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Game theory in marketing science Uses and li tations Kalyan CMmEm&Gary L. LILIEN * t This paper reviews some major concepts in game theory and indicates how they may apply to marketing science. The theory of games provides a framework for addressing problems of competitive strategies and of buyer-seller interactions. These Lsues are important in studying industrial markets where there are a small number of buyers as well as for studying how to hcoqorate howledgeable, active competitors into consumer marketing mix models. Few marketers have seen much benefit in the past from developments in game theory. This is partly because of the historical preoccupation of game theorists with complete information, zero sum gamcs. The richer area of games of incomplete information may have much more to offer the marketing scientist. Im this paper we review how gario~theoreticapproaches (interactive models) differ from most .previous approaches, look at how which are olptimkhg an! asymmetric. We.these alternative approaches apply to two problem areas wmpetitive entry and bargaining. "I%mwe review potential appLica~onsof game theory in marketing and the value of applying marketing science approaches in game theory. We condude with a perspective on future developments in this field. - Recently, there has been a revived interest among marketing scientists in the use of game theory as a tool for analyzing problems of competition and negotiation in marketing. This has led to major survey artic!es by Moorthy (1984), which introduces and sum* Comespondence address: G.L. U e a , Pennsylvania State University, 113 Business A-stration Building n, University Park,PA 16802, USA. The authors wish to acknowledge the assistance of Eunsang Yoon, Intern. J. of Research in Marketing 3 (1986)79-93 l ~ o r t h - ~ ~ ~ ~ d 63167-8116/86/$3.50 Q marizes new developments in game theory and by Eliashberg and R Chattejee (1984), which examines models of compe~tion.in marketing in an implicitly gametheoretic framework. Game theory has also become an increasingly frequent mode of analysis in economictheory, where the preoccupation with models of perfect competition is giving way to discussions of more interesting market and infomation structures. (The previously cited papers by Moorthy and Eliashberg and R. Chatterjee discuss some of these approaches.) Despite this surge of interest among theorists, marketing practitioners often remain dubious about the usefulness of game theory. Their views may be summarized in the:following statement in Wagner's (1975) popular operations research textbook: 'In practicing operations research we have f o d that game theory does not contribute any momgerial insights into real competitive and cooperative decision-der behavior that are not already familiar ta church-going poker players who regularly read the Wall Street Javnal. ' @. xi) Lazer and Thomas (1974: 578-592) also regard it as '(. ..) highly unlikely that game theory will be used to solve any practical marketing problems9. On the other hand, Henderson (1984: 5) says: m e emergence of grand strategy concepts for business has been severely handicapped by the lack of a comprehen&ve general theory of dynamic competition Olnly in game theory has a systematic and methodical approach been developed.' The critics of game theory have usually concentrated their criticism on the rationality and informational requirement of the theory - notably the assumption that the payoffs of 1986, Elsevier Sdience Publishers B.V.(North-Holiand) Liiie~/ Game theoty dl competitors from any choice of strategies are common knowledge. Work in game theory following Harsanyi (1967,1968a, b) has substantidy relaxed this troubling assumption and has thus brought the theory more in h e with the real world. However, there still remain doubts about the underlying assumptions and the value of the results of a gametheoretic analysis to a marketing practioner. This paper examines the potential value of and possible pitfalls in applying game theory and we hope that the nature of the remaining doubts will be clarLfied in the course of the disc=atssion, In the next section we analyze how game-theoretic models differ from previous marketing models. Our answer, in brief, will be that the earlier models were primdy optimizing, and asymmetric, taking the point of view of a single decision-maker, while gametheoretic models are interactfae, seefig to determine an equilibrim among-several active decision-makers. The equilibrium, however, is not the competitive equilibrium that appears in economic theory, though for large numbers of economic agents the two notions could approximately coincide (see Debreu (1952), and Wilson (1978)). The following two sections will then illustrate the advantages and disadvantages of each approach in two different application areas. In the first application area, that of competitive entry, we shall discuss the papers of Hauser and Shugan (1980), Eliashberg and Jeuland (1982), and Saloner (1982) as illustrations of different approaches to competitive entry problems. The second area, that of bargaining, discusses the papers of Neslin and Greenhailgh (1983) and the approach advocated by Raiffa (1982) as well as the f o m d gametheoretic models with incomplete information that have appeared recently. In the final section, we offer concluding comments. This paper does not aim to be an exhaus- tive survey of marketing applicarions or to be a l~toridlon game theory. The choice ob' illustratioas reflects the interests of the authors, but we hope that they throw some light on the uses and tations of game theory in marketing. 