a —retailer’s local advertising level; q—manufacturer’s national brand name
investment t —fraction of total local advertising
expenditures which manufacturer shares
11
3.Stackelberg equilibrium
We first solve for the reaction function in the
second stage of the game:
r is a concave function of a
Setting
to ato
the first be zero:
13
3.Stackelberg equilibrium
Next the optimal value of q and t are
determined by maximizing the manufacturer’s profit subject to the constraint imposed by Eq(5).Hence,the manufacturer’s problem can be formulated as
14
3.Stackelberg equilibrium
Substituting into the objective yields the following problem (9):
15
3.Stackelberg equilibrium
Solving Eq(9),and substituting the outcome into Eq(5),we have the unique equilibrium point of the two-stage game:
16
3.Stackelberg equilibrium
Proposition 1:If
m 1 r
(1)the manufacturer offers positi retailer ,otherwise he will
offer nothing;
21
4.Nash equilibrium
In this section,we relax the leader-follower relationship and assume a symmetric relationship between the manufacturer and the retailer. The manufacturer and the retailer simultaneously and noncooperatively maximize their profits with respect to any possible strategies set by the other member .
22
4.Nash equilibrium
Hence,the manufacturer’s optimal problem is:
The retailer’s optimal problem is:
23
4.Nash equilibrium
It is obvious that the manufacturer’s
The relationship is that of an employer and an employee!
20
4.Nash equilibrium
Recent studies in marketing have demonstrated that in many industries retailers have increased their power relative to manufacturers over the past two decades. Especially,for durable goods such as appliances and automobiles, the retailer has more influence on the consumer’s purchase decision.
for the retailer; (3)the increase of
such that
m 1 r
will cause an increase in the sales and then
will give the retailer incentive to do local
advertising without manufacturer’s
This paper is intended to discuss the relationship between co-op advertising and efficiency of manufacturer- retailer transactions.
6
1.Introduction
Three co-op advertising model: 1.a leader-follower noncooperative
game:manufacturer is a leader; 2.a noncooperative simultaneous move
game; 3.a cooperative game.
7
2.Assumptions
S—retailer’s sales response volume function of product;
Expected sales response volume:
S (a ,q ) a q 9
2.Assumptions
The manufacturer’s,retailer’s,system’s expected profit functions are as follows:
Note: “cq” should be “q” 10
3.Stackelberg equilibrium
We model the relationship between the manufacturer and the retailer as a sequential noncooperative game with the manufacturer as the leader and the retailer as the follower.
(2)
17
3.Stackelberg equilibrium
Three implications: (1) if retailer’s marginal profit is high,retailer has strong incentive to spend money in local advertising to stimulate the sales, even though the manufacturer only shares a small fraction of local advertising expenditures or doesn’t help;
24
4.Nash equilibrium
We then obtain the unique Nash equilibrium advertising scheme as follows:
25
4.Nash equilibrium
Three implications: (1)since the manufacturer’s allowance policies does not influence the sales response volume function, independent actions taken by both members simultaneously make no impact of the sharing policies on the determination of the
8
2.Assumptions
m maneu srdf' o am c llta a urrp rgrionfa
rreta sd iloem lrl'a arrp grio nf a
One-period sales response volume function:
S(a,q) a q
~
~
0, ,, 0,E() 0
The main reason for a manufacturer to use co-op advertising is to strengthen the image of the brand and to motivate immediate sales at retailer level.
financial help.
19
3.Stackelberg equilibrium
In this game,the manufacturer holds extreme power and has almost complete control over the behavior of the retailer.
18
3.Stackelberg equilibrium
(2)the higher (the lower) the retailer’s
(manufacturer’s) marginal profit,the lower
the manufacturer’s advertising allowance
5
1.Introduction
Most studies to date on vertical co-op advertising have focused on a relationship where the manufacturer is a leader and the retailer is a follower.