Author By : ROBERTO CELLINI and TIZIANA CUCCIA University of Catania, Faculty of Economics Corso Italia, 55 – 95129 Catania (Italy) Published in 2012

1. Artist and art dealer as a marketing channel*
ROBERTO CELLINI and TIZIANA CUCCIA
University of Catania, Faculty of Economics
Corso Italia, 55 – 95129 Catania (Italy)
tel. +39-0957537728, fax +39-0957537710
e-mail: cellini@unict.it, cucciati@unict.it
Abstract: We study the relationship between artist and art dealer, interpreting them as
the members of a marketing channel, as defined by the industrial organization and
marketing science literature. The results for both parties depend on the individual efforts
of each of them. Uncoordinated efforts lead to inefficient outcome. The efficiency of
different institutional settings and agreements are studied. Different ways to reach
efficient outcome are suggested and discussed, with specific reference to the case of
visual arts.
Keywords: Marketing channel, effort, mechanism design.
JEL Codes: Z-10, L-83, L-13.
RUNNING TITLE:
Artist and art dealer as a marketing channel
CORRESPONDING AUTHOR:
Roberto Cellini
University of Catania, Dept. of Economics and Business
Corso Italia 55 – 95129 Catania – Italy;
e-mail cellini@unict.it
* We are indebt to Guido Candela, Isidoro Mazza, and Antonello E. Scorcu for helpful
comments. The usual disclaimer applies.
1
Electronic copy available at: http://ssrn.com/abstract=2016860

2. Artist and art dealer as a marketing channel
In economics and marketing science literature, marketing channel denotes the
set of actors, practices and activities, to transfer goods from the point of production to
the point of consumption. In the simplest case, a particular product is made by a
manufacturer, and delivered to a retailer who sells it in the final market. Manufacturer
and retailer are the two members of the marketing channel. If they act uncoordinatedly,
channel inefficiencies arise, in the sense that the outcomes of the channel members are
lower than they could be under coordination. This inefficiency is due to strategic
behaviour in the presence of interdependence between manufacturer and retailer.
Available literature suggests different ways to overcome inefficiency, using tools of
industrial organization and marketing practice.
Here, we shall study the relations between artist and art dealer, interpreting them
as the members of a marketing channel. Figurative artist and art gallery manager are our
main reference example. Singer (or performing art company like theatre company or
orchestra) and event organizer may represent different specific examples of marketing
channel in artistic fields. All these cases in arts share some features with the case of a
manufacturer and a retailer of industrial production: the success of artistic production
depends on the artistic effort of the “creator” (the manufacturer), as well as on the
promotion effort made by the art gallery manager or by the live event organizer (the
retailer, or the dealer) –in perfect symmetry with the success of industrial production
whose revenues depend on manufacturer’s and retailer’s course of actions.
Usually, the behaviours of each member of a marketing channel affect the final
sales, and hence the outcome for manufacturer and retailer. Industrial organization and
marketing studies and practice analyse the outcome of different institutional
arrangements between the channel members, and make suggestions of specific
arrangements, to improve the results of the channel. In the real world, a variety of cases
can be observed: marketing channel members can take their decisions simultaneously or
sequentially, with different roles of leader and follower. Either of the channel members
may take the role of leader (that is, the first-mover) and may set incentive schemes to
2
1. Introduction
Electronic copy available at: http://ssrn.com/abstract=2016860

3. lead the follower to specific actions. Under particular cases, peculiar objective function
can be the true goal of the channel members, and sometimes altruistic behaviours are
observed: a channel member may aim at the maximum joint-result rather than at the
maximum individual profit.
At the same time, the artistic production presents peculiarities with respect to
industrial production. For instance, the production of arts provides the artist with utility
per se, and artist enjoys welfare from her own fame, apart from the economic results.
Even art dealers’ behaviours are sometimes characterized by art for art’s sake.
Furthermore, competition takes place in arts’ market under peculiar forms, and the role
of price competition or quantity competition needs to be specifically qualified as
compared to “standard industrial goods”. More importantly, peculiar arrangements are
observed between producer and retailer, in artistic fields: perhaps the most prominent
one is that sales sharing is the rule, rather than profit sharing, as documented by a large
body of evidence (see, e.g., Caves, 2000, specifically p. 41, or Velthius, 2011a,b).
Again, mechanism designs typical for industrial goods, like quantity discounting
schemes, are clearly inappropriate (if not impossible) in the case of arts.
Our goal is to provide a formal model, consistent with peculiarities of arts, but
inspired from industrial organization and marketing science literature, to show that the
marketing channel inefficiency is a feature also in the case of the arts, and –more
interestingly– to study the efficiency property of different arrangements, commonly
observed in the real world of arts. Finally, we aim to suggest mechanisms to overcome
the marketing channel inefficiency. We believe that the consideration of different
approaches, developed by industrial organization and marketing science, applied to the
study of the relation between artist and art dealer, may be fruitful, under both a
perspective of description of observed actions, and a normative point of view.
2. Insights from different research lines
In this paper, we bring together two research lines. On the one side, we consider
the marketing channel literature, developed by both marketing and economic literature.
Jeuland and Shugan (1982) can be considered the seminal model, even if several
3

