Dynamic Strategic Interaction: A Synthesis of Modeling Methods by Timothy J. Richards 1

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2 Dynamc Strategc Interacton: A Synthess of Modelng Methods by Tmothy J. Rchards 1 Agrbusness n the western U.S. no longer conssts only of atomstc producers sellng nto homogeneous commodty markets. Rather, marketng concepts such as value-added, dfferentaton, brandng and supply-chan management are now as famlar to growers, grower cooperatves and marketng boards as they are to food processors and retalers downstream. From Pnk Lady apples n Washngton State to Shamrock foods n Arzona and Sunkst n Calforna, commodty marketers are developng a level of sophstcaton on par wth the most aggressve consumer good manufacturers. Wth ths ncreased level of marketng sophstcaton, however, comes a new defnton of competton. Competton no longer mples passve acceptance of a market prce, but rather actve desgn of a marketng program ntended to develop and explot strategc prcng opportuntes. Economc analyss can help managers better understand the opportuntes they may face. Indeed, much of the recent emprcal research n both marketng and ndustral organzaton focuses on the nature of strategc nteracton among rval frms (Fechtnger, Hartl, and Seth, 1994; Slade, 1995). However, economsts tend to take a postve approach n testng whether market power or strategc behavor exsts, whle marketng researchers buld normatve models that make optmal use of lmted marketng budgets. For both purposes, however, each must estmate parameters that descrbe strategc conduct. In theory, these two dsparate approaches should yeld dentcal results, but n practce ther fundamentally dfferent modelng technques often leave ths smlarty n some doubt. Whle most researchers agree that marketng strateges based on advertsng, promoton, prcng, product attrbutes or product lne must be cast n a dynamc framework, that s where the agreement ends. Indeed, the heart of the dscrepancy between the two modelng approaches les n competng assumptons regardng how to treat the dynamc mpacts of marketng nvestments. Essentally, there are two broad model types that appear n the ndustral organzaton and strategc marketng lteratures, respectvely: (1) Nerlove-Arrow, or goodwll models, and (2) Lanchester, or market share models. Among the frst studes to ncorporate advertsng dynamcs, Nerlove and Arrow (1962) mantan that advertsng expendtures are n fact nvestments n a long-lved captal asset they termed goodwll. Because goodwll s both slow to develop and deprecates (n an economc, rather than accountng sense) slowly over tme once establshed, the mpact of an nvestment made n one perod can be felt for many perods nto the future. As a result, economc models that descrbe the effect of advertsng on sales must be nherently dynamc. Wth ths approach, goodwll becomes the sngle state varable. Examples nclude Roberts and Samuelson s (1988) dynamc conjectural varatons model of strategc advertsng nteracton n the cgarette ndustry, Gasm, Laffont and Vuong s (1992) treatment of marketng actvtes n the soft drnk ndustry, or Slade s (1995) analyss of prce and advertsng rvalry among bscut makers. On the other hand, authors n the strategc marketng feld regard market share as the relevant state varable. Specfcally, Vdale and Wolfe (1957) and Kmball (1957) develop a model of dynamc market share rvalry based on Lanchester s (1921) study of battlefeld strategy. By assumng marketng actvtes by duopolsts act drectly on the rate of change of ther respectve market shares, Lanchester-type models reduce a potentally complex problem to one consstng of a sngle state varable. Examples of ths approach nclude Deal (1979), Sorger (1989), Erckson (1992, 1997), and Chntagunta and Vlcassm (1992, 1994). Whle both requre the estmaton of strategc response parameters, t s perhaps surprsng that nether has sought nsght from the other on how to accomplsh ths. Nonetheless, such a synthess s possble and potentally desrable. Despte the compellng logc of ether approach, each has ts conceptual and emprcal strengths and weaknesses. Whereas the noton of advertsng contrbutng to a captal asset that has a lastng effect on sales s ntutvely plausble, Nerlove 1 Power Professor, Morrson School of Agrbusness, Arzona State Unversty East, 7001 E. Wllams Feld Road, Bldg. 20, Mesa, AZ Phone: emal: trchards@asu.edu. Fnancal support for the Natonal Insttute for Commodty Promoton and Research Evaluaton of Cornell Unversty s gratefully acknowledged.

