Strategi Informative Advertising in a Horizontally Differentiated Duopoly Levent Çelik Otober 006 Abstrat Consider a horizontally differentiated duopoly market where potential buyers are unertain about their mathes with either produt. Would informative advertising by a firm about its own produt dislose any information about the other produt when firms know how their as well as their rival s produt mathes buyers preferenes? I answer this question in the ontext of a television (TV) market that lasts for two periods in whih viewers are unertain about the attributes of the upoming programs. A symmetri perfet Bayesian equilibrium (PBE) in whih advertising deisions of the TV stations depend on the attributes of both programs exists, and is the only suh strategi equilibrium. Although not fully revealing, it enables viewers to narrow down their priors. When this PBE is unattainable, the only other equilibrium is one in whih the advertising deision of a station is independent of the other program s attributes. While it is welfare improving to ban suh advertising if the latter PBE arises as the market outome, this is not neessarily true for the former one. This raises an obvious empirial question: Do TV stations at strategially while advertising their own programs? Keywords: Informative Advertising, Tune-ins, Unertainty, Sampling, Signaling. JEL Classifiation: D83, L3, L8, M37 I would like to thank my dissertation advisors at the University of Virginia, Simon Anderson and Maxim Engers, for their invaluable help during the progress of this paper. CERGE-EI (a joint workplae of the Center for Eonomi Researh and Graduate Eduation, Charles University, and the Eonomis Institute of the Aademy of Sienes of the Czeh Republi), Politikyh Veznu 7,, Praha, Czeh Republi. Email: Levent.Celik@erge-ei.z.
Introdution There is a broad range of onsumer markets where the differentiation among produts is mainly in their physial attributes. Although the information about the existene of these produts may be ommon knowledge, many people may have limited or even no information about their attributes. This lak of information may be due to the fat that the produts are newly introdued, or that the osts assoiated with gaining information are relatively high. Television (TV) industry is a good example. It is almost impossible for people to know the attributes of all of the programs at different TV stations. Gaining aurate information through TV guides or internet is often ostly. Furthermore, individuals have limited memories. The present paper proposes a two-period model of informative advertising in a TV market with two TV stations when potential viewers are unertain about their math values with the programs in the latter period. A ruial element of the model is that the TV stations know how their own as well as their rival s program fits viewers preferenes. It is shown that this information struture leads to an equilibrium in whih the deision of a TV station to advertise its own program may strategially depend on its rival s program, and viewers orretly antiipate this strategi interation. The use of advertising has been inreasingly rising in reent years. Total U.S. spending on advertising in 003 had been reorded as $45.5 billion. Approximately 5% of this amount had been devoted to TV ommerials at network and able TV stations (network: 7.%, able: 7.7%). A ompany had to pay over $600,000 for a 30-seond ommerial during the popular show Amerian Idol in 004. Three major broadast stations, CBS, ABC and NBC, reported advertising revenues over $5 billion for the year 003. The prie of a 30- seond ommerial during Super Bowl has been over $ million sine 999 ($.6 million in 006), yet the TV stations airing the event have ontinued to devote approximately 0% of the non-program time to tune-ins (preview advertisements of their own programs). During 000 Super Bowl, 6.5 of a total of 87 non-program minutes were used for tune-ins. These simple statistis reflet the importane of tune-ins for TV stations. Had viewers already been fully informed about the attributes of these programs, there would be no need for tune-ins.
Çelik (006) takes a look at the extent to whih a single TV station is willing to air a tunein. The model is developed in a simple Hotelling framework in whih there is a ontinuum of potential viewers distinguished by their ideal programs. This is represented by assigning a unique loation to eah potential viewer along the unit line. As usual in Hotelling models, a viewer s net utility is lower the further away the atual program is from her ideal program. There is a single TV station that airs two onseutive programs. The loation of the first program is assumed to be ommon knowledge. This may be thought of as the evening news program. The loation of the seond program is ex-ante unknown by viewers. However, the viewers know that the TV station is privately informed about its loation. Therefore, they rationally antiipate that the TV station would ommuniate this piee of information with the first-period audiene unless it is worse off by doing so. The ost of airing a tune-in is the forgone revenue from a ommerial advertisement during the first program. In this setting, it is shown that there exists a unique perfet Bayesian equilibrium (PBE) in whih the TV station airs a tune-in as long as the advertising revenue generated by the viewers ontinuing to wath offsets or exeeds the ost of airing it. In the absene of a tune-in, no one from among the first-period audiene keeps wathing TV. In order to extend the analysis above to inlude a seond station, one has to introdue the possibility of swithing from one station to the other. In fat, Çelik (006) introdues as an extension the possibility of swithing off after sampling a few minutes of a program. While a PBE similar to the one desribed above remains to exist, it is no longer unique. For ertain parameter values, there exists another PBE in whih the TV station never airs a tune-in. In this paper, I move one step further by inorporating viewers swithing behavior into the same setup when there are two TV stations. I assume that the amount of time required for learning the atual loation of a program is fixed and the same for all programs and individuals. However, this proess entails an opportunity ost if an individual does not ontinue to wath the program she hose to sample. The proess of ostly sampling plays a ruial role for two reasons. First, for an equilibrium that involves the use of tune-ins to exist, sampling ost (or equally swithing ost) has
