AN ADVERTISING OLIGOPOLY

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1 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), 03 AN ADVERTISING OLIGOPOLY Ph.D. Student Alina Irina GHIRVU Faulty of Eonomial Sienes and Business Administration Babeş Bolyai University, Cluj Napoa, Romania Abstrat: This paper proposes a model of advertising ompetition based on the Cournot oligopoly model using a dynami system, the equilibrium points of whih an be determined analytially. We onsider several ases for explaining the way in whih firms will adapt their own advertising volume, depending on the number and the advertising volume of their ompetitors, in the ontext of an online video game used for advertising purposes. The dynami setup is given by online Internet onnetion that allows interation and ommuniation and the high level of tehnology that permits nowadays real-time advertising insertions. Key words: advergame, dynami system, Cournot oligopoly, advertising, video game JEL lassifiation: C7. INTRODUCTION The development of omputer and Internet tehnology made video games beome highly omplex and interative. Companies interested in new marketing extensions from lassi models gained upon their ompetitors by using video games as a ommuniation tool for inreasing reeptiveness of the brand message. Video games were first studied in the aademi world only reently, the year 00 being onsidered to be the moment when video games began to be treated seriously. The fast impat on the audiene made video game beome a real breakthrough in advertising and a powerful ompetitor for traditional media as television and movies. Advertising and video games meet in two major ways: advergames and in-game advertising. An advergame represents a video game onstruted around a brand or produt, sponsored by a marketer and onstruted for delivering the brand messages. It has an immersive mix of advertising and entertainment and an be aessed online through orporate or brand websites. In-game advertising represents an integration of advertising messages in a video game that has a story already reated and is oordinated and sold by independent gaming organizations, using dynami ad-insertion networks (Winkler and Bukner, 006). The purpose of advertising using video games is to inrease brand awareness and familiarity with the brands and produts advertised, to build long time relations with the onsumers, positive feelings, sympathy and fidelity and to inrease purhase intention that will be later transform in atual sales and inreasing profits.. BACKGROUND The existing literature regarding dynami models of advertising inludes multiple studies on how advertising works. Studies about diret relations established between the sales rates of hange and the advertising effort of firms have their origins bak to Vidale and Wolfe (957). Most relevant works approah the issue of optimal advertising in a duopolisti market disussed by Leitmann and Shmitendorf (978). There were several attempts to bring dynami analysis of advertising ompetition to an oligopoly setting, in whih more than two ompetitors are involved. The model that Feihtinger (983) proposed was an extension from a differential game between two profit maximizing firms to the ase of general effetiveness funtions for advertising. Analysis of Nash equilibrium solutions was applied to the Leitmann-Shmitendorf advertising model for investigating the struture of 8

