Game theory as a marketing tool: uses and limitations

The growth of complexity of the business environment in which firms operate, calls for more effective tools, able to consider the effect of the strategic choices of the actors of the market and to supply information useful for managerial decision
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  Gandolfo Dominici/ Elixir Marketing 36 (2011) 3524-3528    3524 Introduction  Game theory has been traditionally used in military strategy(Siiman & Cruz, 1975; Bacharach, 1977). Kotler and Singh(1981) pointed out that competition in markets is somehowsimilar to competition in the battlefield. Since the firstformalisation of game theory by Von Neuman and Morgastern(1944), researchers have been debating about the possibility toapply game theory to solve marketing problems, and inparticular to use it as a tool to predict competitive behaviour(Herbig, 1991). Later on the debate has been extended to all theother possible uses of game theory in marketing. Managementdecisions about marketing mix have to be taken in situation of competition and variability in the business environment. Porter(1980) clearly states the relevance to consider the possibleeffects of competitor’s strategic decisions on every level of managerial decision process.According to many authors the assumption on which gametheory is based are too constrictive and is too theoretic to bewidely employed in managerial practice (Wagner, 1975; Lazer& Thomas, 1974; Moorthy, 1985; Tullock, 1987). Furthermorethe axiomatic approach to define the player of the game clasheswith the marketing research approach which is based onempirical observation, measurement and analysis of consumers’response. Although game theory has apparently a great potentialfor marketing (Re, 2000), its role is still controversial in themarketing literature and its use as a marketing tool is very rare.This paper, through a literature overview, sheds the light onthe criticalities and highlights the limits of the application of game theory to marketing management, trying to answer to thequestions:Why the use of game theory in marketing is rare? Can gametheory be an effective tool for marketing decisions? Basic assumptions of Game Theory T   he aim of game theory is to: “provide a formal language todescribe conscious and goal-oriented decision processes thatinvolve one or more players” (Shubik, 1972). In its srcinalformulation, game theory includes some of the assumption of neoclassic economic theory (Herbig, 1991):I. Complete information: every player knows all the rules of thegame and the preferences of the other players for each result.II. Perfect information: every player is exhaustively informedabout all the choices foregoing the time of his decision.III. Rationality of decision process: every player takes decisionsbased on the maximization of his utility function; in case of uncertainty the player makes subjective predictions based onprobability in order to calculate his utility function.IV. Intelligence: every player is rational and able to predict thechoices of other players, thinking about what would be therational choice he would take if he was in the same situation of an other player.V. Competitive and non cooperative behaviour: as aconsequence of the previous assumptions, individual choices arebased on the maximization of each individual utility functionand not on that of all the players as a whole. There is a noncooperative bias which, from a systemic point of view, brings tonon optimal choices, like in the prisoner’s dilemma.VI. Dynamism: player’s situations, as well as environmentalfactors, are changeable; therefore most games are non-static anddo not supply a single move solution.VII. Interdependence: the results of each player are mutuallyrelated with decisions of other players; thus unilateral decisionsare not possible.VIII. Time: the result is affected by the length of the game.IX. Interactivity: game theory attempts to establish equilibriumbetween different players. Criticisms about the basic assumptions of game theory  D   espite of the possible analogies between some of theassumptions of game theory and the situations in which themanagement has to take strategic marketing decisions(dynamism, time, interactivity and interdependence), marketingprofessionals do not use game theory to take decisions.As already pointed out, the axiomatic approach to definethe player of the game clashes with the marketing researchapproach, which is based on empirical observation,measurement and analysis of consumers’ responses.The main reason of the scarce use of game theory formarketing decisions has to be found in the strong limitationsgiven by its basic assumptions (Wagner, 1985; Lazer & Thomas,1974; Kreps & Wison, 1982; Herbig, 1991). The hypotheses onwhich game theory is founded are considered far from reality,  Elixir Marketing 36 (2011) 3524-3528   Game theory as a marketing tool: uses and limitations. Gandolfo Dominici Faculty of Economics,   University of Palermo. ABSTRACT The growth of complexity of the business environment in which firms operate, calls formore effective tools, able to consider the effect of the strategic choices of the actors of themarket and to supply information useful for managerial decision process. Game theoryseems to be an ideal candidate for this scope. Nevertheless, because of its axiomaticapproach, its validity to highlight and define marketing issues has many critics. This paperanalyses the main literature about the use   of game theory for marketing managementdecisions and highlights its limits in this field in order to answer to the question: Can gametheory be an effective marketing tool? © 2011 Elixir All rights reserved.   