3 - Arrow models are dffcult to apply because goodwll s nherently latent or unobservable. Moreover, t s a deprecatng asset, yet the rate of deprecaton s typcally underdentfed n most emprcal applcatons. Perhaps due to the fact that the objectve n applyng ths type of model s usually only the estmaton of response parameters and not the complete parameterzaton of an optmal control problem, they also tend to be very complex wth many state and more control varables. Although market-share state varables n Lanchester-type models are readly observable and result n very smple, elegant solutons, there are a number of reasons why ths approach s perhaps overly restrctve. Frst, n order to retan the mathematcal tractablty of dealng wth only one state varable, researchers tend to apply the Lanchester framework only to duopoles (Sorger, 1989; Chntagunta and Jan, 1995; and many others). Erckson (1997) recognzes ths weakness by extendng the model to nclude dynamc conjectural varaton terms wheren several compettors respond to changes n market share wth contngent advertsng strateges, but he uses synthetc parameters to solve for the optmal path of advertsng and does not estmate response parameters. In contrast, structural game theoretc models do not face the same restrctons on the number of potental rvals because they do not purport to solve for equlbrum control paths. For example, Slade (1995) employs a dfferental game approach smlar to Karp and Perloff (1993) n analyzng both prce and advertsng competton among several rval brands of crackers n a local olgopolstc market. Roberts and Samuelson (1988), Gasm and Vuong (1991) and Gasm, Laffont, and Vuong (1992) adopt smlar structural approaches, but restrct ther analyses to duopolstc rvalry n order to focus on the problem of competng wth multple-tools. Ther econometrc models could, however, easly be extended to nclude more general olgopolstc rvalry at lttle cost. Second, n consderng only market-share rvalry, Lanchester models do not allow for aggregate market growth as a result of compettve advertsng. Although ths lmtaton also apples to condtonal demand models, t s possble to ncorporate aggregate market mpacts through two-level demand systems (Rchards, van Ispelen, and Kagan). Thrd, although notable exceptons exst, such as Chntagunta and Vlcassm s (1994) model of advertsng and detalng by pharmaceutcal marketers, studes n the Lanchester tradton typcally nclude only one strategc varable. Clearly, ths approach s not entrely realstc because most marketng managers now recognze the potental for complementarty among the tools at ther dsposal, such as promoton and advertsng or merchandsng and new product development. Fourth, whle the dfferental equatons descrbng the evoluton of duopoly market share are mathematcally plausble, they are ad hoc as they are not grounded n any theoretcal model of consumer choce. Rather, because market share evolves as consumers respond to marketng varables n an optmal way, changes n market share should be fully consstent wth constraned consumer optmzaton. Lang (1986), Chntagunta and Jan (1995), Chngtanunta and Rao (1996) and Cotterll and Putss (2000) each present alternatve ways to ncorporate consumer demand nto models of strategc rvalry, but none of these studes represents a fully dynamc approach to the problem at hand. By groundng a dynamc, strategc-marketng model n consumer theory, we may be able to estmate a system of equatons that provdes a more realstc descrpton of the lkely outcome of market share rvalry. We propose a model that addresses each of these weaknesses by ntegratng features from both ndustral organzaton and marketng research models of strategc rvalry. Frst, by treatng each frm wthn an olgopoly as beng n an us versus them battle for market share, we are able to condense a potentally ntractable olgopoly problem nto one that s mathematcally manageable. Ths s a realstc approach n that olgopolstc frms rarely sngle-out partcular rvals for a targeted prce cut or advertsng campagn. Second, we explctly account for the fact that marketng strateges can, and do, nclude