4. previous contributions could be listed, containing similar ideas (e.g., Bucklin, 1966).
The models within this research line consider the relation between a manufacturer of a
specific brand, and a retailer. In the simplest version, only one manufacturer interacts
with one retailer. A market demand function is assumed, depending on retail price, set
by the retailer, and other characteristics of the good related to choices (and efforts)
made by the manufacturer. Advertising can play some role. Thus, the choices of both
manufacturer and retailer affect the outcome of both. Early models focus on pricing
problems (Jeuland and Shugan, 1982, Moorthy, 1987). Subsequent contributions
underline that non-price aspects are equally important (e.g., Bergen and John, 1997). In
the absence of coordination, inefficiency arises, due to opportunistic behaviours.
Coordination hardly may emerge endogenously, because the best reply of each channel
member to the cooperative choice of the counterpart is not the cooperative choice: a
typical prisoner dilemma occurs. It is true that, in the presence of repeated transactions,
cooperation could emerge tacitly, along the lines of the Folk-Theorem story, but the real
world documents that explicit contracts are often signed, introducing explicit
mechanisms that clearly aim to mitigate inefficiency. A number of mechanisms can be
observed, and studied under a theoretical point of view: we may mention a variety of
pricing schemes, including quantity discounts, quantity surcharges, two-part tariffs;
specific rules of profit sharing among the channel members; advertising allowances, or
subsidies to promotion costs. Jorgensen and Zaccour (1999, 2002) deal with the
dynamic optimal problem of a marketing channel, and present some models taking a
differential game perspective. Dynamic mechanism designs are proposed, based on
incentive schemes regarding price setting or advertising efforts (see also Jorgensen,
Sigue and Zaccour, 2000, 2001; Jorgensen, Taboubi and Zaccour, 2006). It is worth
mentioning that the marketing channel can be also interpreted as a particular case of
team production (à la Alchian and Demsetz, 1972), in which there is no firm owner, but
the team members share the joint result deriving from their personal skills and efforts:
Levin and Tadelis (2005) and Kaya and Vereshchagina (2009) study how the properties
of the productive process determine the optimal contract design, and the optimal sorting
patterns among many agents. The conclusions of these lines of research can be
summarised, by stating that a number of price- and non-price mechanisms are available
4

5. to channel members, to overcome inefficient outcomes due to opportunistic behaviours,
both in static and in dynamic framework.
On the other hand, cultural economics shows that artistic production shares a lot
of aspects with standard industrial production, but presents at the same time important
peculiarities, so that the results developed by industrial economics can be extended to
cultural sectors with caution. Production and distribution channels are clearly present in
many artistic sectors: artists, managers, representative agents, gatekeepers and retailers
play important roles: Caves (2000), Sacco (1998), Throsbe (1994a), just to mention a
few, have studied the relations among the subjects in production and distribution
channel of artistic productions; Velthuis (2011a) reviews the specific literature on art
dealers.
Here, it is particularly important what Caves (2000, Ch. 2) or Velthius (2011b)
report: they describe the main aspects of the relationship between artists and dealers,
with particular reference to the visual arts sector.1 Common features of observed
contracts or arrangements in arts’ marketing channels are:
- Artist and dealer typically make informal agreements concerning their “efforts”;
formal contracts are generally avoided (even if formal contract are more and more
frequent in recent times);
- Artist’s effort can hardly be defined, but number and type of works proposed are
objects of the agreements, and can be interpreted as proxy variables for artistic
effort; dealer’s efforts mean advertising and information campaigns, organisation of
meetings or events, and other possible forms of promotion of artistic production;
- In agreements or contracts between artist and dealer, the rule is the gross revenue
5
sharing, rather than the profit sharing;
- Sometimes artists are called to participate to the financial efforts for promotion
campaign;
- Fixed payments from dealer to artist are rarely observed (such cases were more
frequent in past times and for well-known artists).
All these points will be ingredients of the model we are going to present. As far
as we know, a formal model borrowing from the marketing channel literature has not jet
proposed, with specific reference to the arts, and we aim at filling this gap.

6. It is worth noticing that the focus on the channel of creation and distribution of
artistic goods leads us to disregard the secondary or resale markets of arts, and the
dynamics of price in such market segments. Hutter et al. (2007) or Shonfeld and
Reinstaller (2007), among many others, stress that the determinants of prices in
secondary markets are different, as compared to primary markets. However, the
research line on the evolution of prices in secondary markets is immaterial to our
present study, even if -admittedly- expected future prices of artistic goods are relevant
on current demand, so that a cautionary note has to be posed, as long as there is no role
for expectations on future prices, in our present model.
6
3. The basics of the model
We present a model, where an artist produces a good, that is sold to final consumers by
an art dealer.
The artist (A) chooses her artistic effort a; her fame, g, is a positive function of
the artistic effort, and some exogenous variable, z0, according to the simple linear
function , 0. 0 g = z +αa α > Artistic efforts entail a cost for the artist, assumed to be
quadratic: = 2 , > 0. A A A c u a u
The retailer (P), that is, the art dealer in this specific case (let us think of an art
gallery manager, for instance), makes a promotional effort, p, to promote the sales of the
artistic production manufactured by A. Promotion efforts entail a quadratic cost for the
retailer, = 2 , > 0. P P p c u p u
The final sales (S) of the artistic production depend on the retailer’s efforts, and
the artist’s fame, according to a function like S =θ + β ⋅ p ⋅ g , withθ ≥ 0, β > 0 . (This
formulation is clearly inspired by Jorgensen, Tabouti and, Zaccour, 2006). We assume
that the fraction π (with 0 ≤π ≤ 1) of the revenues from the sales goes to the artist, and
the fraction (1−π ) goes to the dealer. Clearly, the larger is π , the larger the share of
sales accruing to the artist. At the moment, π is an exogenous parameter; in the real
world, π is a contracted variable, depending on the relative fame of artist and dealer.
Note also that the hypothesis that sale-share are contracted, rather than profit-share is