Marketing ARTICLE INFO Article history: Received: 18 May 2011;Received in revised form:8 July 2011;Accepted: 18 July 2011;  Keywords Game theory,Marketing management,Rational choice in marketing.  Available online at Tele:E-mail addresses:© 2011 Elixir All rights reserved  Gandolfo Dominici/ Elixir Marketing 36 (2011) 3524-3528    3525 hence game theory is considered useless in the complex world of marketing.T   he most common criticisms regarding the application of game theory in marketing are:Game theory analyses the behaviour of rational players. AsHarsanyi (1982) points out: if a psychologist attempts to explaina player’s move in a game, he has to describe his behaviouraccording to a rational- normative approach or as anunderstandable deviation from it. In marketing, instead, therelation between price and objective quality of a good is not themain driver of consumer’s purchase. Intangible and irrationalfactors prevail on physical and price factors as determinants of consumers’ choice, for almost all the markets (with partialexception for few undifferentiated product). Marketing existsbecause the consumer is not a homo oeconomicus; consumer ismainly irrational. Moreover it happens often that managerialstrategic choices do not aim to the maximization of profit ormarket share and that their goal are not the same of those of other competitors (for example they can have different timehorizons or different concern about reputation).In the real world, the environment is not known and certainand not completely knowable. Managers have to take marketingdecisions in markets with increasing levels of uncertainty. It isnot possible for all the players to surely know the rules of thegame, hence the assumption of complete information in not   realistic and game theory is not suitable to be used for marketingdecisions.In many games the results are not fixed but they arearticulated in terms of probability. Managers do not like to usetools which express unsure results.C   ompetition prevails on cooperation. This is not what oftenhappens in the market.Game theory doesn’t consider the process of creation of firm’s image and its effect on the market. Arguments in favour of game theory for marketing decisions D   espite the strong criticisms, we can find also severalauthors supporting the value of game theory for marketing,giving partial answers to some of the criticisms.According to Di Benendetto (1986), it is possible todemonstrate, with few logical revisions, the relation between theeconomic definition of game and marketing decision process.According to Bacharach (1977), game theory has thefollowing attributes:a) a well defined set of possible ways of action for each player;b) Each player has well defined preferences within the possibleresults of the game;c) Relations and results are determined by the choices of theways of action made by the players;d) Every player has complete knowledge of the attributes above.According to Di Benedetto (1986), the choices about marketingmix taken by middle management coincide with the ways of action (a); player’s preferences correspond to the product’s   objective decided by top management (b); relations and resultsdepend on competitors’ choices in the market (c); the bestinformation optimizes the decision process (d).The assumption of rationality is the main limit for theapplication of game theory to marketing. However, irrationalitycan be comprised in game theory model using the “bluff andthreats” (Chatterjee & Lilien, 1986; Herbig, 1991; Kreps eWilson, 1982b). An irrational action can be included in the gameif the player is able to assert the bluff. Hence, a behavior thatwould be considered irrational by game theory with completeinformation becomes possible in situations of incompleteinformation (as for bluff and threats).Kreps and Wilson (1982) included the reputation factor intheir game model, stating the effect of a player’s reputation onthe behavior of other players.Regarding the assumption of complete information, it isvery difficult to think backwards to determine the intents of eachsingle manager and translate them in payoffs of a game matrix.To solve this problem some authors (Chatterjee & Lilien, 1986;Di Benedetto, 1986; Cho e Kreps, 1987), proposed that gametheory model could be extended to comprise incompleteinformation about payoff functions.Di Benedetto (1986) points out that it is possible to integrateinformation about competitors’ intentions with qualitativeinterviews and surveys submitted to managers and experts in theindustrial sector. The results of these surveys can then be used totest the empirical soundness of the model.Cho and Kreps (1987) highlighted that it is possible toestablish equilibrium also in case of games with incompleteinformation, gathering information from marketing signals (asdefined by Eliashberg & Robertson), which indicate thepreference of a player for a specific move and his possiblereactions.From the point of view of competition, game theory gives arewarding model to analyze interdependences and the effects of    competitors’ interactions. Interesting development in this fieldare those coming from the coopetition approach (Branderburger& Nalebuff, 1995 e 1996), which brought to the creation of win-win games, widening the horizons of game theory beyond themere description