to be positive. Had it been zero, viewers ould ostlessly learn the programs at both stations and make their deisions without any unertainty. Therefore, there would be no need for tune-ins. Seond, a positive sampling ost may reate an inentive for a station to hoose not to air a tune-in. This is beause the ost of sampling beomes sunk one a viewer hooses to engage in sampling. That is, when there is ostly sampling, some individuals may end up wathing a program that they would not hoose to wath with omplete information. By the same token, an individual s final deision may not be the one that maximizes her utility with omplete information. That a positive sampling ost is neessary for the existene of tune-ins is empirially onfirmed by the statistis given earlier. It is harder to establish empirial support for the seond one beause of limited individual-level data. However, Shahar and Emerson (000) report that 65% of viewers ontinue to wath the same network station, inluding the times when a tune-in has not been aired. When the TV stations are informed about eah other s program ontent, their deision to air a tune-in may transmit information about not only their own program but also their rival s. Sine sampling is ostly, a station is relatively more inlined to air a tune-in in order to lok-in its urrent viewers when its rival has a more similar program. However, this may signal to the reipients of that tune-in that the program at the other station is more likely to be a good math than what they thought before. Similarly, if a station does not advertise its upoming program, it does not neessarily mean that it is a bad math for that station s viewers. It ould rather be the ase that it is a better math than the other program. In this paper, I am primarily interested in exploring the nature of suh strategi behavior, and ultimately in finding out if an equilibrium in whih viewers priors are hanged at an interim stage exists. I show that suh an equilibrium exists although it is not unique. Without any restrition on viewers beliefs, there is another equilibrium in whih viewers beliefs about either program are unhanged regardless of the tune-in deisions of the stations. Signaling has traditionally been investigated within the ontext of vertially differentiated produts. When onsumers are uninformed about the atual quality of an experiene good, it has been shown that a high-quality seller an redibly signal this information by setting 3
a high prie or by spending a non-trivial amount of money on uninformative advertising. My findings suggest that signaling is also possible in horizontally differentiated markets. Signaling ours whether a station hooses to or not to air a tune-in. In the former ase, only information about the other program is signalled. In the latter, information about both programs is signalled. However, a fully separating equilibrium is not possible in the urrent setting; viewers annot loate the programs with ertainty. For ertain program loations, the model an also be interpreted as one with vertial differentiation. To be more speifi, when a station s upoming program is better suited to all of its urrent viewers than the other station s upoming program, the two programs are effetively vertially differentiated for those viewers. In suh a situation, I find that the former station does not air a tune-in. Although this result is strikingly different than what traditional models of signaling predit, a diret omparison may be misleading sine TV programs are not experiene goods. Neverthless, it is interesting to note that signaling is possible even in the absene of advertising. I also analyze the welfare effets of a possible ban on the use of tune-ins. I find that when it is not a redible strategy for a station to behave strategially, it may be welfare improving to ban tune-ins. In suh a situation, the stations advertise their programs more often. Although viewers enjoy a higher surplus as a result of improved information, soial welfare is redued beause the derease in revenues of the TV stations overweights the inrease in onsumer surplus. Previous Literature Diretly informative advertising has been the topi of several previous studies. Butters (977) was the first to model the informative role of advertising. In his paper, produts are homogeneous and advertising onveys information about pries, hene also about the existene of the produts indiretly. However, muh advertising involves informing onsumers about produt attributes other than just about pries. Grossman and Shapiro (984) study an extended model in whih onsumers are heterogeneous in their preferenes and advertising 4
informs them not only about the existene but also about the harateristis of the produts. Common to both of these papers is that the advertising tehnology is exogenous and people annot hange their likelihood of reeiving an ad. The urrent paper has several similarities with the latter of the mentioned papers; onsumers are heterogeneous in their preferenes and seek to purhase the produt yielding the highest (expeted) benefit, produts are horizontally differentiated, and advertising provides information about produt attributes. I assume that it is free to wath TV, and that the number of total non-program breaks is given exogenously. Therefore, my analysis does not involve prie advertising. However, I depart from Grossman and Shapiro (984) in several ways, mainly in how advertising is modeled. Advertising in this paper is exlusive; only the viewers who wath the first program may reeive a tune-in of the seond program at that station. It is also strategi in the sense that a station s deision to air or not to air a tune-in onveys information about the programs at both stations. Confining attention to the literature that fouses on informative advertising in an oligopoly market with horizontally differentiated produts, a related paper is Meurer and Stahl (994). They analyze the welfare properties of