A MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME

Transcription

1 A MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME Vesna Radonć Đogatovć, Valentna Radočć Unversty of Belgrade Faculty of Transport and Traffc Engneerng Belgrade, Serba Assstant professor Full professor Abstract In a hghly compettve telecommuncaton market each servce provder (SP) tends to mprove hs poston n relaton to compettors. In order to acheve hgher market share and consequently hgher proft, a SP n addton to mprovng qualty of servce should mplement effcent prcng and marketng strateges. In ths paper we propose a repeated game approach for modellng the competton among ratonal SPs wth smlar reputatons n the same telecommuncaton market. We defne the servce demand and payoff functons as SPs proft functons. Ths model may be applcable for obtanng the optmal trade-off between the avalable strateges, consderng current reputaton n the market and concurrent SP s actons. Keywords Nash equlbrum, payoff, prce, proft, repeated game, servce provder.. INTRODUCTION Prcng telecommuncaton servces s determned by varous factors, among whch the most mportant are servce demand and compettveness of servce provders (SPs) n a telecommuncaton market. Therefore demand functon has to be defned precsely and should take nto account the servce prce offered by the observed provder as well as prces of the same servce offered by hs compettors []. Relatons between SPs are complex because they don t have always strctly opposng nterests but also have to cooperate. Game theory s a promssng soluton for modellng competton n growng markets, such as telecommuncaton markets. Repeated games are sutable for modellng stuatons where players repeatedly nteract wth each other. In such stuatons, a player can condton hs behavor at each pont n

2 the game on the other players past behavor [], [3]. In ths paper we observe two SPs as players n telecommuncaton market. We use repeated game model for analysng competton between SPs and Nash equlbrum concept for determnng the optmal strateges. The paper s organzed n the followng way. In Secton we defne servce demand and servce provders proft functons consderng the servce offered by two SPs wth smlar reputatons n the same telecommuncaton market. In Secton 3 basc assumptons n game theory and components of games are brefly presented. In the same Secton repeated game model for analysng competton between two servce provders s descrbed and we also dscuss the Nash equlbrum of the repeated game example. Concluson s gven n the Secton 4.. SERVICE DEMAND AND SERVICE PROVIDERS PROFIT FUNCTIONS For the same or smlar servces there s multple nterdependence between a prce and demand for a servce. Hgher demand for the servce allows the servce provder to ncrease the servce prce and to smultaneously acheve hgher revenue from ths servce. On the other hand, f demand for the servce decreases, the prce must be reduced n order to attract new customers. Competton between servce provders also affects prcng. Customers wll prefer a provder offerng the servce wth the best qualty/prce relaton. If a provder reduce the cost of a servce he wll attract more customers and wll earn more revenue, whch wll affect the ncome of other provders n the market that offer the same or a smlar servce. The expected reacton of compettors s to reduce the prce of ther servces to retan customers []. For the purpose of ths study, we defne a total demand for a servce n the market wth two servce provders - SP and SP: D t = D + D () D D b p b p D () t D m D b p b p D (3) m b b p b b Dm D D (4) D p where: D - postve constant representng the total demand of SP s servce f the servce was free p - servce prce set by SP b - senstvty of SP s customers to ts prce change

3 b - senstvty of SP s customers to prce of SP. It ndcates what effect of changng the prce p compared to p wll have on the customer ntenton to purchase the gven servce. D m - ncrease n demand caused by marketng promotons. SP s proft: p D c (5) c - operatonal cost c = c b + c m (6) c b - basc cost c m - marketng cost We assume the same marketng cost for both SPs: cm csa (7) s c s - SP s cost parameter a s - SP s advertsng effort Proft change s defned as follows: ntal proft f p p c c f p p c c (8) 3. REPEATED GAME SETTING FOR MODELLING COMPETITION BETWEEN TWO SERVICE PROVIDERS Game theory s a feld of appled mathematcs that descrbes and analyzes nteractve decson makng stuatons. It conssts of a set of analytcal tools that predct the outcome of complex nteractons among ratonal players [3]. Basc components of a game are players, the possble strateges of the players and consequences of the strateges,.e. outcomes or payoffs. The players try to ensure the best possble consequence accordng to ther preferences. The preferences of a player can be expressed ether wth a utlty functon, whch maps every consequence to a real number, or wth preference relatons, whch defne the rankng of the consequences. The most fundamental assumpton n game theory s ratonalty. Ratonal players are assumed to maxmze ther payoff. If the game s not determnstc, the players maxmze ther expected payoff [3], [4]. It s also assumed that all players know the rules of the game well.