of competitive scenarios.T   hese “mixed strategies” can be considered as interestingattempts to overcome the limits of complete information of theclassical game theory, thus making it more suitable to be used inmarketing decisions concerning competitive strategy. Game theory for pricing decisions W   hile we can find a wide literature about the application of game theory to auctions, there is very little about its possible useto price decisions of firms operating in the business to consumermarket. This is probably due to the difficult application of gametheory in scenarios including a great number of players.An attempt to use game theory for pricing is that of Rao andShakun (1972), which developed a quasi-game theoretic modelfor price fixing model for the introduction of a new product.They used the concept of “acceptable interval of prices” (Gabor& Granger, 1966) and several postulates.They hypothesized the existence of two groups of consumers: one believing that price is an indicator of quality,thus they are prone to pay for the most expensive product; and asecond group of consumers which believe that all products in themarket have an acceptable level of quality, as a consequencethey buy the cheapest product. They derived the probabilities of purchase for each product as a function of price for two products   and for three products. Then they developed their “quasi gametheoretic model” (In this model the authors regard informationas not complete and they apply game theory thinking withoutconsidering complete information) considering the possiblebehaviours of the two groups of consumers for each of the twoor three products. From this they calculated the optimal price forthe introduction of a new product for each of the consumer’sbehaviour options.There are several other studies about the application of game theory considering price as a quality indicator. When it is  Gandolfo Dominici/ Elixir Marketing 36 (2011) 3524-3528    3526  not possible for the consumer to judge quality before thepurchase the only factors on which consumer can establish his   choice are price( Kreps & Wilson, 1982), reputation of the seller(Milgrom & Roberts,1986) or both of them (Bandyopadhyay etal. 2001).Milgrom and Roberts (1986) created a model with severalparameters. They set cost of production of high quality productsbeside to the cost of production of low quality products and theyconsidering also the level of advertising expenditure. Accordingto this model, for some of the levels of cost, price is a goodsignal of quality, while for other levels of cost (as for examplewhen costs are the same for both high quality and low qualityproducts) it is necessary to budget a certain level of advertingexpenditure to obtain higher prices.Bandyopadhyay et al. (2001) highlighted that price can bean imperfect indicator of the quality of an experiential good, if supported by producer’s reputation.Argoneto (2007) analysed the case of the music band Radioheadwho in 2007 gave access to download their new album fromInternet at a price chose by the customers; the consumer couldchoose how much to pay to download the album, could alsodecide to pay nothing. A rational player would not pay todownload the album, but results showed that consumers are notrational. About 50% of consumers decided to pay and theaverage price payed for the download was of   € 6.00. Consumers   do not follow the axiom of homo oeconomicus. Game theory and advertising T   here are quite a few outdated models that attempt todetermine the optimal advertising budget using game theory.Montgomery and Urban (1969) described five models of    advertising budget allocation based on the assumption the bestway to allocate advertising budget was to apply game theory towhat other competitors do. Shakun (1965) used a mathematicalapproach creating an exponential function to sales response toadvertising, which is similar to that of Vidale and Wolfe (1957).Shubik and Leviatan (1980) proposed a matrix for advertisingexpenditure decisions as in figure 1. Figure 1. Decision matrix for advertising expenditure low expenditurehigh expenditure Payoff  1 10Payoff  1 6Payoff  2 10Payoff  2 12Payoff  1 12Payoff  1 7Payoff  2 6Payoff  2 7 Source: Shubik e Levitan (1980) p.46 Player 2    P   l  a  y  e  r   1   l  o  w  e  x  p  e  n   d   i   t  u  r  e   h   i  g   h  e  x  p  e  n   d   i   t  u  r  e   In the matrix in figure 1, the payoffs can be considered asgains in term of short term profit for each firm. The matrixshows that if only one firm spends a lot in advertising, it obtainsan advantage on the other firm, but if both firms spend a lot boththe payoffs decrease. The profit is maximized if both firmsdecide to cooperate. According to the authors if the equilibriumis known it is possible to think backwards to determine thebehavioral assumptions of the players.But in the real world firms do not need to think backward! Game theory and product decisions According to Weiner (2002), theoretically, game theory canbe applied to decisions about the introduction of new products. Itcan be useful to understand if there is a first mover advantage,the possible moves of competitors about new products and totake decisions about defensive strategies.In spite of this theoretic possibility there is very littleliterature about new product decisions using game theory.Among the best studies in this field there are those of Mitchell &Hustad (1981) and Kaiser (2001).Kaiser (2001) states that product innovation increasesconsumer’s utility but is