2. Optirniiing and interactive models 2.1. Optimizing (arymmetric) models Most of the markehg decision models that appear in the literature (see, for exmple, those discussed ia Lilien and Kotler (1983)) adopt the point of view of a single, active decision maker. Competitors are either assumed not to react or the d&sion adker subjectiveiy assesses what the reaction could be. Given this mode of handling competition, the model than helps the decision-maker choose one or more elements of the marketing mix in order to optimize some objective function (to maximkc profits or sales respons, for example). We shall refer to such rically prescriptive models as 'opt modells. These models use a variety of tecbques. When the en*oment is known (that is, mder certainty), mathematical pro g or its dynamic version, optimal control theory, are the tools frequently employed. For example, see, Little and Lodish (1969) for media scheduling, Lodish (1980) for broadcast spot pricing, and Sethi (1973) for advertising spending. Under uncertainty, the appropriate framework is that of Bayesian decision analysis, where the ddsionlmaker chooses a, decisiclia or sequence of decisions t jwtive expected utility an servation using Bayes' theorem. The proponents of Bayesian decision theory often do not distinNsh between natural uncertainty (for example the uncertainty associated with tomorrow's weather) or strategic uncertainty k: Chatterjcre, GL, Lilien / Game rheoy (uncertainty about the actions of competitors). In their view, then, the analysis of competition could pro the f ~ a t n e ~of~ an ~k opaimliz;ling, decisian-mdytic model with the appropriate subjective probability distributions on the competitors' possible choices. This point of view is expressed forcefully by Kadane and Larkey (1982). To them, the essential task is collecting enough empirical data about the behavior of wmpetitors and, in w e d , other decision makezs, to be able to msess a ' probability distribution. Thw: deta 4.. .I suppoft the mnclusioos (hat opponents tend to be "'actually at potentidly irrationaf" and bent@ we &kt& mgmcy to fhther p.sych~Xo&t rescareh on actual behavior of people making decisions in g m situatiofts.' ( U a n e sad L E E(1982 ~ ~ :124)) 'l.. .I the em&ical This is appropriate in situations where the actions of competitors are 'decoupled from one's own actions and where'.such data is normally available. Highly diffuse markets with little concentmtiorr of market share, in which the indifferent competitor-weak buyer paradigm is appropriate, fit this framework. However, many non-consumer markets are characterized by a small number of buyers, each of whom may yield significant power. In these markets, the competition tries to guess may be doing and to what any major optimize against that set of actions. Competitors' likely actions may not, therefore, correspond to their past behavior on which data may be available, but may be based on raa tional optidzing behavior. ParadoxicaIly, it seems that only firms with a relatively or market share position can expect competitive strategies to be dmupled from their own strategies, 2.2. dnteraa:tiue modefs The potential inadequacy of the asymmetric, o p M ~ n framework g is therefore its lack of interactive considerations the fact that -, one's opponent is also using an op model. Game theory provides solution concepts that take into w a n t this mutual intesaction of optimizing models. The most popular and frequentfy used one is that of non-cooperative (Nash) eqabrium. T h i s concept will be discussed shortly. However, we should dedsbn-analytic approach has a number of strengths. It is simple to use and it can generate a large number of expg&t reco ations to problems too complex to be analyzed by game theory. Naive application of this kind of nnodel may be dangerous-, but sophisticated (with a-strong dose of formal or informal game theoretical insight~thrown in) may, k fact, be best option for a mmager, Since Moorthy (1984,m a g others, has expanded on the equilibrium notion in detail, we shall not do so here. We do include a brief discussion of the basics of game theory in order to make this paper self-conthd. Our concern is with non-cooperadiue game theory since this seeins particularly appropriate for a discipfine focused on compedticm. The cruGial differen= between noncooperative and a cooperative situation is that, in the former,situation, agreements between decision-makers have to be self-enforcing. That is, each decision maker must find it in his best interest to choose the action recornmended in the agreement, since binding contted or not enfoxed. tracts are not p The 'best interest' of a decision-makm i s represented by a von Neumann-Morgenstern (cardinal) utility function. Every decisionmaker is assumed to have one and, in games of complete infomation, all &ese utility knowledge. The car&e is for the we s, which we shalt mention briefly later. The interested decisionmakers are called plnyers; each has a set of possible strategies (or decision sequences) which is usually assumed to be convex, corn- K Chatterice, G.L &lien / Gamd theory pact and (one hopes) non-empty. If environmental uncert~tyis present, then anohex 'player', chmee, i s added. Chance 'chooses' a with some mmmonly-how probability distfiutioa:, The normal fonn of the game (as the decision-making context is labelled) specifies the outcome (in terms of the payoffs in expected utility to each player) corresponding