This includes a summary of all relevant theory for the Economics of Markets and Organizations course. This is an elaborate summary that could be largely used as a substitute for reading the course material.
Main book: Games, Strategies, and Managers - John McMiller.
Chapter 5 Gaining bargaining power
What are the sources of bargaining strength?
Seller is said to have bargaining power if (i) the buyer believes the seller refuses to settle for anything
less than a large share of the gains from trade; and (ii) the seller knows that the buyer believes this.
The typical bargaining situation:
(1) Room for cooperation to increase size of pie
(2) Various efficient ways of splitting the pie.
An outcome is first-best efficient if it maximizes total surplus (sum of all players’ payoffs).
The Archetypical Bargaining Game
The prisoner’s dilemma is somehow limited because there is only one outcome that cooperation can
lead to in the prisoners’ dilemma. In reality, many efficient outcomes usually exist, resulting in the
possibility of conflict over how the gains from cooperation are to be shared (additional layer of
conflicting interests). Bargaining occurs over which one of the many efficient outcomes is to be
reached.
At first, we start with the simple model where people know what the item is worth to the other. E.g.
seller wants at least $1000, buyer is willing to pay $1100, the bargaining is over the $100.
This simple game is similar to the prisoners’ dilemma in that there is a possibility of an inefficient
outcome: failure to reach agreement in this model. But it is more complicated than the prisoners’
dilemma in that there are many efficient outcomes. Any agreement causes maximization of the
pie.
Does this model predict a particular negotiation outcome? The seller, in deciding how much to
ask for, must think of how much she can get away with; the highest price the buyer is likely to
accept. Similarly, the buyer, in choosing whether he should reject, must estimate what price the
seller would agree to. Is it rational for him to accept the offer? It is, if he believes that in other
rounds the seller will never yield but keep demanding the same price. Is it rational for the seller
to ask this amount? Only if she believes that the buyer believes that the seller with not settle for
less. We cannot yet predict the outcome of the negotiation process. This depends crucially on
each negotiator’s belief about what price his/her opponent will find acceptable.
How much bargaining power do either of the bargainers have in this situation? Bargaining power
is a notoriously vague and slippery concept.
o The seller is in a strong bargaining position if, first, the buyer believes the seller will
refuse to settle for anything less than a large share of the gains from trade; and the seller
knows the buyer beliefs this.
o So, it depends on what each bargainer believes. Where do these beliefs come from?
Forming Beliefs
Addition: Each of the bargainers has some alternative to fall back on should the negotiations fail (e.g.
a firm offer from someone else $1040; or another shop selling another car $1090). Suppose,
moreover, that each bargainer knows the other’s alternative => the effective gains from trade are
now $50 dollar rather than $100. The alternative opportunities shrink the range of prices to be
bargained over and the range is shrunk asymmetrically: the range of possibilities have shifted in the
seller’s favour, reflecting the fact that the seller’s fallback is more attractive than the buyer’s.
, The more attractive a bargainer’s alternative opportunities, the better the negotiated outcome
will be for that bargainer. The alternative opportunities affect each bargainer’s expectations of
what the others will settle for, and shaping the terms of the agreement.
Credibility of bargaining positions is key. It is credible to believe bargainers will hold out of a deal
if they have a better option.
Alternative opportunities are, therefore, a source of bargaining power (Appendix).
Even if you are thinking of “cooperating” it might be good to have a fallback option for the sake
of negotiating/bargaining.
One potent way of improving your fallback position is to generate competition on the other side
of the bargaining table. Also, your bargaining power is inversely related to how good your
opponent’s alternatives are. Knowing what the other’s alternatives are is crucial to a realistic
assessment of what you can expect to achieve in bargaining. An aggressive bargainer might even
try to worsen the other’s alternatives.
A second determinant of the strength of bargaining positions, is the relative cost incurred by the two
bargainers if the agreement is delayed. Time is money.
E.g. during negotiations over the price of a car lets the seller lose the interest she could be
earning if she had the money from the sale; the buyer must pay taxi fares while he does not own
a car.
The costs of delay shape the terms of the negotiated agreement, for they shape each bargainer’s
expectations of what the other will agree to. The more impatient your opponent is to settle, the
better is the agreement you can hold out for.
Thus, the higher one party’s cost of delay, the smaller that person’s share of the rationally
negotiated gains from trade.
Thus, patient bargainers –those with low costs of delay- get their rewards now.
Sometimes, imaginative ways can be found to increase the opponent’s cost of delay in
agreement.
o A union negotiating with a restaurant owner, instead of simply striking as the
restaurateur expected, arranged for 100s of sympathizes to enter the restaurant, order a
cup of coffee and occupy all the tables for the duration of lunch hour.
o Strikes.
Thus, as a negotiator, you should try to find out your own and your opponent’s cost of delay. If
yours is lower, you have an advantage: you may be able to get a better deal explicitly or implicitly
threatening to delay the agreement. The terms of agreement will move in your favour if you can
reduce your own time costs or raise those of your opponent.
What shapes beliefs?
- Outside options clearly matter. Create good ones yourself, ‘destroy’ those of opponents.
- The relative costs of delay of agreement. Signal patience.
- Focal points, outcomes that are attractive for some reason (e.g. custom habit, moral reason).
Reaching some agreement may be more important than the exact agreement.
- Commitment: “the power to constraint and adversary depends on the power to bind oneself”.
Focal Points
There is an inherent indeterminacy in bargaining: often there are many possible points of agreement.
