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Table 1 Note: m, > mg. The parameter A measures the degree of willingness of consumers to switch to other stores if their preferred brand is not available in their preferred store. The functions L.. are boundaries for the various zones of A.

Table 1 Note: m, > mg. The parameter A measures the degree of willingness of consumers to switch to other stores if their preferred brand is not available in their preferred store. The functions L.. are boundaries for the various zones of A.

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ment parameter @. This figure is drawn based on the following observations. First, the range for the coef- ficient of brand attachment, ©, and for the functions L1, L2(A) and L2(B) is clearly [0,1], and hence we have a unit box. Secondly, it is easy to show that the assumption m, >m, makes the function L2(B) greater than L2(A) for all ©. Third, at @=0, the function L1 is infinity, while both L2(A) and L2(B) are some constants; hence, at and near @ = 0, L1 is greater than both L2(A) and L2(B). At @=1, itis easy to show that L1 < L2(A). Thus, we find that all the three functions decrease with @, L1 decreasing from infinity at @ = 0 to a value lower than L2( A) at © = 1. The point of intersection of L1 and L2( A) is @},, and that of the functions L1 and L2(B) is 0".
ment parameter @. This figure is drawn based on the following observations. First, the range for the coef- ficient of brand attachment, ©, and for the functions L1, L2(A) and L2(B) is clearly [0,1], and hence we have a unit box. Secondly, it is easy to show that the assumption m, >m, makes the function L2(B) greater than L2(A) for all ©. Third, at @=0, the function L1 is infinity, while both L2(A) and L2(B) are some constants; hence, at and near @ = 0, L1 is greater than both L2(A) and L2(B). At @=1, itis easy to show that L1 < L2(A). Thus, we find that all the three functions decrease with @, L1 decreasing from infinity at @ = 0 to a value lower than L2( A) at © = 1. The point of intersection of L1 and L2( A) is @},, and that of the functions L1 and L2(B) is 0".
In Fig. 2, we have shown the various equilibrium strategies of the manufacturers in the case of 0, > ©, and m, >m,. We will concentrate on the two areas x’-d’-d’-x’"-x’ and x”-x'”-e’-e’-x”. In the for mer, B rejecting the contract and A accepting is the Nash Equilibrium, while in the latter it is the reverse. The intuition is as follows. For a given coefficient of store switching, A, the stronger manufacturer, i.e., one with a larger value of the brand attachment parameter, © (i.e., B) is more likely to reject the contract than the weaker manufacturer (i.e., A), be- cause his customers will switch stores irrespective of the availability of the competing brand. This results in the area x’-d’-d’-x”’-x’, the extent of which de- pends on the value of the coefficient of store switch- ing, A, and on how strong the stronger manufacturer is. ‘© However, as the value of the store switching
In Fig. 2, we have shown the various equilibrium strategies of the manufacturers in the case of 0, > ©, and m, >m,. We will concentrate on the two areas x’-d’-d’-x’"-x’ and x”-x'”-e’-e’-x”. In the for mer, B rejecting the contract and A accepting is the Nash Equilibrium, while in the latter it is the reverse. The intuition is as follows. For a given coefficient of store switching, A, the stronger manufacturer, i.e., one with a larger value of the brand attachment parameter, © (i.e., B) is more likely to reject the contract than the weaker manufacturer (i.e., A), be- cause his customers will switch stores irrespective of the availability of the competing brand. This results in the area x’-d’-d’-x”’-x’, the extent of which de- pends on the value of the coefficient of store switch- ing, A, and on how strong the stronger manufacturer is. ‘© However, as the value of the store switching
where the subscript ‘acc’ refers to the manufacturer who accepts and ‘rej’ to the one who rejects the contract. Theorem 9. If the coefficient of brand attachment, @, and the coefficient of store switching, A, are such that one manufacturer rejecting the contract and the other accepting it is the Nash Equilibrium, then under the following condition the retailer’s threat will be credible:
where the subscript ‘acc’ refers to the manufacturer who accepts and ‘rej’ to the one who rejects the contract. Theorem 9. If the coefficient of brand attachment, @, and the coefficient of store switching, A, are such that one manufacturer rejecting the contract and the other accepting it is the Nash Equilibrium, then under the following condition the retailer’s threat will be credible:
Proof. Note the function L12(B) is given by the curve d-x”-h, L6 by the curve j-n, and L5 by the curve a-h in Fig. 3. The left side inequality is easily proved by equating the functions L5 and L6, and the right side inequality by equating L1 and L6. Noting that L12(B) is less than L1 by definition (see Fig. 3) we have the result.
Proof. Note the function L12(B) is given by the curve d-x”-h, L6 by the curve j-n, and L5 by the curve a-h in Fig. 3. The left side inequality is easily proved by equating the functions L5 and L6, and the right side inequality by equating L1 and L6. Noting that L12(B) is less than L1 by definition (see Fig. 3) we have the result.
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