Buyer Group and Buyer Power When Sellers Compete

We study how buyer group affects buyer power when sellers compete with non-linear tariffs and buyers operate in separate markets. In the baseline model of two symmetric sellers and two symmetric buyers, we characterize the set of equilibria under buyer group, the set without buyer group and compare both. We find that the interval of each buyer's equilibrium payoffs without buyer group is a strict subset of the interval under buyer group if each seller's cost function is strictly convex, whereas the two intervals are identical if the cost function is concave. Our result implies that buyer group has no effect when the cost function is concave. When it is strictly convex, buyer group strictly reduces the buyers' payoff as long as, under buyer group, we select the Pareto-dominant equilibrium in terms of the sellers' payoffs. We extend this result to asymmetric settings with an arbitrary number of buyers.