7. typical to the arts sector (see Caves, 2000). We finally assume that the art dealer cares
only on his net result, R (1 )S u p2 P P = −π − , while the artist cares also on his fame, and
her net result is: R S u a g A A =π − 2 +δ ; the positive parameter δ describes the
importance that her own fame plays into the net result perceived by artist: the presence
of such a term in the utility function of artist is common in cultural economics models,
consistent with the fact that artists care not only on the monetary outcome of their
activity, but also on non-monetary, intangible recognition, like fame (Frey, 1997; see
also Throsby, 1994a, 1994b and, more recent, the formal model of Cuccia and Cellini,
2009).
Without loss of generality, and for the sake of simplicity, we will develop the
model under the following parameter assumptions: = 0, = = 1/ 2, = = 1/ 2 A P θ α β u u ,
so that the model can be summarised by the following equations:
2 a R gp g a p z a A − 
1 1
2
=π ⋅ +δ − =  π ⋅ +δ

R g p p 2 1 p z 1
a − p P 2
7
1
[1] g z a
2
0 = +
1
[2] S = ⋅ g ⋅ p
2
[3]
1
2 2
2
2 2

 + 
0


(1 ) 1
[4] ( )
2 2
1
2 2
2
0

= −π ⋅ ⋅ − = −π  +
Artist aims at maximising [3], setting her choice variable a, while the art dealer aims at
maximising [4], setting his choice variable p. However, the result of each player (i.e.,
marketing channel member) depends also on the choice of the other player, so that a
strategic interdependence situation is operative. The specific choices of players will
depend on the “institutional framework” at work. For instance, we could imagine that
the choices will be set simultaneously and independently by artist and dealer, or we
could imagine that the choices are independent but sequential, with the possibility that
the first-mover is the artist or the dealer. Again, we could imagine that artist and dealer
agree on their choices, aiming at the joint result maximization. All these different
settings will be analysed in what follows. From the point of view of the realism of

8. different settings, we note that it would be too easy (and hence false) to say that in the
real world, firstly the artist sets her efforts, and then the dealer sets his promotion
efforts: this situation clearly may happen, and perhaps it is the rule in most cases, but it
is far from true that this arrangement covers all cases: in some cases –for instance, in
the performing art shows– advertising campaign for a show starts before (or during) the
show is under construction. The different institutional settings provide different
ordering of individual and aggregate results for the channel members.
8
4. Results
4.1. The simultaneous game
Let us imagine that artist and dealer set their decision simultaneously. We denote this
setting as the “Cournot setting”, borrowing the label from the oligopoly theory. The
artist maximizes objective function [3], with respect to a, and derives the following
optimal rule, which represents her reaction function:
[5]
+ ⋅
a 2 p
4
=
δ π
The dealer maximizes function [4], with respect to p, and derives the following reaction
function:
[6]
2(1 ) (1 ) 0 z a
4
p
− + − ⋅
=
π π
The optimal effort of the artist depends positively on the promotional effort of the
dealer, and the promotional effort of the dealer is a positive function of the artistic effort
of the artist: the reaction functions are positively sloped, so that the choice variables are
strategic complements, in the terminology of oligopoly theory. The Nash equilibrium is:

9. δ z π π a COU
2[ 4 + (1 −
)]
δ z π π δ z π π R COU
A
2[4 + (1 − )][4 + ( − +
32]
9
[7]
16
2
0
− +
=
π π
[8]
z δ π
2(4 )(1 )
16
0
− +
2
+ −
=
π π
pCOU
where the superscript COU stays for “Cournot”, i.e., simultaneous choice setting; note
that both variables in equilibrium are positive, and increasing in δ and z0;
correspondingly, the maximum outcomes reached by artist and dealer, in equilibrium,
are respectively:
[9] 2 2
2
0 0
( − +
16)
=
π π
π z δ R COU
P
2(1 − ) (4 +
)
[10] 2 2
2
0
2
( − +
16)
=
π π
The result obtained by the dealer is strictly decreasing inπ (the higher the revenue share
for the artist, the lower the equilibrium result for the dealer), while the result obtained
by the artist is increasing in π for 0<π <½ , reaches its maximum in π =½ and is then
decreasing over ½<π <1: for high levels of π , further increases of this share parameter
lead the dealer to lower his effort to such an extent, that the artist’s result decreases.
4.2. The sequential games
We firstly consider the case in which the dealer sets his promotional effort after having
observed the artistic effort chosen by the artist: in this case we are in a sequential game,
à la Stackelberg, where the artist is the first-mover (or leader) and the dealer is the
second-mover (follower). The leader can anticipate the choice of the follower, and can
insert such a reaction function into her objective function: this amounts to saying that
the artist-leader maximizes her objective function [3], considering the constraint
represented by the reaction function of the dealer-follower [6]. The solution of the
leader’s problem provides:

10. z π − π + δz +
δ
10
[11]
δ z π π
2[2 + (1 −
)]
8
2
0
− +
=
π π
aSTAL
.
(where the superscript STAL stays for “Stackelberg, with artist leading”), and the choice
of the dealer-follower is:
[12]
π z δ
(1 − )(4 +
)
8
2
0
− +
=
π π
pSTAL
The efforts exerted by both the artist and the dealer are larger than the respective efforts
in the simultaneous choice case. Thus, it is not surprising that the individual results
obtained in equilibrium by both parties are larger in this Stackelberg case, as compared
to the Cournot equilibrium. Equilibrium results, when the artist is the first-mover, are:
[13]
8
2 (1 ) 8
2
2
0
2
0
− +
=
π π
R STAL
A
π z δ R STAL
P
(1 − ) (4 +
)
[14] 2 2
2
0
2
2( − +
8)
=
π π
The opposite case of sequential moving, in which the dealer is the first-mover, and the
artist follows, is conceivable as well. In some cases, the promotion campaigns for shows
or specific events start before the preparation of the show is finished, so that it is true
that the artistic effort is set after the promotion effort is made. In such a case, the dealer
is the leader, and he can anticipate the choice of the artist-follower. Analytically, the
dealer-leader maximizes his objective function [4] under the constraint represented by
the reaction function of the artist [5]. The optimal choice of the dealer turns out to be:
[15]
π z δ
(1 − )(4 +
)
8
2
0
− +
=
π π
pSTAF

11. where superscript STAF stays for “Stackelberg with artist following”, and the reaction
of the artist, in equilibrium is
δ π π z π π aSTAF
( − + 16) + 4 (1 −
)
0
z π π δ π π δ π π z π π R STAF
A
[4 (3 − 3 + 32) + ( − + 16)][ ( − + 16) + 4 (1 −
)]
11
[16]
2
4( 8)
2
− +
=
π π
The artist is led to make an effort, as second-mover, larger than the effort set as a first-mover.
As far as the art dealer is concerned, his effort, as the leader of the Stackelberg
game, is equal to the effort made as the follower of the Stackelberg game.
By straight substitutions into the objective functions, we obtain the results of
both parts in equilibrium, when the dealer leads and the artist follows:
[17]
2
32( 8)
0
2 2 2
0
− +
=
π π
π z δ R STAF
P
(1 − ) (4 +
)
[18] 2 2
2
0
2
16( − +
8)
=
π π
By simple comparisons, we can state that, for any π (with 0 <π < 1, that is excluding
the limit cases),2 the following relations hold:
;
;
;
;
COU STAL STAF
a < a <
a
COU STAL STAF
STAl
P
p < p =
p
R < R <
R
STAF
P
COU
P
STAF
A
STAL
A
COU
A
R < R <
R
This means that each player prefers any sequential settings to the simultaneous choice
setting, and –in the sequential settings– each of the players prefers to be the follower
rather than the leader. This ordering of individual outcomes is consistent with analogous
results obtained in games in which choice variables are strategic complements.

12. 4.3. The cooperative setting (joint result)
If channel members aim at the maximum joint result, they face the following problem:
[ 2 2 ]
Max R R R 1 z a p a p A P
(2 )(2 ) 2 2
4
, 0
12
JOINT
a p
= + = + δ + − −
We could label this setting as the coordinated setting (or the cartel setting, borrowing
from oligopoly theory). From the first order conditions we obtain:
[19]
2(4 ) 0 z
p JOINT +
15
=
δ
[20]
2( 4 ) 0 z
a JOINT +
15
=
δ
Some comments are in order. First, the efforts of each part are the highest, with
respect to all considered settings. This means that the maximum joint result requires the
highest efforts by both parts. Second, both the Cournot setting and the Stackelberg
settings provide the players with individual equilibrium results whose sum is smaller as
compared to the sum of results they can obtain in the coordinated setting. In other
words, strategic interaction leads to inefficient outcomes; this result is well known by
marketing channel literature. Third, parameter π disappears from the problem of the
coordinated setting, consistently with the fact that π captures an aspect related to the
division of a common result, that is immaterial to the maximum of the common result in
itself.
Of course, the problem of the division of the common result remains open, after
the coordinated choices are set. As far as the division of result is concerned, we assume
that the artist obtains the share π of the sales, and the dealer obtains the complement
share 1−π , while the term δa goes entirely to the artist; needless to say, this is only one
–rather obvious– assumption concerning the division of the “cartel result”. Under the
above mentioned rule of sharing, the dealer and the artist obtain the following
individual results:

13. [21] 2 [ (32 1) (7 )(16 2 2
)]
2
0 R JOINT = z π − + +π δz + δ
A
R JOINT = 2 − π z +δ
P
13
225
0
[22] 2
0 (1 2 )(4 )
225
and hence, under the above mentioned rule of sharing, the cartel situation provides the
artist a higher result with respect to the Cournot situation for any π >0.1350, and
provides the dealer with a higher result as compared to the Cournot situation for any
π <0.24085. Similar comparisons can be readily made with respect to the Stackelberg
settings. In any case, apart from the cartel situation, any other setting is Pareto-inefficient
– in the sense that a different situation can be found, with appropriate sharing
of the result, where each player can be better off.
As is well-known, the choices associated with the efficient outcome do not
represent a Nash equilibrium, at least in the one-shot game. This amounts to saying that
informal or non-binding agreements concerning socially efficient levels of individual
efforts are not self-enforcing. In Section 5 we study how it is possible to replicate the
efficient outcome, on the basis of more-complex self-enforcing agreements. Eventually,
we will discuss the degree of efficiency of different types agreements, observed in the
real world of arts’ markets. Remember that formal binding contracts (ideally replicating
the efficient outcome) are rarely observed in the filed of arts, also because their
enforcement is difficult, due to the fact that relevant key variables (like the artistic
efforts) are hardly definable and measurable.
5. Replication of efficient outcome
The available literature on marketing channel has suggested several contract designs,
able to lead the parts to replicate the choices associated to the efficient outcome. In the
cases of industrial goods, for instance, specific profit share designs, advertising
allowances, quantity discount schemes, are possible solutions: it is a well-established

