Download Game Theory in Marketing Science: Uses and

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
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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
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(1967)) Or the
of gamemtheoretic
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