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Auctions
18
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CHAPTER
In oral or English auctions, the highest bidder wins by
outbidding the second- highest bidder. This means that the
second-highest bidders’ value determines the price.
A Vickrey or second-price auction is a sealed-bid auction in
which the high bidder wins but pays only the second-highest
bid. These auctions are equivalent to oral auctions and are well
suited for use on the Internet.
In a sealed-bid ﬁrst-price auction, the high bidder wins and pays
his value. Bidders must balance the benefits of bidding higher
(a higher probability of winning) against the costs of bidding
higher (reduced margin if they do win). Optimal bids are less
than bidders’ private values.
2
Bidders can increase their proﬁt by agreeing not to bid against

one another. Such collusion or bid rigging is more likely to
occur in open auctions and in small, frequent auctions. If
collusion is suspected,
do not hold open auctions;
do not hold small and frequent auctions;
do not disclose information to bidders—do not announce who
the winners are, who else may be bidding, or what the winning
bids were.
In a common-value auction, bidders bid below their estimates to
avoid the winner’s curse. Oral auctions return higher prices in
common-value auctions because they release more information
than sealed-bid auctions.
3
continued
Bell Telephone
In 1885, Bell Telephone Company of Canada established
Northern Electric to manufacture its telephone equipment.
By 2000, the company (now Nortel) had a market share of over
$200 Billion
Decade of bad investments, declared bankruptcy in 2011
Nortel approved for sale by bankruptcy court
The court was unsure of the value of some of the company’s
assets, such as the 6000 patents, and decided to sell these assets
with an auction.
The bidding started at $900 million but was pushed up to $4.5
billion after successive rounds of bidding.
4

Introduction: Auctions
Auctions are simply another form of competition, like price
competition or bargaining.
CarBargains is one company that uses auctions to help car
buyers.
In these auctions, though, sellers not buyers are competing.
Local car dealers offer prices to a single consumer in a sealed-
bid auction.
Auctions set a price and identify the high-value buyer or low-
cost seller.
Auctions are often used in combination with bargaining, e.g.,
first an auction is used to identify the high-value buyers and
then there is a negotiation over the final price.
5
Oral Auctions
Definition: In an oral or English auction, bidders submit
increasing bids until only one bidder remains. The item is
awarded to this last remaining bidder.
Example: Suppose there are five bidders with values equal to
{$5, $4, $3, $2, $1}.
The $5 bidder will win the auction, and bids only slightly over
$4 to do so.
The “price” or winning bid is $4, or slightly above.
The winning bidder is willing to pay $5 but doesn’t have to, so

the losing bidders determine the price in oral auctions.
Auctions identify the high-value bidder (“efficiency”) and set a
price for an item, with no negotiating necessary. For these
reasons, economists love auctions.
6
Benefits of auctions
Example: auction vs. posted-price
A retail store is unsure whether they should price high ($8) or
low ($5) for a certain item.
If the store prices high, they sell to only high-value buyers (half
the time). If the store prices low, they sell to all customers at a
lower price.
If MC = $3, then pricing high is preferable
(.5)($8-$3) = $2.50 [versus (1.0)($5-$3) = $2.00]
If the store uses an auction instead, and two bidders show up
with values $8 and $5 – meaning there is again a .5 chance of
selling to a high-value costumer – what will the revenue of the
sale be?
7
Oral Auctions (cont’d)
8

Second-Price Auctions
Definition: A Vickrey or second-price auction is a sealed-bid
auction in which the item is awarded to the highest bidder, but
the winner pays only the second-highest bid.
This at first seems counterintuitive – why leave money on the
table? But second-price auctions encourage bidders to bid more
aggressively.
William Vickrey and James A. Mirrlees shared the 1996 Nobel
Prize in Economics for their work inventing the Vickrey auction
and establishing that there is no difference in outcome between
an oral and second-price auction.
9
Second-price auctions (cont’d)
Because the winning bidder pays the price of the second-highest
bid, bidders are willing to bid up to their values, so the outcome
is the same as an oral auction.
Second-price auctions are easier to run than oral auctions
because the bidders can bid in remotely, and asychronously (at
different places and times).
Discussion: Why are eBay auctions equivalent to second-price
auctions?