14. result that a multiplicity of effective solutions exist, to overcome the inefficiency of
decentralised decisions in marketing channel situations. In order to make such
arrangements self-enforcing, it is necessary to assure that each part obtains a larger
result, as compared to the individual result obtained in uncoordinated setting.
Here we focus on the case at hand and we limit to propose two different
solutions: the first one has a theoretical interest, but it is hardly implementable in the
real world; it is appropriate for the context in which choices are set simultaneously. The
second one is appropriate when the artist set her artistic efforts firstly, and the dealer
follows –a situation more frequently observed in the real world; for this reason we will
spend more attention on it.
The relevant question can be posed specifically as follows: How is it possible to
lead the artist to set her effort at the efficient level given by [20], and the dealer to set
his effort at the efficient level [19]?
5.1. Linear subsidies in the simultaneous choice setting
Consider the case in which artist and art dealer set their choices simultaneously.
Assume that artist has to pay a subsidy ψ to the dealer for each unit of promotional
effort he makes; at the same time, the dealer has to pay a subsidy ω to the artist for
each unit of artistic effort she makes. The problems of artist and dealer can be written,
respectively, as follows
1 2
[23] Max R =  ⋅ p +

z 1
a a p a a A
π 
δ  + 
− − ψ + ω 1 
2
14


2 2
2
0
[24] Max R ( )p z a p p a p P
1 1
2
= −  +
ω ψ π − + − 

2 2
0
From the first order conditions, the following reaction functions can be easily derived:
π ⋅ + 2δ + 4ω
[25]
4
a = p

15. (1 ) 2 (1 ) 4 0 −π ⋅ + −π + ψ
= a z
p
πψ δ ω π π z
2[2( + 2 + 4 ) + (1 −
) ]
z δ π ψ ω π
2[(4 + )(1 − ) + 2(4 + (1 −
))]
15
[26]
4
The corresponding equilibrium efforts are:
[27]
16
2
0
− +
=
π π
a
[28]
16
2
0
− +
=
π π
p
Appropriate levels of ψ and ω can be computed, to render the effort levels [27] and
[28] equal to the efficient levels [20] and [19], respectively; the solution is:
[29]
2 (4 ) 0 π δ
15
ψ
+
= z
[30]
= z
(1 )(4 ) 0 π δ
30
ω
− +
The subsidy levels given by [29] and [30] lead each member of the channel to set the
individual choice that replicates the efficient outcome of the maximum joint result. Note
that the higher is the share for the artist, the higher the amount of unit subsidy that she
has to give to the dealer. By appropriate substitutions, it is possible to compute the
individual results obtained by channel members under such arrangement, and to
compare them with the result obtained in the uncoordinated Cournot setting. It is
immediate to verify that only over a limited range of parameter configuration, each
member receives a larger outcome as compared to the uncoordinated setting; outside
that range, appropriate transfer are necessary to make the socially efficient arrangement
convenient even for each members under a strictly individualistic point of view.
It is also interesting to note that: (a) in the limiting case where π = 0 , the
efficient levels of unit subsidies become ψ = 0 and (4 ) / 30 0 ω = z +δ : this arrangement
describes a situation in which all revenues from sales go to the dealer, but he commits to
give the artist a subsidy for her artistic effort; (b) in the limiting case where π = 1, the

16. efficient outcome is reproduced by the subsidy scheme ω = 0 , 2(4 ) /15 0 ψ = z +δ ,
which means that all revenues from sales go to the artist, but she commits to give the
dealer appropriate subsidy for each unit of promotional effort of his. Also in these
limiting cases, the efficient solution is reproduced, but appropriate lump-sum transfer is
necessary to make the arrangement dominant for each member also from a strictly
individualistic point of view.
The real implementation of the subsidy design in this simultaneous moving
setting, however, should require that artistic efforts are definable and measurable – a
hardly tenable assumption. One could also observe that if this mechanism design is
implementable in the real world, no reason exists why a formal contract concerning
directly the efficient levels of efforts is not implementable. The substantial obstacle to
contract enforcement in the case of arts rest on the possibility of defining and measuring
artistic efforts. Such obstacles can be avoided in the sequential setting, if artist set her
efforts firstly.
5.2. Quadratic subsidy in the Stackelberg setting, with artist leader.
Consider the case that the artist sets her artistic effort firstly, and then the art dealer sets
the promotional effort; equilibrium levels of efforts in the uncoordinated setting are
given by [11] and [12], which represent an inefficient allocation from a marketing
channel point of view.
Imagine that the artist commits herself to give a subsidy (σ p) to the dealer
(with σ ≥ 0 ), for each unit of promotional effort of his, so that the total subsidy from
artist to dealer is σ p2 . The net result of artist and dealer, under such an agreement are
respectively:
R 