2 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), 03 optimal advertising rates. By setting up a dynami advertising model in a duopoly ompetition setup, Erikson (985) provided important aspets on the ways that advertising an operate in ompetitive and dynami markets. A group of studies about dynami models of advertising originates from Nerlove and Arrow (96) and deals with using advertising for inreasing the stok of goodwill and reommendation, onsidering that the umulate effet of past and present advertising expenditures influenes the urrent demand for the goods that the firm provides. His model was later used in studies of Sethi (977), Fersthman (984) and Jorjensen (999). The game theory groundwork of dynami differential games allows to foreast strategy adopted by the players and to antiipate their moves. Studies about advertising strategies used differential games to analyze urrent outomes of a firm, advertising deision effets and advertising impliations in the future of a brand or produt. Many differential game models applied numerial, analytial, qualitative and empirial methods for studying situations that involve dynami advertising ompetitions (Erikson, 995). The problem of optimum in advertising was treated in terms of promotional budget alloation in a two-person zero-sum game with a mini-max solution and pure strategy game (Friedman, 957). The author onsiders that the major fators governing advertising alloation are ompetitive expenditures and that the ompetitive effet is a key element for determining real advertising budget alloations. Advertising dynami games ware disussed also in a two-person, nonzero-sum stohasti games to analyse dynami advertising models with a disrete-time Markov deision proess (Dirven and Vrieze, 985) Researhers investigating advertising ompetition models used the Cournot oligopoly model as a way of analyzing different matters involved in the deision making proess. Differential oligopoly games were disussed with different setups: when firms whih are engaged in a Cournot ompetition on a market with homogeneous goods and invest in advertising for inreasing the onsumer s reservation prie (Cellini and Lambertini, 003). Authors ontinued this researh with a model of differential game of advertising under both Cournot and Bertrand ompetition (Cellini et. all, 008). Simulation models based on the Cournot analytial model of duopoly were used in investigating the field of industrial organization eonomis (Martin, 00). Several studies (Dixit, 979; Perloff, 008) determined the Cournot equilibrium using an analytial approah. In a study on how benefits of mandated generi advertising vary with firm size in an asymmetri Cournot oligopoly market, with a fous on unit-assessment funding, researhers found that the effet of suh a program on an individual firm s profit depends on the nature of the hange in market demand, and also on the firm s market share (Zheng et. all, 009). As an be seen, previous studies regarding the effet that video games have on onsumer did not approah game theory models for investigating the way that advergames or in-game advertising works. Furthermore, there are no previous studies in the field that are using a Cournot oligopoly model for explaining the dynami proess of advertising volume adjustment for firms that advertise through video games. 3. GENERAL CONSIDERATIONS ABOUT THE MODEL In this paper we try to set up a model based on the Cournot oligopoly model for explaining the way in whih firms will adapt their own advertising volume, depending on the number and the advertising volume of their ompetitors. We onsider several ases that an be investigated in a video game ontext. The dynami setup is given by the internet onnetion that allows real-time interation and ommuniation and the high level of tehnology that is used nowadays for ontrolling and ordering online insertions. 9

3 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), 03 Further, we investigate only the advertising effet on sales, so the prie will be negleted. We assume that any extra advertising unit will reate supplementary effet on onsumers and that firms will insert as muh advertising units that the environment allows. After a ertain advertising exposure level, the player s memory will beome agglomerated and it will generate resistane. In other words, a higher volume of advertising will immunize the onsumer. This an happen under exess exposure of a single or multiple brands. During onstant gaming sessions, players are onstantly exposed to advertisement insertions, whih an take the shape of a banner, poster, interative objet that an used in the video game, and beome familiar with the features and properties of the produts advertised in this way. In time, users an develop strong beliefs and positive feelings about the produt or brand, whih an lead to purhase intention and atual aquisitions. 3. THE MODEL The advertising ompetition model proposed in this paper is based on the Cournot oligopoly model with the following setup: - There is a single type of advertising insertions that n firms insert into a ertain online video game; - The profit of firm i is a funtion of all the ompetitors outputs. Aordingly, assume sales q i, onditioned by the effet of advertising x i, an be expressed as: i i i j j n q ax bx x () Where: a - is the initial effet on sales from a marginal unit of advertising, and. b - represents an immunizing effet on onsumers from total advertising The maximum volume of advertising that a video game an take is the volume at whih sales beome zero, i.e., when a qi 0 xj () b The use of online video games for advertising purposes has an effet on onsumers that is diffiult to quantify for variables suh as brand awareness, sympathy or sharing game experiene, therefore in this paper it will be measured in final aquisitions of the produts, meaning atual sales for the firms. The profits obtained by a firm will depend only on advertising amounts and, to fous only on advertising effet, we simplify by ignoring the effet of ommodity prie. If there are several ompeting ommodities, the pries of all ommodities will be taken as equal, and normalized to unity. Advertising has a unit ost i assoiated with it. To simplify, we onsider all i equal so the profit that a firm obtains is: STRATEGIC GAME: iaxi bxi x j xi (3) - players: n firms with rational omportment that buy advertising units in a ertain online video game; - the market: the online video game spae; - eah firm s set of ations: set of all possible insertions that a firm an make in a video game; - eah firm s interest is represented by profits obtained by atual sales aused by advertising; 30