informative advertising in a duopoly where a fration of buyers are uninformed about the produt harateristis. There are two types of buyers. One type is ideally mathed with one firm and the other type is ideally mathed with the other firm. As in Butters (977), Grossman and Shapiro (984) and many others, a firm hooses its advertising intensity and a random fration of onsumers reeive the ad. Advertising informs a buyer of her best math. Firms hoose their pries after advertising takes plae. They treat produt information as a publi good, whih implies that information about one produt provides information about the others as well. They haraterize a unique subgame perfet Nash equilibrium in whih the level of advertising provided may be more or less than soially optimal. While advertising improves the math between onsumers and produts, it gives firms a higher market power by inreasing brand loyalty. Within the same strand of literature, another related paper is Anand and Shahar (006). They use the same setup with that of Meurer and Stahl (994) with three major differenes. 5
First, a firm an only advertise through one or both of the two available media hannels, and onsumer preferenes over produt attributes are perfetly orrelated with their hoie of media hannel. So, for instane, if onsumers of media hannel are ideally mathed with produt, then firm an target these onsumers by advertising through media hannel. Seond, advertising messages are noisy in the sense that onsumers may get the wrong idea from a firm s informative ad. Therefore, firms advertise more than one. Finally, firms do not hoose pries, whih are therefore suppressed in the analysis. In suh a setting, Anand and Shahar (006) haraterize a separating equilibrium in whih a firm advertises only to those onsumers for whom that produt is the ideal one. As long as the ads are not ompletely noisy in whih ase the ads would equally be interpreted right or wrong there exists a threshold amount of advertising whih asertains a onsumer that the advertised produt is her best math. Thus, regardless of the ontent of the ad, eah onsumer purhases the produt that she was advertised to. There are major differenes between my model and those of Meurer and Stahl (994) and Anand and Shahar (006). First, in both of these papers, produts are experiene goods, so onsumers do not have the option of obtaining produt information by a ostly searh. In the urrent paper, I treat TV programs as searh goods sine program sampling is a ommon pratie in real life. If I rather treated them as experiene goods, the unique symmetri equilibrium would involve no strategi behaving by the stations. Therefore, sampling plays a ruial role for the results in this paper. Seond, there are only two distint types of onsumers in both papers, one ideally mathed with one produt and the other with the other produt. In Meurer and Stahl (994), this assumption implies that an informative ad by one firm neessarily informs the reipient about the other firm s produt, and therefore plays a ritial role for their results. In Anand and Shahar (006), it is a neessary assumption for perfet separation. In my model, on the other side, there is a ontinuum of people who may or may not be ideally mathed with either program. Therefore, the tune-in deision of a station is a funtion of the program loation of the other station. Third, advertising in my model is purely informative unlike as in Anand and Shahar (006), and reahes a 6
nonrandom group of onsumers unlike as in Meurer and Stahl (994). In this sense, I use a different advertising tehnology in the urrent paper. The urrent paper is also weakly related to the literature on quality signaling. To the best of my knowledge, the only two papers that address quality signaling when firms have ommon knowledge of produt qualities are Matthews & Fertig (990) and de Bijl (997). In Matthews & Fertig (990), this is introdued in the ontext of an inumbent-entrant setup where produt quality of the entrant is known to both firms while that of the inumbent is ommon knowledge. Pries are exogenous and the inumbent may advertise in order to inform onsumers about the produt quality of the entrant; i.e. may ounterat misleading attempts by a low-quality entrant. In sharp ontrast to the existing models of quality signaling, they show that a high-quality entrant an suessfully signal its quality by spending an infinitesimal amount on advertising. De Bijl (997) analyzes entry-deterrene in a market for searh goods when produt quality of the entrant is known to both firms while that of the inumbent is already established. It is shown that when the inumbent s prie is informative about the produt quality of the entrant, entry of a high-quality entrant is failitated. 3 The Model The basi setup is that of Çelik (006) with the exeption that there are now two TV stations, station Y and station Z, eah airing two programs in two onseutive time periods. The programs are haraterized by their loations on the unit line. They are of the same length and have zero prodution osts. There are A available non-program breaks during eah program in eah period. Thereisalargenumberoffirms that are willing to pay up See also Hertzendorf & Overgaard (00) who analyze signaling with prie-only when firms have ommon knowledge about produt qualities. The assumption that the number of non-program breaks is fixed is ertainly restritive. However, while U.S. broadasters are free to hoose the number of their ommerial breaks, advertising eilings are imposed on broadasters in most European ountries. Therefore, in most ases, espeially in the prime time, the number of ommerial breaks that maximize a broadaster s revenues falls below the imposed eiling. I believe that this empirial fat onstitutes a good justifiation. Aside from the empirial side, there are tehnial reasons for this assumption. First, if TV stations were allowed to hoose the number of non-program breaks, then people would rationally form priors about it. Seond, and most importantly, 7