to a choice of strategy by each player and by chance. Note that in calculating the sod form, players are assmedl to. choose their strategies simultaneously in a oneshot game. This is not a real restriction, sine we can model a sequence of moves and counter-moves (known as an extensive form of the game) in this &mework by d e f ~ n ga strategy suitably. Notice we defined a strategy as a decision sequence, not as a decision; a strategy specifies a decision at every 'distinguishable move. For details, see Luce and Raiffa, (1957), which stiU remains the most lucid exposition of the basics of game theory. Formally, the notion of Narh equilibrium definecT with referace to the normal form asks us to look for a n-tuple of strategies (if there are n decision-m&ers) consisting of strategies that are best responses to one motha, ]In. ;a two-playa game, if we Eind a pair of strategies such that player A's strategy is optimal for A giuen B's strategy and moreover B's strategy is optimal for B gioen A's strategy, we are at an equilibrium. Neither playa can gain by a unilateral switch to a non-equilibim strategy. (However, as the Prisoner's Daemma game shows - see Luce and Raiffa (1957) - this does not mean that t imp1cove by a joint deviation.) The notion of equilibrium is, in some sense, an interactive extension of an associated (implied) asymmevic decision analytic model. Suppose A develops an expectation of what B is likely to do. Suppose that A's conjecture of B's strategy is, in fact, B 's equzb~urn strategy. In that case, A could do no better than choose his o m equilibrium strategy (using an op model with a sinde-point probabili t of B '8 strategy). s-the 'right9 conjecture about A's choice of an equifikrfiium strategy, B 9 s model wiU yield his equilibri strategy as a respume. The choice of the fiat conjecture thus enables the two separate op to be finlked. The arises, -can one expect one's opponent to choose the &librim conjecture? (The question b S more acute if there are multiple q a b r i a which we shall not consider here.) is where the frequently criticized concmt of game-theoretic rationality enters. A rafionat player will be able to calculate the e ~ u i tibrium and see that the pair of conjectures entailed by it is mutally consistent. Moreover, he will never underestimate tris opponmt and will assume a 0 be rational as w d . In his reply to Kadane and Larkey (1982), Harsanyi (1982: 125) states: e '(. ..) game theory f., .) is -daIty a question of how to act in game situations against highly r a t i w l agponents, (...) this line of inquiry ac is, and always has k n , @e main intellectual attracGon of gslne tfteory ,.. No psychdoest st\Kiying how p q i c perfom aribetkc camp@- ing behavior Gthout bowing ari knowing the rrormtiue t b r y of correct comparta&ans for he must explain any giver).~0mputati01~ move gtitiiw as the eorreef move tive or as a ps*ologidy rent kthmetic p to explain a mow by a given player ia a game mwt -lain it eeither as a move j u s t w by normagve gsmetheoetical r a d o d q or rrs a psy&ol@cdly from it.' Other recent work on the equil tion has proceeded to attempt to r number of equiEibria that could be considered reasonable outcomes of a game. The most promising of these refinements is the concept of perfectness in the extensive form (Selten (1975), Kreps and Wilson (1982)). This is discussed in Moorthy (1984) so we shall not give a detailed exposition. The K CkutteQee, G.L L2lit.n / Game theory that an equiifibTiutxh h the n o d form may, in fact, be unreasonable if it hv01yes a player m&ixrg f f i r a t s that wodd be hatiorrd fcrr es necessary to do ,it may sustain an but there is no r w o n for it to be not imply that threats will mt be made or that bluffs w i U not be used. It simply means that a player must p attention to the credibility of the threat and thax the analyst must see that threats that are made are crer4ible. The notion is used in the papers in the next section. Table 1 per-$ fibr5uan. 8- A equi- a &d Player B &t 62 (0,o) 64, plarc=r+d X' a2 @a,-10) -51 <-%,21 mation is less precise than it actually is. The more competitive the market-situation, the more one expects to see this phenomenon occur* 2.3. Mixed strategies 2.4. Incomplete information The azomal farm game in table I does not have a pure strategy equilibrium. However, since it is a game with a finite nmber of pure strategies for each player, it does have mixed strategy equilibrium. For ekmgie, Player A should play a, with probabiliv 12/17 and a , with probability 5/17. Marketers and decision analysts in general have always needed convinchg about the value of mixed strategies. It is not easy for a subordinate to tell a supenlor that a decision should be based on the spin of a sou1ette wheel. The rationale game theorists give for mixed strategies is that of maintaini~lgsecrecy. One's dways capable of going opponent is as h o u & every link in the most intricate chain of reasoning but cannot be expected to foretell the outcame of a random. event. Randomizadon i s then a way to prevent one's strategy choice from being fully anticipated m d mutered. strategy would never need to etric decision analytic features that distinguishes the interactive equilibrium soluGon concept from the o p t i e g one. fn our opinion, a key insight from the potential use of mixed strategies is that, if using a pure strategy commicates private information perfectly, ta bebave % if' the inforit may be op The game-theoretic model is capable of being exknded to incorporate incomplete in- fannation about