4 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), 03 - deisions regarding the output (advertising quantity inluded into the video games) are made onseutively. Every firm bases his deision on the moves of the other ompetitors. In the sequel, we analyse several partiular ases. 3. MONOPOLY CASE For a monopoly there is just one firm, say number ; then quantity demanded and the profits obtained due to advertisements are: q ax bx (4) and axbx x (5) respetively. The maximum advertising volume x that the firm ould insert in the online video game is reahed when the marginal revenue equals to 0. This means that if firm inserts another advertisement unit into the video game, another banner or branded item, it will no longer bring any additional inome and the users will not buy any extra produt. Profits are maximal when the first derivative of the profit funtion is zero, i.e. when marginal revenue equals marginal ost. So: a a bx 0 x (6) x b Unlike the ase of oligopoly with several ating firms, there is no issue of dynamis or stability for the ase of monopoly. The monopolisti firm hene has no need to modify the quantity a x, unless anything, suh as a parameter value, hanges, given, of ourse that the seond b order maximum ondition b 0 holds, whih it obviously does. x The monopoly firm, of ourse, only stays in business when it obtains, not only a maximal, but a positive profit, i.e. when (5) with x substituted is positive. This b a a a a means a b 0, or, in plain words that the initial effet of b b b 4b advertising exeeds its unit ost. The possible alternative is a<, for whih ( a) 0holds. It is irrelevant that the advertising quantity aording to (6) would be negative. 3.3 DUOPOLY CASE If in the virtual spae of an online video game where a firm is in monopolisti equilibrium, another firm enters, the advertising insertions state an be destabilised. For two ompetitors duopoly equilibrium might emerge instead. The sales funtion for the firms will be: q axbx( x x) (7) q ax bx( x x) And the profits: 3

5 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), 03 Maximizing profits: Solving for, axbx( x x) x ax bx ( x x ) x abx bx 0 x abx bx x 0 x x in (9), we find the reation funtions for the firms: a x ( x) x b a x ( x) x b (8) (9) (0) Both firms are ative if their profits are positive. Otherwise, they would drop out of the market. As a negative reation has no sense, we have the restritions 0, 0 for the reation funtions: a a xi, xi b b xi () a 0, xi b The Cournot equilibrium point is obtained at the intersetion of the two lines defined by the system (0). In basi linear algebra, the intersetion of two straight lines in the plane defined by linear equations ax ay a3 () bx by b3 an be the empty set, a point, or a line. If the equation system has a unique solution, the intersetion of the two lines is a point, its oordinates satisfy both equations and an be found using substitution method. If the two equation system have no unique solution, either the lines are parallel and the system has no solution, or they are oinident and the system has an infinite solution- set. By solving system (0) we find the volumes of advertising inserted in the online video game when there are firms present in the same video game environment. To solve for the Cournot equilibrium point, we first add the reation funtions (0): a x x ( x x ) (3) b Moving to the left side all the ( x x) we have 3 a ( x ) x b Solving for the sum of advertising volumes a x x (4) 3 b Using x, x obtained from (4) in (0) we find the Cournot equilibrium point: 3

6 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), 03 a x 3 b a x 3 b (5) 3.4 TRIOPOLY CASE Consider that in a stable duopolisti system enters a third firm. Then, for 3 ompetitors, the equilibrium point might be destabilized. In this ase the sales funtions are: q axbx( x x x3) q ax bx( x x x3) q3 ax3bx3( x x x3) (6) and the profits axbx( x x x3) x ax bx ( x x x ) x ax bx ( x x x ) x (7) i Maximizing profits 0 and solving for x, x, x 3 we obtain the reation funtions: x i a x ( x x3) ( x x3) b a x ( x x3) ( x x3) b a x3 3( x x) ( x x) b (8) On a market with three ompetitors we an again onsider their ations in a dynami system. If they take deisions based on naive expetation, they will move in eah urrent period aording to the previous moves of all their ompetitors. The iterative map in this ase is: ' x ( x x3) ' x ( x x3) (9) ' x3 3( x x) Similarly to the duopoly ase, we an find the equilibrium point by solving (8): a ( x x x3) 3 ( x x x3) b 3 a ( x x x3) (0) 4 b Substituting ( x x3),( x x3),( x x) from (0) in (8) we find the Cournot equilibrium oordinates: 33

