introduced loyalty models to study theISP price setting game in different market scenarios. We usea discrete event simulator [19] where each ISP has someusers as their actual market share. We suppose the local ISPmarket is saturated, i.e. no user leaves or enters the market.This market situation is valid for those places where every-body can afford an Internet access and this connectivity is
essential. We normalized the market size to 100%, if an ISPhas the half of the market, his market share is 50%. For sim-plicity reasons, we suppose that the market is infinitely di-vidable between the ISPs.
Each ISP can set her own price at the beginning of therounds. The price of the Internet access is always between 0and 100; the upper bound of the price is actually the max-imal price at users still buy connections. The ISPs marketshares can change at the end of the rounds because of theuser migration. The volume of the switchers is a function ofthe applied loyalty model. If a user leaves her ISP she willchoose the cheapest ISP as her new service provider, if thereare more than one cheapest ISPs then they split the usersevenly.
The ISPs want to maximize their current profit in eachround. In our simulations, every ISP uses the same greedyprice setting strategy: they suppose that the others will notchange their current prices. With this assumption the ISPsearches for a price where her profit is maximal and thenplays it.
We present the profits of the ISPs, the total profits, themarket shares and the prices of a price setting game inFig. 14 where the threshold-based price difference depen-dent loyalty model was used. In this simulation, 40 per-cent of the users can change their ISPs in a single roundwith three service providers compete on the market, withequal initial market shares. The threshold value of the pricedifference dependent loyalty model is 40. The ISPs playrepeated game, where the discount factor is 0.99, the to-tal profit of an ISP is calculated using the discount factor.Every part of the presented scenario is deterministic (userschoose their providers based only on the prices, the compa-nies choose their next price based on common knowledge)thus the charts of the three ISPs are overlapped.
We can see the prices of the ISPs in every round inFig. 14(a). As we have mentioned, each player uses the samestrategy, thus sets exactly the same prices. The pattern of thegraph is a good illustration of the price difference dependentloyalty. The first price is 50 because they want to have someprofit but they do not want to loose their actual users. Thenthe players want to maximize their profit so they set a highprice where they still can keep their subscribers. This priceis higher than the previous price with 40 which is the loyaltythreshold. In the next round, the ISPs want to grab to wholemarket to have maximal payoffs resulting a price which issmaller than the previous one minus the minimal price dif-ference. This pattern continues until a price where it is betterdealing with own customers than setting a too small price.
In the next figure (Fig. 14(b)) we present the marketshares (number of subscribers) of each ISPs. Because of thedeterministic model everyone will retain her initial marketshare, which was a third of the market.
As the market shares and the prices are equal, the profitsof the ISPs are also the same in every round as it can be
T.A. Trinh et al.
Fig. 14 Simulation results of price dependent loyalty (threshold=40)
seen in Fig. 14(c). The profit graph inherited the shape ofthe price’s graph but the amplitude of the variation is thirdof the minimal price difference, which is a consequence ofthe market share ratios.
Finally, we examined the total profits of the ISPs(Fig. 14(d)). The total profit is calculated based on the pre-vious profits which are discounted with the discount factor.
7.4 The impact of the loyalty model
The following plots show the price, market shares and prof-its when three ISPs are on the market, their market sharesare not equal, ISP1 has all the users at the first round. In asingle round 40 percent of the users can change their serviceprovider, the discount factor is 0.99 which we used to calcu-lated the total profits while the minimal price difference is40.
In Fig. 15, we present the prices of the ISPs. The effect ofthe models is significant because if a price difference basedloyalty model is used the prices are larger than at the originalmodel. We can read the minimal price difference from thegraphs because the changes of the prices are based on thisdifference.
Figure 16 shows the market shares of the ISPs. Beforethe first round ISP1 has 100 percent of the market, the othertwo providers have 0 percentage. The variance of the marketshares is lower at price difference dependent loyalty modelsthan it was at the original model. The threshold-based model
Fig. 15 Impact of loyalty model on prices
Fig. 16 Impact of loyalty model on market shares
Understanding the impact of loyal user behaviour on Internet access pricing: a game-theoretic framework
Fig. 17 Impact of loyalty model on profits
can create almost constant market share distribution after theinitial inequalities are equalized.
The profits of the service providers, shown in Fig. 17, arederived from the above two properties, the profit in a specificround is the product of the actual price and the market share.These graphs have the same oscillation as the prices had.The total profits are calculated as the sum of the discountedprofits, therefore the loyalty model has a great impact on thetotal profits. The total profits at threshold-based case are atleast double of the original model’s total profits.
The original model introduces the loyalty-based pricing,however, it is not realistic that the prices of the ISPs are socheap and fluctuating. The threshold-based loyalty modelcaptures the socio-economic aspect of the users loyalty; atoo small price difference is not enough for the users tochange their ISPs. The combination of this two model ispresented under the uniformly distributed model, where theuniform loyalty results more realistic market description.The last model, the normally distributed, incorporates theuncertainty of user decisions due to its stochastic behav-iour. A pattern of real world scenario would have similarsubscriber loyalty trends as this model. To close this shortdiscussion, we note that any kind of user loyalty profilecan be included in our price difference dependent loyaltyframework, therefore real world loyalty samples, e.g. cre-ated based on a survey, can also be used.