payoff fmcejtons. Harsmyi (1967,1968qb) introduced the idea, which was to model player A's uncertainty about player B's payoff by a chance move at the beginning of the game tree. The resolution of the uncertainty is then /supposed to be cummdcated to player B and not to player A who knows only a known probability distribution over the possible payoff functions far player B. The equilibrium concept is extended to this kind of game by defining a strategy as a mapping from a player's Somation to his decision, rather than as the deckion itself, The use of incomplete infomation models often, paradoxically, makes formal analysis more tractable in addition to m realistic. This is because a pure strategy equilibfim becomes more tiEreIy. (A player's un~ r t & t y about the other player's payoff function mimics a ro&te wheel.) Incolnplete infomation models in barg the number of equilibria or provide focal equilibria that are more likely to be picked by the players. We shall fiat ctiscuss here the nuances of Harsan9's formuration. The interested reader Eilien is referred to the clear exposition in Myerson qlass). In this section we contrast asymmetric optimizing models with formal interactive models with respect to the solution concepts that each type of model employs. We have also provided a brief discussion of various criticisms of game-theoretic notions and possible resolu~om. 3. Handling competitive response in marketing modteIls Most marketing models use the consumer packaged good paradigm as a model of the marketplaw: several sellers and a very large er of buyers. OperatibnaHy-oriented marketing modelers have traditionally handled competitive behavior in one three ways: (1) by ignoring it; (2) through a judgmental model approach (Little (1975), Buzzell (1964), General Electric Company (1980), Kotler (19651, Simon (1978)), or (3) thtough the reaction matrix approach (Lambin, Naert and Bultez (19751,Bensousson, Bultez and Naert (19781,Lambin (1976), Schultz and Hanssens (1976), Hanssens (1980)). These models/approwhes have, deterministically or probabilistically, assumed the nature of competitive response (via a decision theory/judgmental model approach) or have tried to infer the nature of response from market data (the reaction-matrix approach). Models based on axiomatic frameworks describing the marketplace have been appearing in recent years both in marketing and in nsaaics, We shall discuss three of these: Hauser and Shugan (1980), Hiashberg and Jeuland (1982), and Saloner (1982). These papers are not directly comparable since they deal with somewhat different problems, but the choice of problem is often indication / Game theory of the power of the methodology. Our exation of these papers is in terms of three modebg features, namely: (i) static models versus dynamic models, (ii) optimizing versus equilibrium models, and (iii) complete versus incomplete h f o m t i o n models. H a w and Shugan (1983) concern themselves with the optimal response of an existin@: a competitive new product entry. The the framework of Lmcaster (1971, 1980) in treating a product as a point in attribute space with consumer tastes being d i ~ ~ b u e over e d this space. At the time of the new entry, there are several existing brands ira, the market (occupying different points in attribute space). If the new entry is 'competitive' in the sense of competing for the same group of consumers, an existing firm may respond optimally by changing its price, its advertising, its distribution or the positiohg of its product. None of the other existing brands is assumed to respond at all, and the effect of any changes in the fkm9s marketing mix is summ&ed through exogenously given response functions. Gven this framework, the authors derive several interesting results aboat the direction of change of price or advertising expense, for example, in an optimal response. An optimal response could be, for example, to decrease price or decrease distribution expense. We shall not go into the results in detail, but will confine ourselves to commentkg about the model Many of our comments are anticipated by Hauser and Sugan themselves in their introdwtory rean~ks. First, the model is a static d e l l in that time does not enter in any essential way. As a result the model does not discuss any responses the new entrant might make to the existing firm's optimal response. Second, the model optimizes for a given alien / Game theory firm assuming that all other brands remain passive. There is also no attempt to expand the problem description to incorporate the viewpoint of the entrant who should, presumably, be able to predict the optimal response derived in the paper and be able to position his product in an optimal way. (This would be akin to deriving a Nash equifibrium in a Stackelberg formulation of the game.) Operationally, this last piece of missing analysis might be especially useful, since a product manager muld then.be able to predict the attribute configuration of a possible entrant and contemplate possible pre-emptive strategies. (One preemptive strategy is briefly mentioned by Hauser and Shugan on page 337.) On page 321 the authors express the hope that their model 'is an important step towards a multiproduct equilibrium'. However, nohg that Lane (1980)had f d e d to obtain explicit andytical results beyond pro* existence of equilibrium, the autbors justify the strong assumptions about competition made in their model. To some extent, this is a justification many optimizing models in different areas can claim. The sequence of