Discussion: Why does eBay use second-price auctions?
10
Sealed-Bid Auctions
Definition: In a sealed-bid first-price auction, the highest bidder
gets the item at a price equal to the highest bid.
These auctions present a difficult trade-off for bidders:
A higher bid reduces the profit if you win, but
Also raises probability of winning
Bidders balance these two effects by bidding below their values
(“shading”).
Experience and knowing the competing bidders are the keys to
these auctions, but in general, bid more aggressively – shade
less – if the competition is strong.
11
Bid Rigging or Collusion
Example: an oral auction with bidder values of {$5, $4, $3, $2,
$1}.
Suppose that in this auction the two high-value bidders have
formed a bidding ring (also known as a cartel).
The two decide NOT to bid against each other, so the cartel
wins the item by outbidding the non-cartel members, i.e., price=
$3. The cartel makes a profit of $1 which typically i s split

evenly between members.
Bid-rigging is a criminal violation of antitrust laws in the US
and many other countries.
In one type of bid-rigging, cartel members re-auction the items
won in a second-auction to cartel members in a second or
“knockout” auction.
12
Bid-rigging / Collusion (cont’d)
Another type of collusion is known as a bid-rotation scheme.
This scheme uses quid pro quo bidding behavior.
Bidders in these cartels submit weak bids or refrain from
bidding against each other until it is their turn to “win.”
In a bid-rotation scheme each cartel member must wait for his
turn to win – a weakness that leaves these schemes vulnerable
to cheating.
Proposition: Collusion is more likely in oral auctions.
Proposition: Collusion is more likely in small, frequent
auctions.
13
Bid-rigging: Frozen Fish Conspiracy
After this cartel was broken the price of fish dropped 23%
Investigators backcast from the competition period into the

collusive period to determine the cartel’s effect, i.e., what the
price would have been, “but for” the conspiracy.
14
Reacting to bid-rigging
The government is frequently the victim of bid-rigging schemes.
Learning from the government’s experience, some tips to avoid
collusion:
Do not rely on purchasing agents (those running the auction)
who have little interest in buying at a low price. Instead, reward
agents for making good (high-quality and low-price) purchases.
Do not entangle purchasing agents with masses of red tape.
Instead, permit them to negotiate (e.g., to bargain with the
bidders) if they suspect bid rigging.
But beware of patronage
Do not use the procurement process to further a social agenda
(small business set-asides, public lands, national defense, etc.)
that is irrelevant to the goal of purchasing goods at low prices.
15
Avoiding collusion (cont’d)
Keep cartels in the dark, so it is difficult for them to organize
and to punish cheaters.

do not hold open auctions;
do not hold small and frequent auctions;
do not disclose information to bidders—do not announce who
the other bidders are, who the winners are, or what the winning
bids are.
16
Common-Value Auctions
Definition: In a common-value auction, the value is the same
for each bidder, but no one knows what it is. Each bidder has
only an estimate of the value.
Be careful in these auctions lest you suffer the “winner’s curse”
If you win, you learn that you were the one who had the highest
and most optimistic estimate of the unknown value of the item
Bidders should reduce their value estimates to protect against
this.
If you are the auctioneer, release info to mitigate winners’
curse.
Winner’s curse is worse when
More bidders
Other bidders have better information
17
Common-Value Auctions (cont’d)

To avoid the winner’s curse bid less aggressively as the number
of bidders increases.
In common-value settings, oral auctions return higher prices
than sealed-bid auctions because oral bids reveal information.
But oral auctions are more vulnerable to collusion.
Discussion: Why do bidders wait until the last minute of the
auction to submit bids on eBay?
18
Bidder 1 Bidder 2 Probability Winning bid
$5 $5 .25 $5
$5 $8 .25 $5
$8 $5 .25 $5
$8 $8 .25 $8
Bidder 1 Bidder 2 Bidder 3 Probability Winning bid
$5 $5 $5 .125 $5
$5 $5 $8 .125 $5
$5 $8 $5 .125 $5
$8 $5 $5 .125 $5
$5 $8 $8 .125 $8
$8 $5 $8 .125 $8
$8 $8 $5 .125 $8
$8 $8 $8 .125 $8
Making Decisions
with Uncertainty
17

