Multilateral Bargaining (new section of Ch 16 for next edition)

The same principle of the previous section—that the party with the better outside option will receive a bigger share of the proverbial pie—can be applied to bargaining among several players. For example, two hospitals bargain to get into a payer (insurer) network; or Coke and Pepsi bargain to get onto the shelf of a retailer.

 To make this concrete, and very simple, imagine that the retailer has only five customers: one who will buy only Coke; one who will buy only Pepsi; and three switchers will buy Coke if Pepsi is not available and vice-versa. If each customer generates $1 profit, then profit is generated according to the following rules:

• No profit if no agreements are made. 
• $4 profit if the retailer sells only Coke. 
• $4 profit if the retailer sells only Pepsi. 
• $5 profit if retailer sells both Coke and Pepsi.

The three switchers put the retailer in a position to capture most of the profit.

 To see how this works, look at Figure X, where the circles denote different combinations of agreements among the three players. When no agreement is reached, no profit is generated, denoted by the bottom circle. If the retailer (“r”) and Coke (“c”) negotiate successfully (left circle), they will split $4, computed relative to disagreement values ($0) of the bottom circle, yielding a profit split of r=$2 and c=$2. Similarly, if the retailer and Pepsi (“p”), negotiate successfully (right circle), the profit is split r=$2 and p=$2. Circles below each agreement circle serve as “threat points” or “alternatives” to the agreements above.

 In the top circle, when the retailer carries both goods, the retailer uses the threat of agreement with one of the parties to extract concessions from the other. For example, when the retailer bargains with Pepsi about how much profit Pepsi should receive when the retailer sells both products, the retailer’s outside alternative is the $2 profit it would receive from agreeing with Coke.  In contrast, Pepsi’s alternative is zero. Theory predicts that the retailer should receive $2 more than Pepsi, or r=p+2, where r and p are the profits going to the retailer and Pepsi when the retailer carries both products. Similarly, when the retailer bargains with Coke, theory predicts the retailer will receive $2 more than Coke, or r=c+2.

 We know that all profit will be distributed among the three players, or that 5=r+c+p, which gives us three equations and three unknowns. The profit split that satisfies these three equations is denoted in the top circle: r=$3, c=$1, p=$1.

 So far, we have shown how the retailer uses the threat of agreement with one of the manufacturers to influence negotiations with the other. Our model tells us:

1.  what matters (the number of switching consumers, which measures the degree of substitution between the goods); 
2.  why it matters (the higher the number of switchers, the better the retailer’s bargaining alternatives); and 
3.  how much it matters (the retailer captures the lion’s share of the profit)

 But we don’t want to lose sight of the point of studying bargaining theory: we use theory not only to show us where self-interest is likely to take us, but also to show us how to do better. In the next two sections, we show how horizontal and vertical merger can improve the bargaining position and lead to a bigger share of the proverbial pie.

 Horizontal Merger: 

 Imagine that Coke and Pepsi were to merge before the bargaining begins, and then bargain jointly. No longer would the retailer be able to use the threat of agreement with Coke to influence negotiation with Pepsi, and vice-versa. Instead, the post-merger profit would be evenly split:

r=$2.50, (c+p)=$2.50

which is bigger than the manufacturers’ pre-merger profit of $2=$1+$1. Intuitively, the merger eliminates competition between the manufacturers which, if significant, may lead to a challenge from the competition agencies.

 Vertical Integration:

 Now imagine that the retailer buys Pepsi (sometimes called “vertical integration” or “vertical merger”), and then bargains with Coke. Intuitively, the acquisition of Pepsi is profitable for the retailer because it improves its outside option in negotiations with Coke (from $2 to $4). As a consequence, the merged retailer will earn $4 more than Coke (r=p+4) for a total post-merger profit split:

r =$4.50, p=$0.50.

This is profitable because the post-merger profit is bigger than the Retailer and Pepsi pre-merger profit ($4=$3+$1).

If you think of Coke as an independent brand like Calvin Klein, and Pepsi as a private label brand, like Kirkland Signature for Costco, we can see that having a captive private label put the retailer in a better negotiating position. If its private label brand is a good substitute for the independent brand, then the retailer can negotiate better deals with the independent brand because if it fails to reach agreement, it will capture much of the profit with its private label brand.