choces over several marketng varables and that these choces are endogenous to market performance and rval strateges. Consequently, we specfy a fully smultaneous model of product demand and strategc-response. Ths s agan realstc as frms allocate marketng budgets among dfferent functons accordng to ther effectveness n counterng rval strateges and n workng wth other marketng actvtes. Thrd, we base the dynamcs governng market share n a model of consumer optmzaton, so strategc nteracton mpacts frm performance not drectly, but through demand for ther product. Ths s a more realstc and plausble motvaton for the evoluton of market share as t goes to the cause of 2

4 changes n share rather than the symptoms of rvals actons. By ncorporatng these three features nto a model of strategc rvalry, we hope to create a synthess that performs better than exstng models. An Emprcal Comparson To facltate comparson, we frst present a bref descrpton of a typcal Lanchester-type model and then offer an alternatve. Wth a Lanchester approach, frms maxmze the present value of future profts subject to the dynamc evoluton of ther market share, whch s n turn determned by the nature of the strategc response of ther rvals. In a duopoly, the sngle state varable s defned n terms of frm I s market share (M ) so that rval market share s the smple complement of ths: M j = 1 - M. Market share growth s assumed to rse wth the effectveness of a frm s own marketng actvtes and the extent of the market not currently beng served. Moreover, each marketng actvty has a dmnshng margnal mpact on a frm s own market share as ntal gans are, qute plausbly, easer than later ones. Wth these assumptons, the equaton of moton for the market share of frm I s wrtten as: M& ( β = M - A α -, t - - φ ) M M + ε, t-1, = ( β A α )(1 - M ) - where M s the change n market share of the th frm, A, A - are a set of j marketng tools avalable to frm I and ts rval, respectvely, and?? s a random error. For example, ths set of tools may consst of advertsng, product development expendture, number of dstnct brands (product lne length) or prce. In ths general form for frm I s market share dynamcs, $? j measures the effectveness of the partcular strategc tool, whereas "? j provdes an estmate of ts curvature. Further, we nclude the parameter N (0 < N < 1) to account for the possblty that market share adjustment from one perod to the next s costly, so t s not nstantaneous f frms behave optmally. Equaton (1) forms the bass of the Lanchester model of market share rvalry. Despte ts smplcty, ntutve appeal, and consderable emprcal support, t nonetheless rests on an ad hoc specfcaton for the evoluton of market share. On the other hand, f the equatons of moton for market share represent a system of consumer demand functons, such as the Almost Ideal Demand System (AIDS) model of Deaton and Muellbauer (1980), then they can be consstent wth optmal consumer behavor. More specfcally, f prces are ndeed endogenous (Lang, 1986; Cotterll and Putss, 2000), then the demand system tself should be wrtten n nverse, or prce-dependent form wth frm-level quanttes as explanatory varables. Ths s the Inverse Almost Ideal Demand System (IAIDS) of Moschn and Vssa (1992) and Eales and Unnevehr (1993). Allowng for the fact that consumer learnng, habts, costly search, and the formaton of a stock of marketng goodwll all mply that demand s nherently dynamc, we wrte the IAIDS equatons of moton as the system of nverse demand equatons: = M t M,t-1+ θ δ j ln Aj + δ -j ln A- j + γ ln q j j + γ ln - q - + η ln Q + v, for all I frms usng j marketng tools, where 2 s the rate of market-share adjustment, q s the unt volume sold by frm, Q s the total quantty ndex, v s a random error term and the other varables are as defned above. Wth ths specfcaton, average prce levels for each rval frm are mplctly endogenous, so they are strategc varables n the IAIDS model, but not the Lanchester model. Note also that ths model can generalze to multple strategc varables and many frms. Next, wth the competng market-share adjustment equatons defned n (1) and (2), we derve equatons for each model that defne the optmal strategc response n each marketng mx varable from the frst order condtons of the frm s dynamc optmzaton problem. 3