to $p per viewer reahed for plaing an advertisement during a program in eah period. On the other side of the market, there is a ontinuum of N potential viewers who are uniformly distributed on the unit line with respet to their ideal program types. To eah possible program type on the unit line, there orresponds a viewer for whom that program is the ideal one. Individuals have the same program preferenes during both periods. An individual derives v units of utility from wathing her ideal program that arries A nonprogram breaks. 3 Formally, a viewer who is loated at a distane of d units from a program obtains a net viewing benefit v d. Not wathing TV yields zero benefits. 4 The parameter λ will be used to represent the loation of an individual, and a partiular individual will be referred to as she when it is onvenient. The loations of the first programs is assumed to be ommon knowledge. Although people know that eah station offers two onseutive program, they do not know where on the unit line the seond programs are loated. Denoting the loation of seond program of station Y with y and that of Z with z, I assume that viewers priors are given by y, z 0,, ª.From their perspetive, eah of these three loations is equally likely to be the atual loation of eah program. The stations know the loation of their own as well as their rival s program, and people know that the stations have this information. They may devote one of the nonprogram breaks in the first period to a tune-in. 5 A tune-in may only inlude information about the atual loation of the upoming program at the same station. I assume that the TV stations annot lie, i.e. they are legally bound to advertise a preview of the atual upoming program in the tune-in. The objetive of the TV stations is to maximize total advertisement revenues (for simpliity, it is assumed that there is no disounting). the number of non-program breaks in the first period would provide information about the seond-period programs. 3 The base utility, v, alsoapturestheeffets of the disutility assoiated with interruptions during a program. Speifially, the effet of an inrease (a derease) in the nuisane ost of a non-program break on a viewer s utility an be aptured by lowering (raising) the base utility. 4 We an as well inlude a onstant, t, infrontofd that measures the disutility assoiated with one unit of distane from the ideal program type. However, sine the value of not wathing TV is zero, we an easily express the utility as r d, wherer = v t. 5 They would never air more than one tune-in beause tune-ins are assumed to be fully informative, and viewers do not swith stations in the first period. 8
Viewers have the option of swithing to the other station or simply turning the TV off after sampling a few minutes of a program. I assume that the amount of time required for learning the true loation of a program is fixedandsameforbothprogramsandforall individuals. This sampling proess entails a ost of, and is referred to as the sampling ost. A viewer inurs one unit of the sampling ost if she samples the programs at both stations and ends up wathing the one that yields a higher utility. If an individual deides the turn her TV off after sampling one of the programs, then her net utility is. If she does so after sampling both programs, then her net utility is. Sine the loations of the first programs are known beforehand, viewers do not engage in sampling in the first period. However, sampling one or both of the stations may be optimal in the seond period. An individual s objetive is to make a deision at eah time that maximizes her total utility. I maintain the following three assumptions throughout the analysis. Assumption + <v<, where>0. 4 Assumption 4 + A <v< A,whereA>0. Assumption 3 The firstprogramsatstationsy and Z are loated at 4 and 3 4, respetively, and this is ommon knowledge. The first and the seond assumptions are made in order to rule out unreasonable equilibria. Thisshallbemorelearastheanalysisproeeds. Notethatitimposesanupper bound on the value of the sampling ost, and a lower bound on the number of non-program breaks. To be more speifi, it is implied that 0 << and A>6. The third assumption 8 is made in order to simplify the analysis. Combined with the first assumption, it implies that viewers on the lower half of the unit line wath station Y and the ones on the upper half wath station Z. Thetimingofthemovesisasfollows. First,peoplemaketheirfirst period viewing deisions. Then the first program starts, and the TV stations make their tune-in deisions during the first program. Having wathed the first program, people update their beliefs 9
about the seond programs depending on whether or not they were exposed to a tune-in. The seond programs start and people make their optimal sampling deisions. After eah individual ompletes sampling one or both (or none) of the stations, they make their final seond period viewing hoies and the payoffs are realized. 3. Equilibrium The equilibrium onept used is perfet Bayesian equilibrium (PBE). That is, the TV stations make optimal tune-in deisions taking the loation of their rival s program and the rationality of people into aount, and people make optimal sampling and viewing deisions after observing the tune-in deision of the station they have wathed. In partiular, people s inferenes (or posterior beliefs) after the first period about the loations of the seond programs must be orret, and the TV stations should not have any inentive to deviate. As disussed in the Introdution, the TV stations may hoose to behave strategially due to their knowledge of the rival station s program. However, regardless of the loation of the rival s program, a station learly never airs a tune-in for a program that none of its urrent viewers would like to wath. This ase arises for station Y when y =, and for station Z when z =0. Given that a station annot ommuniate any information with the viewers of the other station, it does not pay off foreitherstationtoairatune-inforsuhprograms. Let β i (y, z) beabinaryvariablethatassumesavalueof if station i airs a tune-in when the two programs are loated at (y, z), and0 otherwise. So, if station Y airs a tune-in for y =0when z =0,thenwehaveβ Y (0, 0) =. The following lemma is immediate. Lemma β Y (,z)=0for all z, andβ Z (y, 0) = 0 for all y. Next, onsider a situation in whih neither of the stations air a tune-in for their upoming programs regardless of their loations. Suppose that these strategies onstitute a PBE. In suh a no tune-in equilibrium, people s priors would be unhanged. This means that all viewers are indifferent between sampling either station. So, if sampling ours, a random half of viewers initially sample Y and the remaining ones initially sample Z. Suppose a λ-type 0