7 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), 03 a x 4b a x 4b a x3 4b () Using the notations: zi xi x for the deviations from the Cournot equilibrium point like in i the ase of duopoly we obtain from (8), (9) and (): ' z ( z z3 ) ' z ( zz3 ) ' z3 ( zz ) () Using the notations: zz z z3 3 z z z3 (3) () beomes: t ' (0) ' t with the solutions (0) ' 3 t 3 3 ( ) 3(0) The Jaobian matrix of () in this ase is: (4) and the harateristi equation beomes 3 3 P( ) 0, 4 4 with the roots,, 3 As the value 3 falls at the limit of unit irle in the omplex plane, the system is neutrally stable, and any perturbation would throw it into an endless osillation. The system will be destabilized if the ompetitors beome more than three (Theoharis,959). Following the same steps, if we alulate for a quadropoly we will find that the roots for the 3 harateristi equation are,,3 and 4. If they are limited by non-negativity onstrains, as negative reation have no sense, they will drop out of the market. 34

8 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), GENERAL CASE If we generalize to n ompetitors, then the sales funtion is qi axi bxi xj and the profits iaxi bxi x j xi. i By maximizing all the profits 0 we an find the reation funtions of the firms as: x i a xi x j (5) b ji It is onvenient to introdue the definition X i x j X x i, where X x j. Then (5) a an be written xi i( Xi) Xi. Taking the sum of all equations we have b a X n ( nx X ) and an solve for the total advertising volume b n a X n b ji (6) The n firms being idential, they take an equal share of advertising, so a xi n b (7) If there are n firms on the market and they at and reat in aordane with the ompetitors moves, we an onsider their ations in a dynamial system. The iterative map is in this ase: ' a xi i( Xi) Xi (8) b Using the notations: zi xi x for deviations from the Cournot equilibrium point and the i definitions: zz z z 3... i zi zi (9)... n zn zn n zz... zn we will see that the differenes will be damped out, whereas the sum is onstantly growing when the number of firms on the market in higher than 3. Equations (9) then beome: 35

9 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), 03 t ' '... ' i i... ' n n ' n n with solutions i i(0), i,..., n g and n n n(0) The Jaobian matrix is: ' ' ' x x x... x x 0... x n ' ' ' x x x (3) x x xn ' ' ' x n xn xn x x x n The harateristi equation in this ase will have n- roots,..., n, and one root n n so that, when there are more than 3 firms ompeting on a market, the last Eigenvalue will always fall out of the unit irle in the omplex plane. In this ase the system will be drawn away from the Cournot equilibrium point as it will expand ontinuously, or in other words will explode. This orresponds to the result that Theoharis (959) found. By the way, his result was previously disovered by Palander (939) twenty years earlier. Both Palander and Theoharis onsidered loal stability only. In a global dynami a linear system would just be damped out or explode. However, if we onsider the non-negativity onstrains oasionally disussed above, the global dynamis of idential firms would make them drop out every seond time period (Cánovas, Puu, Ruiz, 006). t (30) CONCLUSIONS The dynami ompetition speifi for today s markets made advertisers use new strategies for improving their brand image and obtain ompetitive advantages. One of these new strategies involves the use of video games for advertising purposes. The advantages are given by the speifi attributes of the online environment and the additional entertainment that a video game offers to a player. The presene of a brand in the highly interative environment of video games an bring serious advantages like a superior reeptiveness of the advertising message, inreased brand awareness and familiarity, long time relations with onsumers, positive feelings, inreased purhase intentions and atual sales. The model proposed in this paper show that in a dynami ompetition when multiple brands are present in the same video game, firms an obtain optimal advantages by reahing the 36