5 The detals of ths dervaton for the IAIDS model are n Rchards and Patterson, but we summarze the logc here. If we assume the frms play a non-cooperatve game n each marketng tool n every tme perod, a closed-loop soluton to the dynamc problem consttutes a Nash equlbrum where each decson varable s a functon not only of tme, but of the current state of the game. In ths respect, we model a sub-game perfect soluton. Clearly, solvng ths problem n more than two market shares.e. n an olgopoly, or wth multple tools s analytcally ntractable. Therefore, we adopt a new approach by consderng the olgopoly soluton as smply a seres of us versus them duopoly games. Ths approach, whle unque, s valuable n two respects. Frst, t reduces the number of state varables, thus makng what would otherwse be an ntractable economc problem easly solvable wth analytcal methods. Second, t s ntutvely preferable because frms do not sngle-out rvals for targeted advertsng or prcng strateges as a complete, mult-frm strategc response model would mply. Rather, they set polces condtonal on the strategc envronment they face, whch may consst of any number of rvals. By optmzng ther marketng decsons gven the optmal reactons of the collecton of other frms, the ndustry equlbrum s stll Nash. Consequently, we estmate a demand system wheren the arguments are the own frm s marketng actvtes, all other frms actvtes, the own frm s quantty, all other frms quanttes, and an aggregate sales ndex. Estmatng ths system n a fully smultaneous model that also ncludes supply, or conduct, equatons for each quantty and marketng actvty provdes a consstent set of response-parameter estmates. Dervng an econometrc model, however, does not guarantee that t provdes a better ft to the data compared to the exstng approach. To examne whether t does, we estmate a smlar smultaneous system of equatons consstng of the equatons of moton from a Lanchester model of market share rvalry along wth the mpled frst order condtons for the optmal choce of each marketng actvty. Because the IAIDS and Lanchester models are not nested n one another, we compare ther emprcal performance usng a battery of non-nested tests consstng of: (1) the J-test of Davdson and MacKnnon (1981), (2) the Lkelhood Domnance crteron of Pollak and Wales (1991), and (3) two measures of predctve accuracy B the root mean square error and Thel s U (Thel 1961). The data for our comparson consst of 65 four-weekly observatons of ready to eat cereal sales, prces and brand ntroducton data taken from the IRI Infoscan data base for the Baltmore / Washngton, D.C. market. We combne these data wth smoothed quarterly observatons on advertsng and product development expendture for the top four cereal companes. In ths example, we fnd that all three methods of comparson favor the IAIDS over the Lanchester model. Perhaps more mportantly, we also fnd that several mportant mplcatons that arse from the IAIDS results are ether absent n the Lanchester results, or the Lanchester model suggests an entrely dfferent strategy. For example, the IAIDS results show that advertsng expendtures and new product ntroductons are complementary, whereas the Lanchester model does not. Gven that frms rarely ntroduce new products wthout advertsng, and never wthout some pror commtment to sgnfcant nvestment n product development, the Lanchester results appear to be of lttle value. Beyond these, and smlar, nsghts nto the conduct of marketng rvalry, the approach llustrated here may be valuable to marketng researchers or managers n general n a wde varety of smlar contexts. In partcular, recognzng that strategc varables affect frm performance only ndrectly through consumer demand s more consstent wth marketng practce than s a smple, mechanstc assessment of the tactcal benefts of puttng captal toward each marketng tool. Indeed, well-planned marketng decsons are taken wth customer-orented goals n mnd so gans on rvals are acheved