viewer hooses to sample one of the programs. If λ is suh that 0 λ v, then this viewer knows that she would only wath a program loated at 0. If the program that she first samples is not at 0, should she also sample the program at the other station? Unless the other program happens to be loated at 0, she would turn her TV off, and her net utility would be sine she would have sampled both programs and ended up taking the outside option. So, the expeted utility of sampling the other station is (v λ)+ ( ). On 3 3 the other hand, if she swithes off without sampling the other station, she would enjoy a utility of. Hene, she should engage in a seond sampling if (v λ)+ ( ), 3 3 or equivalently if v λ. Theleft-handsideisdereasinginλ, soifthisinequalityis satisfied at λ = v, it has to be true for all λ v. Evaluating at λ = v, we get v whihisalwaystruebyassumption(). We also need to hek if engaging in sampling is optimal at all for this person. Expeted utility of doing so is (v λ)+ (v λ)+ ( ), where the seond term is due to 3 3 3 3 thefatthatitisalsooptimaltosample theotherstationwhen thefirst program sampled is not at 0. If this is nonnegative, then it is optimal to engage in sampling for viewers with loations λ v. Rearranging, expeted utility beomes [v λ ], whihisthe 3 same ondition as in the previous paragraph, and therefore is nonnegative. Now, take a viewer with loation λ v, 4 and suppose that this viewer samples station Y.ShestaysatY if y is loated at 0. If it turns out that y =,shemayalsowant to hek out station Z inthehopeoffinding out z =0. But there is also the hane that z is or. If z =, she would swith bak to station Y. If, on the other hand, z =, she would be indifferent between the two stations. So, the expeted utility of swithing to station Z when y = is (v λ)+ 3 3 v + λ. If this expression is greater than the utility of staying at Y, v λ, she should swith to and sample the program at station Z. Thisissatisfied when λ< 3. So, when y =, it is optimal to also sample 4 Z for the viewers with loations v λ< 3. Finally, suppose it turns out that 4 y =. The expeted utility of swithing to Z is (v λ)+ 3 3 v + λ + ( ) 3 whih equals 3 v 4.Thisisgreaterthan when v >, whih is again true
by Assumption (). The analysis above equally applies to other possibilities as well. So, as a general rule, stopping sampling is optimal when the loation of the program first sampled is at most at adistane + 3 from a viewer s own loation. We an now express the audiene shares 4 of stations Y and Z for all possible values of (y, z) under the assumption that there are no tune-ins. Suppose, for instane, that (y, z) = 0,. A random half of the viewers sample station Y first. Among these viewers, those with λ + 3 stay at Y while the rest swith 4 to Z. Sinez =,thosewithλ> + v + turn their TVs off. From among the other half who hose to sample Z first,theoneswithλ 3, 3 + 3 4 4 stay at Z while the others swith to Y. Those with 3 <λstay at Y. The same is not true for λ> 3 + 3. The 4 4 program y =0is not favorable for them, so those with loations λ 3 + 3, + v + 4 swith bak to station Z whiletherestswithoff. Arguing along similar lines, we get the following audiene shares: z = 0 z = z = v+ y = 0 v + 4 y = v + + v + v + + 4 4 v+ y = v + 4 Table a. Audiene share of station Y in the no tune-in PBE z = 0 z = z = v+ y = 0 v + + v + 4 y = v + 4 4 y = v + v + + v+ 4 Table b. Audiene share of station Z in the no tune-in PBE Now, suppose Y aired a tune-in when (y,z) =(0, 0). For the indifferent viewer from the first-period audiene of station Y, the expeted utility of swithing to Z is (v λ)+ 3 3 v + λ + (v λ), where the first term is the utility she would enjoy at Z when 3 z =0, the seond term is the utility she would enjoy at Z when z =,andthethirdterm is the utility she would enjoy at Y when z =. This expression equals the utility of staying at Y, v λ, for the viewer loated at 4 +, so the viewers with λ 4 + do not swith to
Z. Sine this is a unilateral deviation, the behavior of the first-period viewers of station Z remains the same. The ones who swith to Z do not ome bak to Y sine they would inur the sampling ost. So, station Y wouldgainanextraaudieneof + 4 v+ = v by 4 airing a tune-in, and thus its seond-period advertising revenue would go up by ANp v 4. The ost of airing a tune-in is the revenue forgone in the first period from a single ommerial, whih is Np. Thus, it is profitable to deviate as long as v. A It will prove useful to analyze in more detail the inentive for airing a tune-in when either station starts from a no tune-in situation. I will heneforth all this situation the no tune-in regime. Suppose the program loations are (y, z) =,. If neither station airs a tune-in, they eah reeive an expeted audiene size of v + in the seond period. From the previous analysis, if station Y airs a tune-in, viewers with loations λ, 4 ontinue to stay with Y while the others, λ<,swithtoz. The ones who swith to Z will 4 stay there one they disover that z =, sine swithing bak to Y means missing the first few minutes of the program at Y. When this is a unilateral deviation by Y,behaviorofthe first-period viewers of Z does not hange. A random half of them still swith to Y right after the first period ends. Among these viewers, the ones with loations λ, 3 + 3 4 stay at Y. The others go bak to Z to hek out the program there. One they disover that z =, those with loations at most v + apart from hoose one of the stations at random as their final destination. Similarly, among those who stayed at Z at first, λ 3 + 3, also 4 sample Y and a random half of λ 3 + 3, + v + stay at Y. Hene, station Y ollets 4 a total audiene size of + 4 + (v + ) as opposed to v +. Sine this is a symmetri game, station Z will have the same inentives. When both stations air a tune-in, they eah get an audiene of v +, the same as before but with different omposition. Thus, we get the following audiene sizes when (y, z) =,, β Z = 0 β Z = 3v β Y = 0 v +, v + +, v + + 4 4 β Y = v + +, 3v + v +, v + 4 4 Table. Audiene sizes of (Y,Z) in a no tune-in regime when (y, z)=, 3
