Payoff uncertainty, bargaining power, and the strategic sequencing of bilateral negotiations
Summary (3 min read)
- When both sellers are strong bargainers, the buyer’s concern for aggressive pricing shifts to the last seller.
- The authors paper belongs to a growing literature on one-to-many bargaining, and complements several papers that address the issue of optimal bargaining sequence without payoff uncertainty.
- In Section 5, the authors show that the buyer’s expected payoff may decrease with her own bargaining power and examine the two procurement policies alluded to above.
2 The Model
- An employer often has to interview a job candidate to determine the match value; a home-owner frequently needs to consult with a contractor for a customized project; and a real-estate developer may require access to the construction history of a land parcel from the landowner.
- It is also conceivable that αi may simply reflect the intrinsic bargaining ability of the seller vis-à-vis the buyer.
- Having obtained the two prices pi and pj , and ascertained her valuations v i and vj , the buyer decides which goods to purchase (if any).
- Thus, the authors call any equilibrium inefficient if it involves less than joint purchase with a positive probability.
2.1 Discussion of the Assumptions
- The authors keep each buyer-seller bargaining simple to better focus on sequencing; nevertheless, their one-shot bargaining can be a good approximation of applications in which the buyer has a short time to acquire the goods, or else the trade opportunity is lost.
- But, such a “monotonic” incentive would then lead to the 12For instance, for many customized goods and services such as home re-modeling and landscaping, contractors give a free price estimate to which the customer needs to respond in a short-time period.
- 6 full disclosure of pi, much like in the literature on signaling a verifiable quality, e.g., Grossman (1981).
- Perhaps, what is more important is that sellers know the sequence.
- The authors envision environments where any meeting between the buyer and sellers is highly visible or publicized, or it can be easily inferred by the sellers from the calendar time.
3 Equilibrium Characterization
- The authors characterize the equilibrium prices for a fixed negotiation sequence.
- Recall, however, that the authors break ties in favor of social efficiency.
- This requires a price coordination with seller j.
- Note also that as the likelihood of having a low-value product j, qj, increases, seller j’s price decreases; but seller i’s price is increasing in qj only when αj is large due to the coordination incentive.
4 Strategic Sequencing
- A key observation from Proposition 2 is that for a fixed sequence of negotiations, the sellers’ bargaining powers and the buyer’s payoff uncertainty each influence equilibrium prices.
- Since, under an efficient trade, the extra surplus due to complementarity is captured by the sellers unless the buyer proposes in both negotiations, the buyer is indifferent to the sequence.
- The authors next finding uncovers how the buyer’s sequencing choice depends on the sellers’ bargaining powers.
- The buyer strictly prefers to start negotiations with seller 1 because, being followed by a strong rival, seller 1 has an equilibrium incentive to coordinate prices by lowering his own.
- 19 According to part (b), even though the buyer is not maximizing the social surplus per se, her sequencing choice increases it.
5 Benefits of Being a Weak Buyer
- Up to now, two robust insights have emerged from their analysis.
- First, the buyer cares about the negotiation sequence when equilibrium trade is inefficient and at least one seller is a powerful bargainer.
- The answer to this question can indeed be affirmative.
- Proposition 6 implies that it may sometimes be in the buyer’s best interest to limit her own bargaining power vis-à-vis the sellers.
- Consistent with their model, these authors define buyer power as “the bargaining strength that a buyer has with respect to the suppliers with whom it trades.”.
5.1 Minimum Purchase Price
- One reason why the sellers may price aggressively in their model is that in equilibrium, the buyer always makes the lowest price offer, namely the marginal-cost, 0.
- In particular, it may entice the leading seller to disregard price coordination with the follower and target the buyer’s entire surplus of 1 instead.
- It is evident that any positive payment by the buyer will allow the sellers to earn positive profits regardless of who makes the offer while reducing the buyer’s own payoff.
- Note that an upfront commitment to w > 0 is crucial here, because, once the leading seller lowers his price offer, the buyer has a strict incentive to lower her offer to 0 in the second negotiation whenever she proposes.
- In the same vein, large employers might favor minimum wage regulations when hiring new employees.
5.2 The Make-or-Buy Decision
- A critical decision for many industrial buyers is whether to make inputs internally or outsource them from independent suppliers.
- If two complementary inputs are required, as in the present setting, the following result shows that the buyer may optimally outsource an input even if it could be costlessly provided inhouse.
- Second, the authors know from Proposition 1 that two powerful suppliers would have the greatest incentives to coordinate and lower their prices.
- In contrast, in their model, a single firm outsources production to raise its own cost for an input to receive a favorable deal from the other supplier of a complementary input.
6 First- vs. Second-Mover Advantages for Sellers
- So far the authors have focused on the buyer’s preference over the negotiation sequence since she is the central agent who initiates the negotiations.
- It is, however, conceivable that the sellers will also have a preference.
- In particular, if, all else equal, the sellers expect a higher profit from being the first to negotiate with the buyer than being the second, then they may actively solicit the buyer’s business by offering a discount for the right to be the first.
- Otherwise, there will be a second-mover advantage since the follower can then have a significant chance to claim the buyer’s entire surplus if the buyer ends up proposing in the first negotiation.
- It is worth comparing their observations from Proposition 9 with those from the standard duopoly theory in which the sellers are price-setters, i.e, α → 1.
7 Concluding Remarks
- Unlike the standard consumer theory, the buyer is not a simple price-taker in many real examples; rather she is a powerful agent who actively negotiates the price with the sellers.
- The authors first set of results have revealed that to the extent that equilibrium trade is efficient, the buyer will be neutral to the sequence.
- The authors believe that this efficiency reasoning is also the driving force behind the similar “indifference” findings in the literature.
- In such cases, it would be interesting to determine the buyer’s incentive to invest in this information prior to negotiations given that her sequencing choice can signal her valuations to the sellers.
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Frequently Asked Questions (2)
Q1. What are the contributions mentioned in the paper "Payoff uncertainty, bargaining power, and the strategic sequencing of bilateral negotiations" ?
This paper investigates the sequencing choice of a buyer who negotiates with the sellers of two complementary objects with uncertain payoffs. The authors show that the sequencing matters to the buyer only when equilibrium trade can be inefficient. Their analysis further reveals that it is sometimes optimal for the buyer to raise her own cost of acquisition to better manage the supplier competition. As such, the authors find that the buyer may commit to paying the sellers a minimum price strictly above the marginal cost ; and that the buyer may outsource an input even though it can be made in-house.
Q2. What are the future works in "Payoff uncertainty, bargaining power, and the strategic sequencing of bilateral negotiations" ?
In this paper, the authors have focused on the sellers of complementary goods, and included the possibility that the buyer can be uncertain of her valuations. Their first set of results have revealed that to the extent that equilibrium trade is efficient, the buyer will be neutral to the sequence. The authors believe that this efficiency reasoning is also the driving force behind the similar “ indifference ” findings in the literature. This commitment can manifest itself in the form of a procurement policy such as a minimum purchase price or the outsourcing of an input when it can be made in-house at the same cost.