by reachng the same set of customers n a more effectve way. Further, ths analyss shows that these strategc goals need not be couched n terms of a seres of one-on-one nteractons wth rvals as n tradtonal olgopoly analyss, but rather as f each frm exsts n a duopoly -- a duopoly consstng of tself and all other rvals. Ths perspectve not only serves to make dynamc emprcal analyss of olgopolstc rvalry mathematcally solvable, but also provdes more general recommendatons as to the optmal polcy of any one ndustry member. In lght of these results, the path of future research n ths area s clear. Namely, broadenng the scope for ntegratng methods from marketng research nto econometrc orthodoxy. 4

6 Reference Lst Chntagunta, P. K. and N. J. Vlcassm, 1992, An Emprcal Investgaton of Advertsng Strateges n a Dynamc Duopoly, Management Scence, 39, Chntagunta, P. K. and N. J. Vlcassm, 1994, Marketng Investment Decsons n a Dynamc Duopoly: A Model and Emprcal Analyss, Internatonal Journal of Research n Marketng, 11, Chntagunta, P. K. and D. C. Jan, 1995, Emprcal Analyss of a Dynamc Duopoly Model of Competton, Journal of Economcs and Management Strategy, 4, Chntagunta, P. K. and V. R. Rao, 1996, Prcng Strateges n a Dynamc Duopoly: A Dfferental Game Model, Management Scence, 42, Cotterll, R. W. and W. P. Putss, Jr., 2000, Market Share and Prce Settng Behavor for Prvate Labels and Natonal Brands, Revew of Industral Organzaton, 17, Davdson, R. and MacKnnon, J. G., 1981, Several Tests for Model Specfcaton n the Presence of Alternatve Hypotheses, Econometrca, 49, Deal, K. R., 1979, Optmzng Advertsng Expendtures n a Dynamc Duopoly, Operatons Research, 27, Deaton, A. and Muellbauer, 1980, "An Almost Ideal Demand System, Amercan Economc Revew, 70, Eales, J. S. and L. J. Unnevehr, 1993, Smultanety and Structural Change n U.S. Meat Demand, Amercan Journal of Agrcultural Economcs, 75, Erckson, G. M., 1992, Emprcal Analyss of Closed-Loop Duopoly Advertsng Strateges, Management Scence, 38, Erckson, G. M., 1997, Note. Dynamc Conjectural Varatons n a Lanchester Olgopoly, Management Scence, 43, Fechtnger, G., R. F. Hartl, and S. P. Seth, 1994, Dynamc Optmal Control Models n Advertsng: Recent Developments, Management Scence, 40, Gasm, F. and Q. H. Vuong, 1991, An Econometrc Analyss of Some Duopolstc Games n Prces and Advertsng, Advances n Econometrcs, 9, Gasm, F., J. J. Laffont, and Q. H. Vuong, 1992, An Econometrc Analyss of Collusve Behavor n a Soft-Drnk Market, Journal of Economcs and Management Strategy, 1, Hausman, J., 1978, Specfcaton Tests n Econometrcs, Econometrca, 46, Karp, L., and J. Perloff, 1993, A Dynamc Model of Olgopoly n the Coffee Export Market, Amercan Journal of Agrcultural Economcs, 75, Kmball, G. E., 1957, Some Industral Applcatons of Mltary Operatons Research Methods, Operatons Research, 5, Lang, J. N., 1986, Prce Reacton Functons and Conjectural Varatons: An Applcaton to the Breakfast Cereal Industry, Revew of Industral Organzaton, 4,

7 Moschn, G., and A. Vssa, 1992, "A Lnear Inverse Demand System," Journal of Agrcultural and Resource Economcs, 17, Nerlove, M., and K. Arrow, 1962, Optmal Advertsng Polcy Under Dynamc Condtons, Economca, 29, Pollak, R. A. and T. J. Wales, 1991, The Lkelhood Domnance Crteron: A New Approach to Model Selecton, Journal of Econometrcs, 47, Rchards, T. J., P. van Ispelen, and A. Kagan. Estmaton of a Two-Level Demand System for U.S. Apple Exports. Amercan Journal of Agrcultural Economcs 79(1997): Rchards, T. J. and P. M. Patterson. Dynamc Olgopolstc Rvalry wth Multple Tools: A New Emprcal Model. Paper presented at Industral Organzaton and the Food Processng Industry Conference, Toulouse, France. June Roberts, M. J. and L. Samuelson, 1988, An Emprcal Analyss of Dynamc, Non-Prce Competton n an Olgopolstc Industry, Rand Journal of Economcs, 19, Slade, M. E., 1995, Product Rvalry wth Multple Strategc Weapons: An Analyss of Prce and Advertsng Competton, Journal of Economcs and Management Strategy, 4, Sorger, G., 1989, Compettve Dynamc Advertsng: A Modfcaton of the Case Game, Journal of Economc Dynamcs and Control, 13,