The Mini-Case “Nash Bargaining over Coffee” applies the generalized Nash product, NP = (R - dR)a (M - dM)1 - a, to bargaining between retailers and manufacturers over the price of coffee. Assume that dR = dM = 0, that a = 0.5, and that manufacturers and retailers divide up a potential combined profit of 100 depending on the price so that R = 100 - p and M = p. What price maximizes the generalized Nash product? What happens if a = 0. Explain.

Nash Bargaining over Coffee

In Britain, France, Germany, the United States, and other developed countries, many managers believe that big-box retail chains such as Walmart and Target are increasingly squeezing manufacturer margins due to the consolidation of the retail sector. To examine this belief, Draganska, Klapper, and Villas-Boas (2010) investigated how grocery store chains and ground coffee manufacturers bargain over the wholesale price that manufacturers charge retailers.15 Draganska et al. (2010) considered two ways in which the Nash bargaining solution might vary with the party’s characteristics. First, a firm’s bargaining position depends on that firm’s disagreement point, dR for the retailer or dM for the manufacturer. Second, Draganska et al. estimated a commonly used generalization of the Nash product, NP = (‑π_R - d_R)^a (π_M - d_M)^{1 - a}, where a indicates the bargaining power of the parties. The larger a is, the more bargaining power the retailer has and the less the manufacturer has.

They estimated how d_R, d_M, and a vary with the characteristics of the firms, using data from Germany’s six largest supermarket chains—Edeka, Markant, Metro, Rewe, Spar, and Tengelmann—which account for 80% of the German grocery market, and its seven largest ground coffee manufacturers—Dallmayr, Eduscho, Idee, Jacobs, Melitta, Onko, and Tchibo which control more than 95% of the ground coffee market.

They found that bargaining power lies mainly with manufacturers: On average, the manufacturer gets more than half of the profits (a < 0.5). The larger the manufacturer’s size, the greater the manufacturer’s bargaining power and hence the larger the manufacturer’s share of profit. Similarly, larger retailers have more bargaining power. In addition, retailers that position their store brands close to national brands reduce the wholesale margins by nearly a quarter (24%).