conjectures followed in reaching an equilibrim may render calculation of that equilibrium particularly intractable. We might then have a very general model with nothing to say. The asymmetric optimizing model, on the other hand, is capable of generating advice for managers. This theory has been extended and marketed under the name of Defender by Management Decision Systems, as a 'new model and measurement system to determine the best response to a competitive new product introduction (cf. Klein (1984:20)). A third characteristics of this paper is that it is basically an analysis under complete infonnafion (though consumers may not be aware of some brands). There is no leamirig about fim characteristics either by other firms or by consuments. There is no explanation given, and this holds for the other models we shall discuss as well, why a particular firm 85 should choose to enter the should enter earlier than suuners are allso not mod the avdabIe products through use, since the model is a static one, The Eliarhberg-JmIand (1982) paper is also a complete info-tion model, although it does incorporate d p h c features and does consider a duopolistic phase. The problem these authors address is essentially one of c madel pricing policy over time in a where one firm enters first and ar second enters (with certainty) a specified period of time later. Once again, the entry decision i s exogenous to the model; firms are not dm lowed to enter before or after the specified length of time. In the duopoly phase, which occurs after the second firm has slnterd, the of a is linearly change in market ferenw betweern the related to the pri two firm:. This is exogenous to the model and could be contrasted with the Bertrrand oligopolistic story in which the firm with the lower price gets the whole rn&ket if its capacity is sufficient. For a homogeneous commodity in a world without search costs and hwmplete information, this relation is diffidt to just@ in equilibrium. However, prodatct diff erentiation and incomplete information enables the model to use this framework in a reasonable: way. The Eliashberg-Jeuland paper thus uses the equilibrium notion in a competitive m ing analysis. The authors obtain app results but on a smaller range of issues than the Hauser-Shugm article discussed earlier in this section. However, in the duopofis~c phase, the advice a manager would receive from Eliashberg-Jeuland would be contingent on assumed eqabrium behavior by the adversary firm as well as on the special features of the model, As a final sample of the game-theoretic models that have appeared recently, we con- &lien sider the work of Salsner (1982). This is closely related to the papers of Matthews and Miman (1983) and Miland Roberts (1982). Saloner considers an existing monopolist trying to deter potential entry by its market behavior (for example, by 'limit pricing'). Potential entrants are, however, uncertain about the monopolist's costs structure and cannot infer it exactly by observing the is accomplished in Sdoner's paper by exogenous market uncertainty.) Based on the observed price, a potential entrant makes probabas~cinferences (using Bayesian learning) about the monopolist's true cost and chooses whether to enter or not. S h e r shows that a 'trigger-price' strategy is followed that is the entrant chooses to go into the market if the price is higher than some cut-off value. The monopolist's market behavior anticipates and optimizes against the potential entrmt9sstratewe This model is dynamic, contains incomplete infomtion and uses (Bayesian Nash) equilibrium as the solution concept. As compared with the Eliashberg-Jeuland paper, with which its subject matter has some similarity, it does not exogenously specify the time of entry independently of the monopolist9s behavior. On the other hand, Eliashberg-Jeuland are able to get stronger explicit characteristics of the pricing strategy of the monopolist over time. We note that as we move from the purely optimizing model to the explicitly interactive ones with uncertainty, the scope of the model becomes narrower and answers to complex problems difficult to obtain. The interactive analysis, however, is valuable in providing insights into competitive behavior that cannot be obtained by treating other decision-makers as passive. 6 4. Bargaining and negotiation models An area largely ignored in the marketing models literature deals with bargaining and / Game theory negofiation. We noted earlier that the typical consumer marketing paradigm includes a set of powerful, knowledgeable active sellers dealing with a large number of relatively weak, passive buyers. But many marketing situations, especially in the institutional or industrial area, deal with a single buyer and seller with some cornon interests and some opposing ones, attempting to reach a comman, cooperative goal of agreement (if it is mutually beneficial) as well as the non-cooperative goal of seeking to vidual payoff. The most typical example deals with negotiati quantity of some product to the buying firm from the though such a&;reemmtsusually entail complications related to quality, delivery, future prices, renewal options, competitive restrictions and the like* Unfortunately, formal mdysis of the strategic process of bargaining in these setting often proves analytically intractable. A possible approach, advocated by Kadane and Larkey (19821, Raiffa (19821, and carried out partially in Chatterjee and Ulvila (19821, is to combine an asymmetric decision analytic model with empgcd studies of the strategies used by