, In some stylized bargaining games there is only one outcome that is consistent with both
bargainers doing the best they can. A multiplicity of outcomes is more typical in bargaining
games.
A bargaining agreement is reached when the bargainers’ expectations converge. This can be at
whatever point. Suppose, however, that there is something about the bargaining situation that
serves to highlight a particular outcome. Such an outcome can be a focal point upon which an
agreement can coalesce.
o The focal point is not precisely defined.
o Possible determinants of focal points: highlighted by precedent (“we do it this way
because it’s always been done this way”; or by some mathematical symmetry (“equal
shares”); or because an impartial mediator suggests a solution.
An experiment was done with token (at the end they would get money).
- The interesting finding of these experiments is the marked tendency for the bargainers to settle
for a 50-50 split, despite the fact that the units by which the 50-50 split was defined were
arbitrary. The 50-50 split was often nominal rather than genuine. In the absence of a unique
bargaining equilibrium, there seems to be a powerful tendency to settle for equal shares. But
how is equality to be defined? It does not seem to matter much. Given the many possible ways
of dividing the pie, what seems to be needed to get agreement is a commonly agreed way of
keeping score: and it does not seem to matter that the units in which the score is kept have no
real meaning.
- Phone precision => the appearance of equal division may be enough to generate agreement.
This is an advantage, as it helps produce agreement.
o Hence, during complicated negotiations, a good strategy seems to be to look for some way
of defining a focal point upon which agreement can coalesce, thus avoiding breakdown.
Find a method for measuring your own and your opponent's concessions, even if the
measure does not really capture their objective value.
Commitment as a Bargaining Technique
Bargaining technique: manipulating the rival’s expectations
- Suppose that the seller, making the first offer, announces that the buyer must take or leave her
offer, saying that if the buyer rejects the offer she will refuse to bargain further and neither of
them will get any of the $100. Moreover, the seller is able to convince the buyer she will indeed
carry out this threat if the buyer rejects her offer. What does the seller demand? The seller
demands all of the $100 minus a few pennies. They buyer is faced with a choice between getting
nothing and getting the small amount the seller is offering: the rationally agrees to the seller’s
demand.
- Some could say that the buyer would not agree because he sees this as an insult. Additionally
you can say that the buyer’s pride has a price. If the buyer prefers getting, say $5 and feeling
aggrieved to getting nothing it all, then the seller rationally demands $95.
- The best bargaining strategy, therefore, is to refuse to bargain. Being able to make commitments
while your opponent cannot means that you have much of the bargaining power.
- Flexibility is in fact useful at one stage of the process: it is good to have a wide range of choice
over what position you are going to commit to. It is good to have flexibility before the
negotiations begin, but to be inflexible during the negotiations.
- Commitment must be all or nothing. The seller must make the buyer believe that her
commitment is irrevocable. Otherwise it would not be rational to accept.
, - Thus a commitment strategy must be believable if it is to work. How can commitment be
achieved? One way is for the seller to put her reputation at stake. If the seller plans to be in
business for a long time, then she can convincingly argue to the buyer that she cannot afford to
renege on the promise she made. The cost of reneging on her current commitment would be the
inability to make credible commitments to others and therefore the loss of bargaining power in
other negotiations.
- Another way of achieving commitment is to hire an agent to do the negotiating, and require the
agent to follow a set of procedures that are publicly known. Trying to bargain with a
department-store clerk is usually futile: the store can make its price quotes firm by requiring its
salespeople to follow its price list.
- A more dramatic way of achieving commitment is to burn bridges; to arrange things so that,
should you renege, you will suffer some severe punishment. For instance, a corporate raider
attempting to take over a company wrote a clause into the loan agreement financing the
takeover that said that, if he raised the price he was offering for the company, his loan interest
rate would rise by 1.5%.
- Defensive tactic: to pre-empt your opponent’s commitments. Or check if your opponent’s
commitment is indeed firm.
- Our discussion has presumed that only one of the two negotiators has instruments with which it
is possible to make commitments. If, however, both have this capacity, they may commit
themselves to incompatible demands. Hence commitment is a risky strategy. If you use it and it
works, its payoff is high: you earn most of the profit from the transaction. But if your opponent
simultaneously tries to use it, the negotiations can be destroyed.
- So, committing yourself before the negotiations begin is the most powerful negotiating technique
if the opponent cannot commit him/herself.
So, for bargaining power:
(1) Commitments
(2) Attractive alternatives
(3) Costs of waiting
(4) In complex negotiations, finding the same way of defining a focal point upon which an
agreement can coalesce.
Appendix 5
We suppose that the negotiation process has the following form: The seller makes the initial offer of
how to divide the $100, which the buyer can accept or reject. If the buyer rejects it, he makes a
counteroffer after a certain time has elapsed (e.g. 1 day). The seller then chooses whether or not to
accept, etc, the process can go on forever.
Bargaining with alternatives to agreement
In the bargaining, there is a chance that events beyond the control of the bargainers will cause the
bargaining to break down irrevocably: at each stage of the game, breakdown can occur with
probability p. Fallbacks are f. Each bargainer knows the other’s fallback.
- Notice that $100 must be more than f a+fb. The total gains to both bargainers from a successful
trade are 100 – fs – fb.
- Solving this clumsy but elementary equation we find that, from the $100, the seller gets an
amount z = [100 + (1 - p)fs - fb]/(2 - p).
o Outside opportunities are a source of bargaining power. Z gets larger as fs increase.
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