The unique Nash equilibrium in this game is (β Y,β Z )=(, ) provided that v A. This is true by Assumption () and thus the stations fae a Prisoners Dilemma situation. That is why a no tune-in regime annot be maintained in an equilibrium. Lemma By Assumptions () and (), it must be true that β Y (0, 0) = β Y, = β Z, = βz (, ) = is satisfied in a symmetri PBE. Note that when (y, z) = 0, or, 0, deviating from a no tune-in regime is profitable for station Y if A + 4 4,orequivalentlyifA. Although this ondition is different from what was shown to be neessary for deviation when (y, z) (0, 0),, ª,it is in general more restritive ompared to v. Together with Assumption (), A A implies v. However, v does not neessarily imply A. An important A A thing to note is that viewers optimal sampling behavior depends on their inferenes from the observed tune-in deisions of the TV stations. As will be argued shortly, a strategy in whih station Y airs a tune-in only when (y, z) (0, 0),, ª annot atually be part of a PBE. So, it is not nesessary to assume that A for this outome to arise. To see this, onsider an equilibrium in whih station Y airs a tune-in only when (y, z) (0, 0),, ª,andstationZ does so only when (y, z), ª, (, ). For these strategies to onstitute a PBE, viewers inferenes from observed tune-in deisions must be orret. Therefore, when station Y advertises y =0, the first-period viewers of Y infer that z =0as well. This means that eah station ends up with an audiene size of v as eah viewer will wath the first station they hoose to sample. Both stations are atually worse off ompared to the no tune-in regime. However, it is in fat optimal for station Y to swith bak to the no tune-in regime if Z isgoingtoairatunewhen(y, z), ª, (, ).Ifaλ-type viewer who is initially indifferent between the two stations ontinues to stay at Y after not seeing a tune-in, she will infer (inorretly) that z is either or upon seeing that y =0. If λ> +, it is worth heking out station Z, too. But when she disovers that z is also 4 0, shewillonemoretimebeindifferent between the two stations provided that λ v +. Similarly, if she starts at Z and sees that z =0, she will infer that y is either or, andwill 4
swith to Y if λ> v+ +. The seond-period audiene size of station Y is thus as opposed 4 to v, whih means that station Y has an inentive to not air a tune-in when (y, z) =(0, 0). But viewers antiipate this orretly and it was previously shown that this annot be an equilibrium either. One way to get around this problem is airing a tune-in more often. That is, when a TV station airs a tune-in for a partiular program loation, its viewers should not be able to infer the exat loation of the other program. For station Y, the strategy of airing a tune-in for y =0only when z =0, (similarly, the strategy β Y,z =only when z =, ) annot happen in equilibrium. This is beause station Y would also air a tune-in when (y, z) = 0, so as to (inorretly) signal to its viewers that z is either 0 or. So,nofirstperiod viewer of Y wouldswithtoz, and thus Y would get an audiene size of v. Ifinstead Y did not air a tune-in as would be antiipated by viewers in a PBE all of its urrent viewers would swith to station Z and would infer that y is either 0 or upon seeing that z =. In this ase, those viewers with λ< would swith bak to station Y and stay 4 there upon disovering y =0. So, airing a tune-in is profitable when v,whih 4 A is true by Assumption (). Note that this ondition is satisfied even when the sampling ost is infinitesimally small. This leaves us with two possible strategies. For station Y, these strategies are (i) air a tune-in unless y is, (ii) air a tune-in unless y or z is. Similarly, airing a tune-in unless z =0and unless z or y =0are the only two possible strategies for station Z. In what follows, I will refer to a strategy in whih a station s tune-in deision does not depend on the program of the other station as a non-strategi behavior, and to an equilibrium that involves non-strategi behavior as a non-strategi equilibrium. Similarly, a tune-in strategy that depends on the program of the other station will be referred as a strategi behavior, and the orresponding equilibrium as a strategi equilibrium. Suppose eah station behaves strategially. How would viewers behave if this were a PBE? Sine the two stations are idential in every aspet exept for the loations of the first programs, the viewing behavior of people in the seond period will be symmetri with 5
respet to whih station they wathed in the first period. Therefore, I will only find the optimal sampling and final viewing deisions of the viewers who hose to wath Y in the first period. There are three ases; Y airs a tune-in for y =0, Y airs a tune-in for y =, and Y does not air a tune-in. Case (): Y airs a tune-in for y =0. In this ase, the viewers of Y infer that z 0, ª. Those with loations loser to will have a tendeny to swith to Z. Whatever the loation of z turns out, none of these people would ome bak to Y. So, the solution is simple; λ stay with Y,theothersswithto 4 Z. Those who swith to Z will have the sampling ost sunk, and therefore <λ v + 4 will stay with Z when z =0. The others just swith off in this ase. If z turns out,then all of them stay with Z. Case (): Y airs a tune-in for y =. In this ase, the viewers of Y infer that z 0, ª. Those with loations loser to 0 will have a tendeny to swith to Z. Similar with ase (), λ 4 stay with Y, the others swith to Z. Those who swith to Z will have the sampling ost sunk, and therefore (v + ) <λ will stay with Z when z =.Ifzturns out 0, then all of them stay with Z. Case (3): Y does not air a tune-in. The inferene of viewers in this ase is that Y did not air a tune-in beause either y =or z =(or both). There are five possibilities: ½ µ µ (y, z) (0, ),,, (, 0),, ¾, (, ) So the posterior probability that y =0is same with the probability that z =0,whihis. 5 Similarly, Pr y = =Pr z = =,andpr (y =)=Pr(z =)= 3. This means that 5 5 viewers are indifferent between the two stations, and a random half will hoose Z first. For those who stayed with Y, the atual loation of y will determine their further behavior. If y =0, they infer that z =. So viewers with loations less than v + stay with Y, and the rest swith off. Notethatforv<λ v + swithing off yields a disutility of, so it is better to stay tuned. 6