10 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), 03 equilibrium point. They an do this by hoosing to at aording to the ations of the other firms present in the game, respetively by adjusting their advertising volumes. The system equilibrium is onditioned bought by the total level of advertising and by the number of ompetitors. The advertising volume reahes its maximal level at a point where the onsumer mind is saturated by the quantity of advertising he is exposed to. At this level, any advertising effort will not bring additional effet on onsumer. The model also shows that the equilibrium of the ompetition an be maintained only if there are maximum three ompetitors. If there are more then three firms present in a partiular video game none of them will obtain optimal benefits from the advertising insertions. The advertisements will have no effets on onsumers who will maintain their initial knowledge, attitudes and preferenes about those brands as before being exposed to the advertising messages, making the promotional ampaign ineffetive. These aspets have important impliations in strategi planning proesses; a firm should hoose a video game whih ontains a small number of advertisements or to deide over an exlusive presene in a video game, i.e., an advergame or an exlusive sponsorship of a video game. Aknowledgment This work was possible with the finanial support of the Setorial Operational Programme for Human Resoures Development , o-finaned by the European Soial Fund, under the projet number POSDRU/07/.5/S/77946 with the title Dotorate: an Attrative Researh Career. The author of this work during the mobility at Centre for Regional Siene (CERUM), Umeå University, gratefully thanks for the hospitality and the help reeived during the staying. REFERENCES. Cánovas, J.S., Puu, T., Ruiz, M. (008) The Cournot Theoharis problem reonsidered, Chaos, Solitons and Fratals No. 37, p Cellini, Roberto, Lambertini, Lua, Mantovani, Andrea (008) Persuasive advertising under Bertrand ompetition: A differential game, Operations Researh Letters Cellini, R., Lambertini, L. (003) Advertising in a Differential Oligopoly Game, Journal of Optimization Theory and Appliations, Vol. 6, No., pp Dirven, C.A.J.M., Vrieze, O.J. (985) Advertising Models, Stohasti Games and Myopi Strategies, Operations Researh, Vol. 34, No. 4, pp , online: 5. Dixit, A. (979) A model of duopoly suggesting a theory of entry barriers, Bell Journal of Eonomis, 0(): Erikson, G.M. (985) A Model of Advertising Competition, Journal of Marketing Researh, Vol., pp Erikson, G.M. (995) Differential game models of advertising ompetition, European Journal of Operational Researh, No 83, pp Feihtinger, G. (983) The Nash Solution of an Advertising Differential Game: Generalization of a Model by Leitmann and Shmitendorf, IEEE Transations on Automati Control, Vol. 8, p Fershtman, C. (984) Goodwill and Market Shares in Oligopoly, Eonomia, Vol. 5, pp. 7 8, 0. Friedman, L. (957) The Alloation of advertising expenditures, presented at the Twelfth National Meeting of the Operations Researh Soiety of Ameria, Pittsburgh 37

11 The USV Annals of Eonomis and Publi Administration Volume 3, Issue (8), 03. Jorgensen, S. (98) A Survey of Some Differential Games in Advertising, Journal of Eonomi Dynamis and Control, Vol. 4, p: Leitmann, G., Shmitendorf, W.E. (978) Profit maximization through advertising: a nonzero sum differential game approah, IEEE Trans. Automati Control AC-3 (978) Martin, S. (00) Advaned Industrial Eonomis, Blakwell: Oxford. 4. Nerlove, M., Arrow, K.J. (96) Optimal Advertising Poliy under Dynami Conditions, Eonomia, Vol. 9, pp Palander,T.( 936) Instability in ompetition between two sellers, in: Abstrats of Papers Presented at the Researh Conferene on Eonomis and Statistis held by the Cowles Commission at Colorado College, Colorado College Publiations, General Series No.08, Studies Series No. 6. Perloff J Miroeonomis: Theory and Appliations with Calulus. Pearson Eduation: Boston, MA. 7. Sethi, S.P. (977) Optimal Advertising for the Nerlove Arrow Model under a Budget Constraint, Operations Researh Quarterly, Vol. 8, pp Theoharis, R.D. (959) On the stability of the Cournot solution on the oligopoly problem, Rev Eon Stud No. 7: Vidale, M.L, Wolfe, H.B. (957) An Operations Researh Study of Sales Response to Advertising, Operations Researh, Vol. 5, pp Winkler, T., Bukner, K. (006) Reeptiveness of gamers to embedded brand messages in advergames: Attitudes towards produt plaement, Journal of Interative Advertising, 7(). Zheng, Y., Bar, T., Kaiser, H.M. (009) Generi Advertising in an asymmetri Cournot Oligopoly, Amerian Journal of Agriultural and Applied Eonomis, 9(3):

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