likely b a r g w g adversaries. Since few negotiations are open for outside observers to study, empirical data on the actual process of negotiation is often hard to obtain. (An exception is Sebenius (1984)' which contains a detailed case study of the Law of the Sea negotiations.) The data must usually be collected in a laboratory setting. Several recent studies in bargaining have reported experimental results: Roth and Malouf (1979), RQth alnd Roth aod Schoumaker (19831, Chatterjee and Lilien (19841,Neslin and Greenhail& (1983), and Eliashberg, LaTour, Stern and Rangaswamy (1984). None of these papers contains explicit efforts to determine what strategies bargainers use in given contexts. Roth and Mdouf (1979) and Roth and M Lilian / Came theory (1982) attempt to test the validity of the assurmptions leading to the fmous Nash barg-g solution (Nash (1950,1953)). These assumptions are often interpreted as informal principles governing the process of bargaining in complete information situations where the status quo point and the utility-possibility set of agreemats are common knowledge. One of the results of these experiments is of potenetric dgrcision tial importance for the analytic program (Kadane and Larkey (1982)) - namely the observation that bargainers often go beyond utility infomation to the physicd monetary values involved. However, to translate this into a strategy that one's opponents will use is not trivial. Neslin and Greenhail* (1983) and Eliashberg et al. (1984) are concerned explicitly with o u t c ~ m eof~ the bargaining rather than the s~ategicprocess. Each paper explores a particular solution concept b s a predictor of the expected outcome and analyses deviations from it in terms of bargaining skill, situational considerations and (in the Washberg et al. paper) the completeness of information. While these studies are valuable in their own. right, they do not help carry out the asymmetric decision analytic program that is needed to close a model with strategic uncertbty, Roth and Schoumaker (1983) conduct experiments on the role of reputation. Their result, that it pays a bargainer to establish a clear preference for some particular outcome, does have strategic implications. Chatterjee and Lilien (1984) look at 'mechanisms' rather than outcomes and study the efficiency of v ~ o u mmha~sms, s that is, various bargainsses. Their results khcow some light procedures an individual might elect to follow rather than on the strategies a bargainer should choose given a procedure. However, since many of the procedures they study have theoretically determined equilibria it is possible to use their results to cast doubt on Bayes equilibrium as 87 a predictor of an individual's actions. Given the paucity of work in empirical requirement of the d program, it is useful to consider the theoretical process modeling that has gone on recently in game theory. Most elassicall models of b concept of complete inform pred3icti:ons of b e h a ~ a rQhat often seem far from reality. Indeed, we have all o b s e ~ d bar&;&&; situations that have resulted in disagreement (suikes, for example) although outside observers may easily point out that a mutually beneficial agreement could have been reached. Although such issues of dip agreement may be expldned by psychological or behavioral factors, it is interesting to note that they can often be explained by as incomplete infomation. B a r g h g under incomplete deals with situa~onswhere each private infomation (about preferences, costs, reservation prices, etc.) that is unavailable to the other side. The research on b under incomplete oha at ion has led to the important result that pareto-inefficient outcomes (outcomes that allow each party to improve its position) can be shown to persist in quilibrium; the most outcome is the existence of even when mutually beneficial agreements exist. This result has generally appeared in single-stage models in which the bargaining is over one issue, There has also been a fafr amount of interest recently in multi-stage models in which the phenomenon of inefficient bargaining expresses itself through delayed ageemat in an enviroment where time msts money. (See table 2 for a of these models.) The bargaining literatwe, notably the work of Myerson (1983), for example, has also generated new notions of efficiency while proving the impossibility of attaining effidency in the classical sense, "Ihe focus in this work is not on the efficiency of the outcome ob- K;Chatregee, G k Eitien / Game theory 88 under hcomplete Morma~on Features ' I. Binmore (1981) 2. Chattexjee aflB S m u b n (1983) 3. C r m t o (1983aji ~ 4, Crawfod 0982) 5, Fudmberg and Thole (1983) 6, Fdmbeag5, m d TkoIe (1983) 7. Rubhteb (1983) 8. Sobe1 and Takahfi (1983) 9. Wilson (1982) a x x x x x x x x x x x x X X * x x x x * x x x x x x x x x x models, these authors incIude this feature. E = Tw8-sided inmplete information. 2 Continuous probability distribud011~. 3 = Both parties make offers. ; - Sequentid Smsrtion ttmonission incoprated in mdeL on more than one diane&ions. 5- B 6 = Explicit consideration of alternatives tikcurrent bargain. 7 = Maay buyers and sellers in market. 8 = Bargainers uncertain before bargaining of the size of gains from trade. 