If y =,theyinferthatz =. So viewers with loations (v + ) λ stay with Y, and the rest swith off. If y =, they infer that z 0,, ª, eah with equal probability. Viewers with loations 0 λ< (v + ) would stay with Z when z =0, should they sample it. So, the expeted utility of sampling Z, E UZ λ, given that station Y does not air a tune-in, β Y (0) = (,z), is, E UZ λ β Y (0) = (,z) = 3 (v λ) 3 () Note that the highest utility a viewer may get in this ase is v, sine she started sampling with station Y and inurred the sampling ost. Viewers would stay tuned if the expeted utility of sampling Z is not less than. Otherwise they turn their TVs off right after the first program ends. For λ = (v + ), the expeted utility of sampling is 3 v (). 3 This is at least as great as if v, whih is true by Assumption (). Sine E UZ λ β Y (0) = (,z) is dereasing in λ, all of these viewers would hoose to sample Z. Viewers with loations (v + ) <λ 4 expeted utility is, E U λ Z β Y (0) = (,z) = 3 would stay with Z unless z =. So, their µ µ (v λ)+ v λ () = µ v 4 3 This expression is greater than or equal to when v, whihisthesame ondition as before. Hene, it is satisfied for all λ, 4. The hoies of viewers with loations on, 4 arejustsymmetriwiththoseon 0, 4,sotheyallsampleZ as well. If theprogramturnsouttobeloatedat0 or, station Z gets an audiene size of N (v + ). If z =,everyoneswithesoff. For those of 0 λ who swithed to Z initially, the subsequent hoies are similar. Now, I need to hek if sampling one of the stations is desirable at all, onditional on not seeing a tune-in. For 0 λ< (v + ), the expeted utility of starting sampling with station Y is, E U λ Z β Y =0 = 5 (v λ)+ 5 ( )+3 5 E U λ Z β Y (0) = (,z) 7
Similarly, for (v + ) λ< 4,itis, E U λ Z β Y =0 = 5 (v λ)+ 5 µv + λ + 3 5 E UZ λ β Y (0) = (,z) We need this value to be nonnegative for a viewer to sample Y. For 0 λ< (v + ), E UZ λ β Y =0 = (v λ) (). This is negative if λ is greater than 3 v. If 5 5 (v + ) is less than (or equal to) 3 v, then all of these people engage in sampling. (v + ) 3 v if. By Assumption (), we must have + <, whih 8 4 implies <. By monotoniity of E U λ 8 Z β Y =0 (inreasing up to λ =, and dereasing 4 thereafter), we an onlude that sampling is desirable onditional on β Y =0. We are now ready to alulate the audiene share of a station. The table below gives the total fration of the population hoosing station Y to wath (after sampling, if any) in the seond period for all possible program loations. z = 0 z = z = y = 0 v + 4 4 y = +(v + ) v + (v + )+ 4 4 y = v + (v + ) 4 4 Table 3. Audiene share of Y in the strategi PBE Does station Y have any inentive to deviate? Suppose (y,z) =(0, 0). If station Y deviates and does not air a tune-in, then a random half of its viewers stay with it while the other half swith. Those who stayed would think that z =upon seeing that y =0,andthe ones with loations less than v + would ontinue staying. Those who initially swithed to Z would think that y =upon seeing z =0, and therefore none of them would swith bak to Y.So,stationY would end up with an audiene share of v+.itisprofitable to deviate if µ A 4 v + < where the left hand side is the marginal per-viewer revenue of a tune-in and the right hand side is the per-viewer ost of a tune-in. So, Y would not deviate if v + +. The A same is true for (y, z) = 0,,, 0 and,. Notethatdeviationisnotprofitable when 8
y =sine station Y an only ommuniate with its own viewers, and none of them would wath a program loated at. It remains to analyze if it is profitable for Y to deviate when (y, z) =(0, ) or,. In both ases, station Y is already getting the highest possible audiene share from its first period without a tune-in. So, airing a tune-in annot inrease Y s audiene size. Therefore, deviation is not profitable in these two ases, either. Proposition The following onstitutes a symmetri PBE if v + + A : Y airs a tune-in unless y or z is, Z airs a tune-in unless y or z is 0. When v + + >, people have no reason to expet the strategies in Proposition () A to be played by the TV stations. This ondition is satisfied when v + is large and/or the number of non-program breaks is small. Intuitively, a larger value of v is assoiated with a higher audiene size sine more viewers end up wathing TV. A higher sampling ost means that if sampling ours in the absene of a tune-in, a higher fration of those who sample stay tuned. When the number of non-program breaks is small, the marginal benefit of promoting the upoming program is lower. So, in all three ases, the inentive for passing up on airing a tune-in is higher. From viewers point of view, the ex-ante expeted value of station Y s per-viewer profits is the weighted average of the profits in eah of the possible nine ases. Per-viewer revenue in the first period is pa in eah ase. Per-viewer revenue in the seond period is the average of the audiene shares given in the table for all of the nine ases, multiplied with pa. Sine Y is expeted to air a tune-in in four of the nine ases, its expeted per-viewer osts are 4p 9 times the audiene share in the firstperiod(whihis ). So, the ex-ante expeted per-viewer profits of station Y an be expressed as (the supersript S stands for strategi), E Π S j = A + (6 (v + )+)A 9 9 p, j = Y,Z What happens when v + + >? Based on the analysis so far, one possibility is when A eah station airs an additional tune-in relative to the PBE in Proposition (). For station Y,thisiswhenβ Y (0,z)=for all z and β Y,z =unless z =,orβ Y,z =for all 9