=  1 π ⋅ p +
δ 
 z + 1
a − a − σ p A [31] 2
2
R 1 p z a p p P σ π + − 
16
2
0 2 2
2



1 1
2

= −  +
[32] ( ) 2
0 2 2

It is immediate to find the reaction function of the dealer:

17. π z a p
1 2 0 <
, 1
for SQS
(3 π − 1) / 2(1 + π ) 1/ 3 < π
≤
1
=
0 0 1/ 3
z for
= RSQS z z
A
2[ (1 + ) + 32 +
4 ]
π δ δ
− −
17
[33]
( )( )
2
− +
= σ
4(1 −
2 σ
)
This reaction function has to be inserted in the in the leader’s problem, and
different cases could be taken into account.
Case I (Digression). The artist aims at her own maximum, and sets σ and a
accordingly. We denote this case as the case of a selfish artist. It is easy to check that
the maximum private result for the artist requires
[34]
  
≤ π
≤
σ
for
2[ (1 ) 16 ]

+ +
π δ
[35] ;
0 1/ 3
1/ 3 1
63 2
2
2
0


≤ ≤
< ≤
− −
=
π
π
π π
a for
a
STAL
SQS
(superscript SQS stays for “selfish quadratic subsidy”). This means that the artist finds
it convenient to give a positive subsidy to the dealer only for sufficiently high levels of
π . Clearly, for 0 ≤π ≤ 1/ 3, that is, in the situation of the corner solution corresponding
to nil subsidy, optimal choices replicate the simple situation à la Stackelberg (without
subsidy) with the artist as the leader, and individual results coincide with [13] and [14].
For 1/ 3 <π ≤ 1, subsidy is positive, and individual results are:
[36] 2
2
0
2 2
0
63 2
π π
= RSQS z
P
16(1 − )(4 +
)
π δ
− −
[37] 2 2
2
0
2
(63 2 π π
)
whose sum is smaller than the cartel outcome. It is interesting to note that, for high
levels of π , it is in the interest of a selfish artist to provide the dealer with a subsidy for

18. SQS turns out to be larger than RA
2 2
2
0 RCQS = z π − + δz π + +δ π +
A ,
0 RCQS = −π z +δ
π π π z δ R RSTAL
(2 + 26 − 12 − 1)(4 +
)
CQS
A is positive only for
18
the promotional effort: RA
STAL for any π included in the
range (1/3,1].
Case II. The artist sets σ in order to lead the follower to replicate pJOINT, and
sets a=aJOINT. This case can be denoted as the case of a cartel-oriented artist (or
benevolent artist, in the sense that he takes care of the whole marketing channel). From
the dealer’s reaction function [33], it is immediate to find that p= pJOINT requires:
[38] σ =π / 2
with 0<π <1 and hence 0<σ <1/2. Correspondingly, the channel members’ net results
are:
[39] [ (16 1) 8 ( 14) ( 14)]
225
0
2
[40] [(1 )(4 )]
225
P
where superscript CQS stays for “cartel quadratic subsidy”. Of course, the sum of the
results given by [39] and [40] coincides with the efficient joint result. However, from an
individualist point of view, each channel member is ready to implement this agreement,
only if it provides a larger individual result as compared to decentralised decisions.
From the dealer’s point of view, result [40] is higher than results [14] or [37], for
any 0<π <1. This means (quite obviously) that the dealer prefers the situation in which
the artist is cartel-oriented rather than selfish.
From the artist’s point of view, we have to distinguish, according to π be larger
or smaller than 1/3.
(i) If 0 ≤π ≤1/ 3 , the result [39] is higher than result [13] only for levels of π
higher than a threshold level. More precisely,
2
225( 8)
2
0
3 2
− +
− =
π π
A

19. ( ) 2 3 26 2 12 1 0
1 f π ≡ π + π − π − > , that is, 0.07 1 π ≥π ≈ . This means that for
1/ 3 1 π ≤π ≤ , it is in the interest of a selfish artist to implement the cartel allocation.
The result that a manufacturer, under given parameter conditions, may find it
convenient to pursue the maximum of the channel is not a novelty in the marketing
channel literature (see, in a different framework, Jorgenson et al., 2006, Section 4). For
1 0 ≤π <π , in order to make the cartel choice convenient for the artist, a further lump-sum
transfer from the dealer to the artist must be required. Let τ denote such a transfer
from the dealer to the artist. If we compare the outcomes (under the quadratic subsidy
and transfer) with the case of nil subsidy, in order to make the arrangement self-enforcing,
we have to fix τ in a way such that: STAL
τ τ τ
< <
( − 2 π − 26 π + 12 π + 1)(4 +
δ
)
(1 − π )(4 π − 8 π + 68 π + 161 π + 31)(4 +
δ
)
CQS
A R +η > R and SQS
P
,
η η η
< <
2( π + 16 π − 35 π + 18)(4 +
δ
)
225(63 2 )
2(1 − π )( π + 4 π − 122 π − 2052 π + 2169)(4 +
δ
)
19
R CQS
+τ > R STAL
and R CQS
−τ > R ,
A A
P
P
which means:
[41]
2 2
2
0
4 3 2
1 2
2
2
2
0
3 2
1
450( 8)
,
225( 8)
;
− +
=
− +
=
π π
τ
π π
τ
z
z
(note that 1 τ is positive for any level of 0.07 1 π <π ≈ ).
(ii) For π included in the interval [1/3, 1], it can be easily checked that
SQS>RA
RA
CQS, and (RA
SQS+RP
SQS)<(RA
CQS+RP
CQS). Thus, a transfer (from the dealer to the
artist) has to be designed, to lead the artist (who sets σ and a) to behave in the interest
of the channel. Specifically, a lump-sum transfer η > 0 can be found, from dealer to
artist, such that SQS
A
CQS
P R −η > R . Simple computations permit to
find that the two conditions correspond to
[42]
2 2
2
0
4 3 2
1 2
2
2
2
0
3 2
1
225(63 2 )
;
π π
η
π π
η
− −
=
− −
=
z
z