4 A game descrbes what strateges the players can take and what the consequences of these strateges are. The soluton of a game s a descrpton of outcomes that may emerge n the game f the players act ratonally and ntellgently. Generally, a soluton s an outcome/payoff from whch no player wants to devate unlaterally. When engaged n a repeated stuaton, players must consder not only ther short-term outcomes but also ther long-term payoffs. The general dea of repeated games s that players may be able to deter another player from explotng hs short-term advantage by threatenng punshment that reduces hs long-term payoff [5], [6]. For the purpose of ths study we observe two servce provders as players n the repeated game. We observe the prce of an ndvdual servce offered by SP ether ndvdually or bundled wth other servces. For SPs wth smlar reputaton n the telecommuncaton market, we suppose three possble strateges: A lower prce, B lower prce combned wth marketng efforts and C addtonal content for the same prce combned wth marketng efforts. The assumpton s that the strategy C, n terms of ndvdual servce, means even a lower prce of the servce when t s sold bundled wth other facltes and therefore the prce s set lower for strategy C compared to strateges A and B. We suppose that choosng strategy C means prce reducton of % compared to the start, and choosng A or B means 5% lower prce n comparson to the startng prce. In ths study, we set the ntal prce to 3MU (money unt) for both SPs and the ntal demand D = D =.4. We have also assumed the followng numercal values: b = b =.4, b = b =. and c = c =.MU. For these values, we have calculated the dfference between the realzed and the ntal proft expressed n percentages for all possble strateges combnaton for both SPs. (Table ). In further text the dfference between the realzed and the ntal proft s denoted as payoff. Table. Servce provders strateges and the correspondng payoffs A B C A (, ) (3, 8) (-6, 7) B (8, 3) (, ) (, 7) C (7, -6) (7, ) (, )

5 Wth the am of modellng the competton among ratonal servce provders wth smlar reputatons n the same telecommuncaton market we assume the followng repeated game settng: In the frst stage of the game, the two servce provders smultaneously choose among ther actons, observe the outcome, and then n the second stage play the statc game agan. The payoffs are smply the dscounted average from the payoffs n each stage. That s, let u represent SP s payoff at the frst stage and u represent hs payoff at the second stage. Then SP s payoff from the mult-stage game s u = u + δ u, where δ (, ) s the dscount factor. Accordng to the proposed game settng and Table, t s reasonable to suppose the followng course of the game: SP : play A at the frst stage. If the outcome s (A, A), play B at the second stage, otherwse play A wth probablty of 3/ and B wth probablty of 8/ at the second stage. SP : play C at the frst stage. If the outcome s (A, C) or (C, C), play A at the second stage, otherwse play A wth probablty of 3/ and B wth probablty of 8/ at the second stage. Snce the strateges at the second stage specfy playng Nash equlbrum profles for all possble second stages, optmal strategy profle for both SPs nclude only strateges A and B. Both provders receve hgher payoffs f they choose dfferent strateges,.e. (A, B) or (B, A), whch s gven n Table. Ths results n playng mxed strategy Nash equlbrum at the second stage. Table. Servce provders strateges and the correspondng payoffs at the second stage of the repeated game A B A (, ) (3, 8) B (8, 3) (, ) In ths case SP wll not devate from the strategy profle (A, B) f 8 + δ*4/ 3 + δ*8,.e. δ 55/64. Smlarly, SP wll not devate f 8 + δ *4/ 3 + δ*3,.e. δ 55/9. We conclude that the strategy profle specfed above s a subgame perfect Nash equlbrum f δ 55/9. In effect, SPs can attan the non-nash effcent outcome at the frst stage by threatenng to revert to the worst possble Nash equlbrum at the second stage.

6 4. CONCLUSION Game theory s especally convenent means for analysng competton between servce provders offerng the same or smlar servce n the same telecommuncaton market. In ths paper we have researched possbltes of usng game theoretc approach for computng compettve prces and profts of two servce provders. We have observed two servce provders, wth smlar reputaton n the market, as players of the repeated game. For the defned repeated game settng we have dscussed and determned a subgame perfect Nash equlbrum. In further research we wll consder possbltes of modellng the competton among servce provders wth dfferent reputatons n the same telecommuncaton market as well as the mpact of dfferent customers behavour. REFERENCES [] V. Radonć Đogatovć, A. Kostć-Lubsavlevć, Telecommuncaton Prcng Fundamentals, Unversty of Belgrade Faculty of Transport and Traffc Engneerng, Belgrade, Serba, 5. [] M. J. Osborne, An Introducton to Game Theory, Oxford Unversty Press, 4. [3] J. N. Webb, Game Theory - Decsons, Interacton and Evoluton, Sprnger, 7. [4] A. Kelly, Decson Makng Usng Game Theory - An Introducton for Managers, Cambrdge Unversty press, New York, USA, 3. [5] V. Radonć, V. Aćmovć-Raspopovć, Local ISPs Prcng Strateges n the Repeated Game Concepts", Proceedngs of TELSIKS 7, Vol., Nš, Serba, September 7, pp [6] B. Sngh, Repeated Games for Inter-operator Spectrum Sharng, Master s Thess, Aalto Unversty - School of Electrcal Engneerng, Aalto, Fnland, 4.