z and β Y (0,z)=unless z =(symmetri for Z). These are summarized in the following table (for station Y only): Strategy Strategy z = 0 z = z = z = 0 z = z = y = 0 y = 0 0 y = 0 y = y = 0 0 0 y = 0 0 0 Table 4. The value of β Y (y, z) in two alternative regimes When Y does not air a tune-in, all of its viewers will swith to Z sine it is highly likely that y =.Ifzturns out 0 or, then they are ertain that y =, and none of them ome bak to Y. When it turns out that z =, however, viewers will get onfused. Station Y mighthaveplayedthefirst or the seond strategy. If it played the first strategy, y ould be or with equal hanes. If it played the seond one, on the other hand, y is 0 or. Without any further information, viewers just assume that two strategies are equally likely to be played, and therefore their inferene will be Pr (y =0)=Pr y = =, Pr (y =)=. 4 But sampling Y would be optimal for all λ 0, with these posteriors. This means that station Y ould have done better by deviating, and reverting bak to the strategy in Proposition (). Sine viewers antiipate this beforehand, we annot have either of these strategies being played in a symmetri PBE. A seond, and the only other, possibility when v + + > is the non-strategi equilibrium in whih the TV stations air a tune-in unless their program is loated at the other A end of the unit line. In this ase, the priors of viewers who wath Y in the first period about z are unhanged regardless of the tune-in deision of Y. Case (): Y airs a tune-in for y =0. Sine there is also the hane that z =, only the viewers with λ> + sample Z. If z 4 turns out to be loated at, theoneswithλ v ome bak to Y. If z =0or,noneof them ome bak. 0
Case (): Y airs a tune-in for y =. This ase is symmetri with Case (). Case (3): Y does not air a tune-in. In this ase, it is inferred that y =, and therefore none of the urrent viewers of Y will wath it. Calulating the audiene share of station Y for all possible program loations gives, z = 0 z = z = y = 0 + + v 4 4 y = + +(v + ) v + v + 4 4 y = v + v + + 4 4 Table 5. Audiene share of station Y in the non-strategi PBE Note that deviation is not possible in this ase, sine none of Y s urrent viewers would keep wathing or would ome bak later when β Y =0. So,theuniquesymmetriPBEwhen v + + A > is the one in whih the two stations play non-strategially. Proposition When v + + >, the unique symmetri PBE is the one in whih Y airs A atune-inunlessy =,andz airs a tune-in unless z =0. Arguing along the same lines as before, the ex-ante expeted per-viewer profits of a station an be expressed as (the supersript NS stands for non-strategi), p, j = Y,Z E A Π NS (6v +4 +)A j = + 9 3 Simple omparison yields that E Π S j is always greater than E Π NS j. Even though it is on average more profitable to behave strategially, the existene of profitable deviations indues the TV stations to behave non-strategially. When v+ A >,evenaninfinitesimally small value of the sampling ost gives rise to the non-strategi equilibrium. When v + +, both equilibria an be supported as PBEs. However, as long as A viewers rationally expet the TV stations to play the less ostly strategies, the non-strategi
equilibrium an be ruled out. To be more preise, provided that v + + A,itisalways optimal to play strategially for the TV stations when the viewers expet them to do so. However, if the viewers are pessimisti in the sense that they only expet the worse when they do not see a tune-in, the unique PBE is the non-strategi one. 3. Soial Value of Tune-ins In this setion, I analyze the effets of a possible ban on the use of tune-ins. I ompare the expeted soial welfare under a hypothetial no tune-in regime with that under no restritions. In the Appendix, I find the expeted utility of a random viewer in all of the possible three situations: the strategi equilibrium (S), the non-strategi equilibrium (NS), and a no tune-in equilibrium (NT). In a regime of no tune-ins, ex-ante expeted per-viewer profit of a station in the seond period is just the average of the audiene shares given in Table, multiplied with the number of ommerials and the per-viewer prie. So, the total ex-ante expeted per-viewer profits of a station are given by, E Π NT j = A 6(v + )+ + p, j = Y,Z 9 Let W denote the soial welfare whih is definedasthesummationofstationprofits and viewer well-being. Then, the hange in expeted soial welfare when the non-strategi PBE arises is expressed as, E W NS W NT = N E λ U NS λ Uλ NT +E Π NS j Π NT j µµ µ 5 p = N 6v 9 3 + A 9 Note that 5 6v 4A < 0 by Assumption () (even a muh smaller value of A would imply the same result). So, E W NS W NT = N 5 6v 4A p 9 3 < 0 for all parameter values. This means that it is welfare improving to ban the use of tune-ins when v + + >, sine non-strategi equilibrium is the unique symmetri PBE for these A parameter values. Although viewers are obviously better off when there are tune-ins, it may
be the ase that lost revenues are too high, and therefore it is better to ban tune-ins. The primary reason for why the stations lose that muh revenue is that fewer people wath TV when there are more tune-ins in general. In the absene of a ban, the no tune-in regime is not sustainable as an equilibrium beause of unilateral deviations. The same result does not arry over to the strategi equilibrium. The reason is that the expeted audiene size in the strategi equilibrium is equal with that in the no tunein regime. Realling that E h i Π S j = A + (6(v+)+)A p, the hange in expeted soial 9 9 welfare when the strategi PBE is the outome is, E W S W NT = N E λ U S λ Uλ NT +E Π S j Π NT j µ = N 3 4p 9 whih is negative when p> 3 4. Proposition 3 If the outome is the strategi PBE, it is welfare improving to ban tune-ins only when p> 3. If it is the non-strategi PBE, on the other hand, it is always welfare 4 improving to ban tune-ins. It immediately follows from Proposition (3) that it may be welfare improving if the two stations ollude and maximize total advertisement revenues. It is optimal to air no tune-ins in suh a ase, and as long as the onditions of Proposition (3) hold, this is better for the soiety as a whole. Tune-ins are learly benefiial for viewers. Without tune-ins, viewers would engage in too muh sampling and some of them would end up wathing TV although this yields a negative utility. If viewers had omplete information about program attributes, TV stations would serve to a smaller audiene size. However, information is inomplete and it is not feasible to inform everyone about TV programs. In a non-strategi equilibrium, TV stations are fored by market fores to air too many tune-ins. This is due to two fators. First, an equilibrium with no tune-ins is not feasible beause of the oligopoly struture; without tune-ins, more people would swith away. Seond, strategi equilibrium is not redible when and/or is A 3