20. One can interpret η as the price that the dealer has to pay to the artist, in order to lead
the artist to behave in the interest of the channel, instead of in a selfish way. In words,
the story can be told as follows. If the artist is the leader of the marketing channel, an
arrangement can be identified, which leads to the efficient outcome, and which is self-enforcing
in the sense that it is impossible to find alternative outcomes in which both
members are better off (i.e., no room for convenient deviation does exist); the
arrangement is as follows: (i) the sales are divided according to the positive fractions π
and 1−π , for artist and dealer respectively, with π >1/3; (ii) the artist gives the dealer
the subsidy σp2 = (π / 2) p2 , linked to the promotional efforts of his; (iii) the dealer
gives the artist the fixed sum 1 2 η <η <η , conditional on the fact that the artist set
a=aJOINT. Under such conditions, the artist finds it optimal to set the efficient effort
a=aJOINT, and the best reply of the dealer is p=pJOINT.
In sum, we have found that for some parameter values ( 1/ 3 1 π ≤π ≤ ), it is in the
(individualistic) interest of the artist, to behave in the interest of the cartel; outside such
a parameter range, a self-enforcing mechanism is found, able to replicate the efficient
outcome. In such a mechanism: (i) sales are shared among artist and art dealer, (ii) the
artist receives an additional fixed amount from the dealer; (iii) the artist pays the dealer
for his promotional effort. The mechanism is efficient because each member replicates
the choice associated with the joint-maximization case, and the mechanism is self-enforcing,
because each channel member has no incentive to deviate from the efficient
20
choices.
6. Comments and concluding remarks
Here we have pointed out that artists and art dealers constitute a marketing channel, in
the sense defined by economics and marketing science literature: in several cases, for
industrial goods, a good is manufactured by a firm, and sold to a retailer which sells it in
the final market; the result for both subjects –producer and retailer, that is, the channel
members– depend on the efforts made by each of them. Like in the more general case of
team production, strategic interdependence and incomplete information generate room

21. for inefficient results, if subjects act in a uncoordinated manner, and each actor is
oriented to his/her individual maximum result. The situation in the arts’ markets is very
similar. Artist and art dealer benefit from results which depend on the efforts of both.
We have shown that the theoretical results obtained by industrial organization and
marketing science hold, by and large, for the arts markets as well. In the arts markets,
however, specific characteristics are worth taking into account.
History and the current real world document a variety of agreements between art
makers and art dealers, in different arts’ markets (visual arts, performing arts, and so
on).3 For instance, employment, direct acquisition and consignments are alternative,
possible forms of agreements in the case of visual arts; however, in current day
experience, the consignment is the most frequent form of agreement. Caves (2000,
especially Chs. 2 and 3) and Velthius (2011a,b), with particular reference to the case of
visual arts, provide a list of “typical” behaviors in the to-day relations between artists
and art dealers. These characteristics have shaped the specific model we have presented
in this paper.
First, formal contracts between artists and art dealers (especially in the cases of
painter and art gallery) are generally avoided, in real world: informal deals (and moral
obligations) are more common forms of agreements. The reasons why formal contracts
are rare can be easily understood: complete terms are difficultly stated in a contract;
monitoring activities are difficult to be conducted; litigations are expensive and
financial compensation from successful litigations nearly impossible to be obtained.
Nevertheless, in recent years, a larger use of written contracts is claimed (especially by
artists) and observed (Vinick, 1997). The absence of a large body of detailed contracts
makes a robust analysis of contracts impossible, and the comment have to focus on
episodic or anecdotic evidence.
Second, the typical agreement has the form of ‘consignment contract’: the artist
consigns her artworks to the dealer (who exhibits them), in order to be sold. The
agreement could prescribe number and type of artworks to be delivered. The dealer
receive a share of the revenues, as a counterpart of his activity of promotion. Pay in
advance and/or regular wage are very uncommon.4
Third, as a matter of fact, the role of the art dealer is more complex than just
selling the artistic items: an art dealer acts as an agent (both for the artist, and for
21