4 I tained in b a r g h g , but on the efficiency of the mechanism or process used in arriving at the outcome. The non-cooperative equilibria of such m sms are compared with one another and principles laid down for choosing a mechanism based on the properties of its equilibtium payoffs. The recent research in bargaining, though much of it is arcane, has provided several bportant insi61;hts. From the point of view of both bargainers, the theory suggests that it rmi@t be desirable to set time limits on the even perhaps to limit it to one offer from each side. (See Cramton (1983b) for results on how much bargainers collectively lose by not being able to enforce this co&tm.ent .) From the point of view of the individual bargainer, the theory prescribes how he should use his private information optimally against another rational bargainer. It lays down for instance, how aggressive he should be (the most aggressive bargainers end up not doing too well) and under what mnditiom 3! concessions over time is optimal as a g m t a 'take it or leave itp strategy. The interesting codwion in some of these mslfelts is that the 'take it or leave it' strategy could be optimal if you could get your opponent to believe that t to stick to your offer, but not ese insights could prove of assistance to marketing scientists in consbcting operational models that purchasers engaged in negotiation might profitably use. From this brief overview eefi& m clear. First, more empscal work in re&tjic business contexts is needed to drive the search for both normative and descriptive theory of bargaining and negotiation. Such a cycle of empirid observation leading to new theory could well lead to models and guidehes that can improve the bargaining and negotiation process. Indeed, this area appears to be quite a fruitful one for further development and apglica~on, 5. Game theory and mwkting: Match or mismatch? Several points emerge in our discussion. First, the problem of competition is important in the marketing area and is often handled in an unsatisfactory m game-theoretic concepts offer for directly addressing competition. gme-theoretic models faequmtly make assumptions about available infomation, about the descriptive nature of market equilibria or about the objectives of competitive rivals that bear little resemblance to real marketing si;ituaaions. We believe that a cross-fertilizatiom is needed. Game theory can provide an approach for addressing some marketing prob- Ufien / Game theory lems that the more conven&iondtools s f the marketing scientist do not address. And the empirical focus of marketing science can help provide the tests that are required for the game theorist to evaluate alternative concepts of equilibria and to assess the descriptive soundness of gamstheoretic models. We elaborate 'below. 5.1. Applications of game theory in marketing As with most methodologies, game theory is being fkst applied in marketing to those situations where it best demonstrates its value, Indurtrial marketing applications of bargaining. The bulk of the marketing science literature focuses on situa~omwhere there is ample data for analysis and where the number of buyers, at least, is large. According to Hill, Alexander and Cross '(1975: 83) however, 'most major purchases' by business, private institutions and numerous government agencies and departments are probably negotiated'. They go on to note, 'The buyer must be cognizant of the cost situation of his own firm as well as that of suppliers ( ...) [he] mst seek every advantage ( ...) to which his . company is entitled' (1975: 84). This quote makes several points that focus on the gametheoretic nature of industrial marketing negotiations. First, the buyer is cautioned to be aware of the cost situation of his firm and that of his suppliers. This awareness permits the buyer to assess the value of a contract to and to his supplier. The value-analysis concept (Lee (1978)), a seminal idea in the industrial marketing area, teaches the seller how to determine the value of a product to the buyer. Here symmetry exists to have both parties calculate contractual equilibria. Second, the stress on 'seeking every advantage' points strongly toward joint evaluation of contractual benefits. Cases like Air and Gas Compressors, Inc. (Corey (1976)) c8emonstraee how buyers and sdlers use infor- 89 mation about each others' costs and objectives to develop fair and profitable relationships. The benefit of using game theory in such situations is that it (a) focuses attention on information that must be collected (costs/ value functions of bargainers) as well as (b) suggesting fair solutions (e.g., identification of a prtleto frontier). Tools to perfarm such analyses are currently under development (see e.g., Eliashberg (1985)). Measwemeet market effiiency. In many commodity markets, competition exists among a smdl number of sellers, with one of &ose sellers acting as a price leader. Due to the undifferentiated nature of the product, competition in those markets incorporates ele rnents such as assurance of supply that are closely related to a selling industry capacity. Many chemicals, metallic products and electrical components are examples of products that complete in such a manner. One example is titanium dioxide. Over the past 20-25 years, the t i t b m dioede macrkea. has been characterized by periodic over-expansion followed by under-capacity. The mechanism during this vicious cycle seems to be a view that competition will remain static while each (active) firm independently da cides whether or not to add capacity. The result is that when demand rises, afI fkm consider adding capacity. Most do, and periodic overcapacity results (Lilien and Yoon (1985)). Improvements in profitability of up to 60% are shown to be possible for a that operates more efficiently in this market. There appear to be major