Fig. 18 Impact of minimal price difference on market shares
Fig. 19 Impact of minimal price difference on profits
7.5 Impact of minimal price difference
We have seen in the game theoretical analysis that the mini-mal price difference has an effect on ISPs’ strategies, there-fore it has an impact on the payoffs as well. We investi-gate the impact of the price difference in a simulation wheretwo players exist on the market with unequal initial mar-ket shares (100 and 0 percents), 10 percent of the users canchange their ISPs in a single round, the discount factor is
T.A. Trinh et al.
0.95 and the border price is 100. In Fig. 18 we present themarket shares of three different price difference (0, 10, 30)while Fig. 19 shows the profit of these cases.
In case of zero price difference, i.e. every user chooses al-ways the cheapest subscription, the market shares are oscil-lating around the fair distribution. If there exist price differ-ence dependent loyalty on the market then the market sharesconverge to the fair distribution without oscillation. In addi-tion, the profits of the ISPs are also constant after the end ofconvergence at price difference dependent loyalty models.The cause of different profits is that the equilibrium price ishigher if the minimal price difference is larger.
8 Conclusion
In this paper, we have investigated the impacts of userbehaviour—user loyalty in particular—on pricing strategiesof Internet Service Providers (ISPs). We showed evidenceof customer loyalty issues in different ISP markets, includ-ing our own survey in Hungarian market. Based on the em-pirical results, we have proposed a customer loyalty modelthat takes into account the difference between the prices be-tween the ISPs. We have applied our user loyalty modelto propose a game-theoretic framework to study the issueson both the static and dynamic markets and both for short-term and long-term analysis. Our framework is capable ofdealing with repetition, incomplete information where equi-librium strategies have been expressed. In particular, in thecase of a dynamic market with where the ISPs have long-term interest, we have shown that if a new ISP enters themarket, the incumbent companies select their prices basedon their a priori believes about future prices, a Stackelbergleader-follower game has been applied for analytical mod-elling. Furthermore, we have presented a method, the leader-follower chain, in order to compute the optimal strategies ondynamic markets. We have applied the derived formulas toquantify the impacts of the future on market shares, prices,and profits. Based on the simulation results, we suggest thaton intensively changing competitive markets, where the ex-pected access price is hard to forecast, ISPs have to considershort-term strategies, while on moderate markets ISPs canuse long-term profit maximising strategies.
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Understanding the impact of loyal user behaviour on Internet access pricing: a game-theoretic framework
Tuan Anh Trinh received his MScand PhD in Computer Science fromthe Budapest University of Technol-ogy and Economics (BME), Hun-gary in 2000 and 2005, respectively.He founded and is a coordinatorof the Network Economics Group(http://netecon_group.tmit.bme.hu)at BME. His recent research in-terests include green networking,architectural issues of the FutureInternet, game theoretic modellingof communication systems, eco-nomics-inspired system design andfairness issues in resource alloca-
tion problems in the Internet. He has published extensively in scien-tific conferences and journals in the above mentioned areas. He is amember of the Program Committee of a number of international con-ferences, including the ACM SIGCOMM E-Energy Conference. He isthe recipient of the Pollak-Virag prize from the Hungarian ScientificAssociation for Telecommunication for his contribution in the analysisof transmission control protocols of the Internet. He is a professionalmember of ACM.
László Gyarmati is currently aPhD student at the Budapest Univer-sity of Technology and Economicsas a member of the Network Eco-nomics Group. He received his MScdegree in computer science in 2008at the same institute. His researchinterest is economic aspects of net-worked systems, in particular theapplication of game theoretic meth-ods. In addition, he is a last yearMSc student in biomedical engi-neering at a joint program of theBudapest University of Technologyand Economics, the SemmelweisMedical University.
Gyula Sallai received MSc degreefrom the Budapest University ofTechnology and Economics (BME)in 1968, PhD and DSc degrees fromthe Hungarian Academy of Sci-ences (MTA) in 1976 and 1989resp., all in telecommunications. Hewas appointed as honorary profes-sor in 1990, as full professor in1997. His professional life is relatedto the telecommunications, then theICT. He was senior researcher intelecommunication network plan-ning, then research director, strate-gic executive director, later deputy
CEO responsible for telecommunication services with the HungarianTelecom Company; then international vice president, after that execu-tive vice president for the ICT regulation and scarce resource manage-ment with the Communication Authority of Hungary. Since 2002 he isthe head of the Department of Telecommunications and Media Infor-matics at the BME. He was the vice-rector of the BME as well. He isalso the chairman of the Telecommunication Committee of the MTA,the president of the Hungarian Scientific Association for Infocommu-nications (HTE) as well as the Inter-University Research Centre forTelecommunications and Informatics and a member of the HungarianAcademy of Engineering. Recently his main research area is the ICTmanagement and regulatory issues. He is a member of the EditorialBoard of the Telecommunications Systems.