effective only if the investments of theinnovating firm in marketing are conspicuous so that thecommunication about the new product can reach the target of consumers. He applies a game based on Cournot’s oligopoly forthe innovation expenditure and demonstrates that both thetendency to marketing activity for new products and that tointroduction of new products decrease when the number of competitors and the level of interchangeability of productsincrease.The most prolific research field on game theory and productis that of “patents” (Muto, 1987; Gallini & Winter, 1985;Fudenberg & Triola, 1987; Park, 1987), which is of minorinterest for marketing management. Game theory and distribution We can find several studies utilizing non-cooperative gametheory to analyze the relations among producers and dealersalong distribution channels. The approach used is usually the“leader-follower” (Weitz & Wang, 2004). Other studiesapproach the problem of competition along distribution channeland demonstrate that the double marginalization is reduced bythe increase of competition at retailer level (McGuire & Staelin,1983; Chouglan, 1985). Chouglan (1985) approaches theproblem of channel choice in a duopolistic market and showshow the integration of distribution function along thedistribution channel creates higher price competition and lowerprices compared to the utilization of dealers.Starting from these results Choi (1991) analyzes a distributionchannel structure with two producers and one retailer sellingboth products. Choi approaches the problem using three kinds of non-cooperative games (two with Stackelberg duopoly and onewith Nash’s equilibrium) and shows how the results depend bythe shape of demand function:In case of linear demand function: o   It is convenient for the producer to have more exclusiveretailers; o   The retailer is stimulated to deal with several producers; o   It is convenient for all the operators in the distribution channeland for consumers that none dominates the market; o   In case of symmetrical reduction of production costs, theretailer gains more than the producer; o   If products are less differentiated, prices grow. −   In case of non linear demand function: o   It is convenient for all the operators in the distribution channelthat producers have exclusive retailers; o   When product’s differentiation raises, if producer uses anexclusive retailer his profit increases, if retailers are notexclusive profit declines.Other studies which analyze the behavior of operators indistribution channels are those of Lee and Stalin (1997) thatfocus on strategic interaction more than on linearity of demand  Gandolfo Dominici/ Elixir Marketing 36 (2011) 3524-3528    3527  function and Jeuland and Shugan (1983) approaching theproblem with non-cooperative games. A recent study of Esmaeili et al. (2009) approaches the problem of buyer – sellerrelations extending the field of study to the whole supply chainusing both cooperative and non-cooperative approaches.The research on this field followed the evolution of marketing.The focus shifted from “leader-follower” models, where retailerwhere prone to producers choices towards new model describingequal relations and coordination between producers andretailers. Conclusions There are several possible applications of game theory formarketing management decisions, but they are all limited tospecific cases. Game theory can be of some utility in marketingdecisions when the number of players is little. This is a biglimitation which excludes it effective application to business toconsumer markets. Moreover game theory cannot be used toprovide precise solutions to marketing problems for thefollowing reasons: −   In most cases it cannot provide a single answer; −   The reality of the market and of the behavior of its playersimplies a number of possible strategic solution that is too high tobe summarized in a game; −   The rationality postulated in game theory has no place in themarket.The bias of rationality is probably the main limit of gametheory for marketing. The whole marketing theory is based onthe statement that intangible and irrational aspects are prominentfor consumers’ choice. In marketing the consumer doesn’tchoose by considering tangible costs and benefits but thinkingand choosing according to the emotional and symbolic value of the goods.Emotional and symbolic issues of the purchase process canhardly be harmonized with neoclassical rationality of the homooeconomicus on which game theory id founded.In a famous experiment, Jensen et al. (2007) applied gametheory ( ultimatum game ) to chimpanzees and pointed out howthese primates act in a perfectly rational way according to thepostulates of  homo oeconomicus . Chimpanzees are rational,human beings are not, chimpanzees would not pay forsomething they can have for free, men do (as for the album of Radiohead). This is because evolving the homo sapiens acquiredthe aptitude to empathy and to abstraction, which differentiateshis behaviour from that of monkeys; consumers are homosapiens and not chimpanzees.This explains also why, although game theory exists sincemore than 60 years, it didn’t raise much interest for marketingresearchers and professionals.Nevertheless, if we keep in mind its limits, it is possible touse game theory in specific areas for marketing decisions. References Argoneto P.  I Radiohead, l’arcobaleno e il piede sinistro di Dio.Saggio sulla teoria dei giochi e le sue applicazioni . 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