inefficiencies associated with asymmetric decision-making of this type. A game theoretic market analysis has the potential to improve overall market efficiency materially in the market. Such a tool might also provide a case for infomation-shdg to produce such efficiency. ~~ / Gum@theory This situation is an example where game theory has a diagnostic or auditing function. approach can identify market situations that are inefficient and suggest the type of marketer-educator (use of applied decisiontools) most likely to add to the market's efficiency.An example where this approach has proven effective is in bidding for oil leases, where many companies (e.g., Oren and Williams (1975)) publish their approaches in the hope of reducing the effect of the so-called er9s curse9. s. occurs when a bidder uderesbates costs or overestimates Peasetract-value and increases his probability of winning the bid due to poor data or poor processing of information. The widescale publication of such approaches is aimed at reducing the effect of this phenomenon and at l e a ~ less g oil-lease money on the table. Market mechanism design. :In many business/industrial markets with on& or several buyers (defense contract markets in particular) the buyer may have the power to design the market; i.e., to structure the conditions under which sales will be made. This problem is critical in certain defense markets where the govement states that it wishes to create wn$itions in which slack capacity exists in peacehe to be used in the event of a "urge" - a rapid military buildup. Game theory provides the solution concepts necessary to d e tennine the market conditions (How many firms share a winning bid? What return is provided for the winner(s)? What cost-sharing does the government provide for cost overruns? What assurance of long-term governto a procufement' program should be provided')) necessary to meet govennroent's need for slack capacity and to encourage firms to invest in cost-reducing production-improvements (Kratz, Drinnon and Hiller (1984), Seshadri (1985)). Similarly, in the private sector, what choreography of offers and counter-offers are most likely to lead to a contract when it is eost-beneficid to do so? Work such as that of Chattejee and Lilien (1984), focusing on the sequence of offers and counter-offers most likely to lead to agreement, suggest that buyer-first offer and seller-first offer procedures appear to dominate shdtaneous offer procedures and multi-stage bargains do at least as well as single stage bargains. These types of results can improve the efficiency in ets made by a buyer-seller combination. 5.2. Applications of m r k ef ing in game theov Much of game theory appears sterile to the marketing scientist. The axiomatic approach players is at odds with the to characte*g observation-based analysis of customer r e sponse which is often the focus of market models. Much of marketing science fwuses on understmhg, m e a s ~ gand affecting customer response. Many scientists characterize the research process as a cycle of theory (or model) building, observation, evaluation, new ~ e o r y / model, etc. (e.g., Bunge (1967)). It is d o u s how infrequently game theorists seem compelled to subject theoretic results to empirical tests. This tendency is despite the fact that the impetus for severd, interesting investigations was provided by classrooms simulations (Raiffa (1982)); as Roth and Mumighan (1982: 2) point out: 'Although it has not yet become standl4 practice to test economic theories with experimental data, b;ugaiging seem to be a subject well suited to the endeavor, both because there is a well-developed body of deductive thwry on the: subject and because, being an activity which cm take plilace between as Pew as two agents, it readfly Lnds itself to reliable hveseigation." These experimental investigations and empirical tests of game theoretic results provide the links between hypothesis, theory and law that are. the glue of scientific inference. The marketing scientist is well suited to help arrange for empirical tests that can raise questions with existing game theory results and to suggest future directions for both theoretical and empscd research, 6. Conelusion: Value, operational problems and future of game theory in marketing apply to c h m e 1 relationships in consumer make& as well. On net, game theory provides a powerful set of concepts and a f& opaationd tools for marketing scientists. The marketing scientist has understanding of and empEcd data on the operational problems e n g in real markets. The challenge to both h e s is to devise realistic models of active e e t i tion that are solidly based on empirical foundations, provide operational ts md that have an impact on practice. We will deal with the points in the title of this section in turn; first, consider the value of game theory in marketing. Managers feei that competition is situation s p d c , is messy and is not related to elegant, abstract models. h t , the value of g m e theory in marketing is to allow the marketing model-builder to t Refe m c e s better about a particular problem. Corporate Be~lsoussan~ A., AIain Bulta and Philippe Naert, 1978.Leadds strategists in a firm who are fa& with dynamic marketing behavior in ~ f i g ~ ?TIM y . sww in pseudo game-theoretic reasoning (Henderson the Maaagemwit Sciences 9,123-1415. (1967)) Or the of gamemtheoretic Binmore, KG., 1981. Mash bsrgaining II. London Sehml of (e.g., Porter's (1980) 'Competitive Strategy*) -- Bunge, M.,1967. 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