22. institutional buyers like museums or private collectors): for this reason, the assumption
that the dealer makes efforts to promote the artistic production is meaningful, in the case
of the arts, and the promotion actions in the hands of an art dealer are wider and
potentially more effective as compared to the typical actions available to a retailer in the
case of industrial goods. An art dealer is expected: to provide information to critics,
certifiers, art writers, museum curators, and media; to organize exhibitions; to provide
items for temporary exhibitions; to compose books and further editorial catalogs; to
make (traditional) advertising campaigns in journals and specialized reviews; to spend
time with prospective clients articulating the artist’s intent (Caves, 2000, p. 38): all
these activities define the dealer’s efforts. Especially in contemporary arts, we can say
the efforts of the dealer contribute to the definition of the characteristics of artistic
product.
Fourth, it is worth stressing, once again, that revenue share, rather than profit
share, is the rule. This aspect is of particular importance, since it entails that the channel
members are not reimbursed for specific expenses. Documented exceptions are rather
limited: in the case of visual arts, for instance, one can seldom observe a participation of
artist in expenses of dealer, e.g. for advertising, catalogues and framework.
Fifth, it is difficult (if not impossible) that dealer can participate to the artistic
effort exerted by the artist. Artist’s effort is hardy observable, and the observable result
of her are weakly linked to the effort (whatever “effort” could mean in artistic fields). In
observed agreements, efforts are at generally linked to the number of pieces that the
artist commits to deliver to the dealer, in a time interval.
Sixth, artists typically complain about the limited efforts of dealers, and dealers
complain about the limited efforts of artists. In the specialized newspaper Art World
News we can read: “An artist fails to deliver quality works in sufficient number. A dealer fails
to promote an artists' work. These are only two types of claims that have recently led to disputes
between artists and dealers” (Vinick,1997, p. 1).
The perceptions of each member of the marketing channel that the other member
does not exert a sufficient level of effort are really very common. The fact that these
perceptions may be well founded is supported by our present theoretical model. The
above mentioned characteristics of typical agreements between artist and dealer lead to
a situation in which each part exerts a lower amount of effort as compared to the
22

23. efficient level: this is due to the strategic interdependence. Possible agreements
concerning socially-efficient levels of individual efforts are not self-enforcing, as long
as each actor has an incentive to free-riding. Thus, in our interpretation, the true root of
inefficiency does not rest on asymmetric information (which in any case, does exist, and
explains why it is nearly impossible to sign formal binding contracts), nor in agency-type,
i.e., principal-agent relationship (which in any case could be appropriate for
describing some aspects of the relations), but simply in the team-type production
process which is relevant for artistic items, as they are sold in today markets, where
marketing channels are really relevant.
We have shown that specific designs for contracts would be able to overcome
inefficiency. Many efficient contracts are in principle possible. Reciprocal cross-subsidies
have been shown to met the efficiency condition, in a situation in which artist
and art dealer exert their efforts simultaneously. A further example has been provided,
for the case in which artist and art dealer take their decisions sequentially (with the artist
leading), and in which artist and art dealer split the revenues from sales: in such a case,
the artist may be required to participate to the promotional efforts of dealer (according
to a quadratic subsidy), and receives a lump-sum transfer; the amount of the lump-sum
transfer has to be linked to the values of the agreed revenue-share, and to the amount of
the subsidy to promotional efforts. Interestingly enough, in accordance with available
results in marketing channel literature, we have found that –under certain parameter
configuration, and specifically under given values of share according to which revenues
are split– there is no conflict between individual and collective incentive, in the sense
that it can be in the egoistic interest of a member of the channel to act in the interest of
the whole channel.
As far as we know, this type of contracts are not used in to-day arts’ market, at
least in the case of visual arts. Under this perspective, our paper may provide useful
suggestions to artists and dealers.
23

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24

25. Throsby D. (1994a), "The Production and Consumption of the Arts: A View of Cultural
Economics", Journal of Economic Literature, 32, 1-29.
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25

26. 26
NOTES
1 Caves (2000), in a different chapter, considers also the cases of writers (editorial industry) and
singers (disco industry), which we overlook in the present paper.
2 Relations in the limiting cases are trivial. For π = 0 , aCOU = aSTAL = aSTAF = δ / 2 , and
(4 ) / 8 0 pCOU = pSTAL = pSTAF = z +δ , so that the individual results coincide across the
different settings; for π =1, aCOU = aSTAL = aSTAF = δ / 2 , and pCOU = pSTAL = pSTAF = 0 , so
that also in this case individual results are the same across the considered regimes.
3 A short history of the relations between artists and dealers can be found in De Marchi and Van
Miegroet (2006, Section 4). The variety of employment status and careers of artists are dealt
with by, e.g., Menger (2006) and Alper and Wassall (2006).
4 Velthius (2011b), lists three main possible forms of agreements between artist and art dealers,
in the case of visual arts: (1) employment with stipend, (2) direct acquisition, and (3)
consignment. However, employment is not common today (exceptions are the low-tail of the
market where artists copy standardized artworks for mass markets); famous cases of
employment with fixed wage concern artists in past times: for instance, art dealer D. H.
Kahnweiler paid (young) Picasso on a regular stipend, believing him as potential well-gifted
artist; similar contracts were used by dealers Russo for Giorgio De Chirico (at the beginning of
XX century) and by L. Castelli for promising young pop-artists in New York around 1960.
Under such an agreement (also known as contrat-mecenat –see Tamperi, 2006), the artist
commits to deliver a certain number of pieces in a given period of time, and receives a fixed
salary, e.g., on monthly base; the art dealer usually keeps all the revenues from artworks’ sale.
Alternatively, under direct acquisition contract, the dealer buys artworks from the artist and
then decides when and at what price to sell them; such a system (also refereed as ‘the French
system’, since it was common in the late XIX century in France) requires large (capital and
financial) resources from the dealers, since they have to buy the artworks, and implies that the
dealer runs the risk that the economic value will be never realized; it is rare in the today world.
The largest part of today agreements base on consignment: the artist consigns her pieces to the
dealer (who exhibit them); if and when a piece is sold, artist and dealer split the revenues, on a
previously agreed terms. We have thought of this kind of agreement, in building the present
model.