CHAPTER
When you’re uncertain about the costs or benefits of a decision,
replace numbers with random variables and compute expected
costs and benefits.
Uncertainty in pricing: When customers have unknown values,
you face a familiar trade-off: Price high and sell only to high-
value customers, or price low and sell to all customers.
If you can identify high-value and low-value customers, you can
price discriminate and avoid the trade-off. To avoid being
discriminated against, high-value customers will try to mimic
the behavior and appearance of low-value customers.
2
Difference-in-difference estimators are a good way to gather
information about the benefits and costs of a decision. The first
difference is before versus after the decision or event. The
second difference is the difference between a control and an
experimental group.
If you are facing a decision in which one of your alternatives
would work well in one state of the world, and you are
uncertain about which state of the world you are in, think about

how to minimize expected error costs.
3
continued
TeleSwitch
A large telecom supplier, TeleSwitch, sold its product only
through distributors.
In 2000, their largest clients wanted to deal directly with
TeleSwitch – and avoid the middle man distributor. TeleSwitch
was unsure what to do.
They might lose large customers if they didn’t switch.
But, they might lose distributors (and their small customers) if
they did.
There is a lower probability of losing dealers (because they
would have to incur costs to change suppliers)
But this would have a much larger impact on profit.
How should we analyze decisions like this??
4
Introduction: Undertainty
This problem illustrates the type of uncertainty that exist in
most business decisions.
This chapter looks at ways to help deal with uncertainty and
arrive at decisions that will best profit your firm.

By modeling uncertainty, you can:
Learn to make better decisions
Identify the source(s) of risk in a decisions
Compute the value of collecting more information.
5
Modeling Uncertainty
To model uncertainty we use random variables to compute the
expected costs and benefits of a decision.
Definition: a random variable is simply a way of representing
numerical outcomes that occur with different probabilities.
To represent values that are uncertain,
list the possible values the variable could take,
assign a probability to each value, and
compute the expected values (average outcomes) by calculating
a weighted average using the probabilities as the weights.
6
Random variables
Definition: a binomial random variable, X, can have two values,
x1 or x2, with probabilities, p and 1-p. The expected value
(mean) for a binomial random variable is:
E[X]=p*x1+(1-p)x2
Definition: a trinomial random variable, X, can have three

values, x1, x2, or x3, with probabilities p1, p2, and 1-p1–p2.
The mean for a trinomial random variable is:
E[X]= p1*x1+ p2*x2+(1- p1-p2) x3
7
How to model uncertainty
“Wheel of Cash” example:
The carnival game wheel is divided like a pie into thirds, with
values of $100, $75, and $5 painted on each of the slices
The cost to play is $50.00
Should you play the game?
Three possible outcomes: $100, $75, and $5 with equal
probability of occurring (assuming the wheel is “fair”)
Expected value of playing the game is
1/3 ($100) + 1/3 ($75) + 1/3 ($5) = $60
But, if the wheel is biased toward the $5 outcome, the
expected value is
1/6 ($100) + 1/6 ($75) + 2/3 ($5) = $32.50
8
TeleSwitch’s Decision Tree
The probability of losing customers is 0.6
The probability of losing distributors is 0.2
9

Entry Decision with Uncertainty
The probability of retaliation (no accommodation) to an entry
decision (as modeled in ch 15) is 0.5
10
Dealing with uncertainty
Discussion: How do you respond to an invitation from a friend
to invest in a real estate venture that depends on uncertain
future demand and interest rates?
Calculate the potential gains and loses based on different
combinations of high and low interest rates and high and low
demand
Whoever proposed the venture probably presented the best case
scenario (low interest rates and high demand) – and that is the
only combination (of four possible outcomes) under which you
will do well.
Either don’t invest or find a way that aligns your friend’s
incentives with your own, i.e., he gets a payoff only if the
venture does well.
11

Uncertainty in Pricing
Uncertainty in pricing arises when the demand for a product is
unknown.
To model this uncertainty, classify the number and type of
potential customers. For example:
High-value consumers willing to pay $8
Low-value consumers willing to pay $5
Suppose there are equal numbers of each consumer group
Discussion: If MC= $3, what is optimal price?
By pricing high, you would earn $5 per sale each time a high-
value costumer shops – or %50 of the time
By pricing low, you would earn $2 per sale but would be able to
sell to both high- and low-value costumers – 100% of the time.
12
Uncertainty in Pricing (cont’d.)
Answer: Price High
13

Price Discrimination Opportunity
If you can identify the two types of customers, set different
prices to each group, and prevent arbitrage between them, then
you can price discriminate.
Price of $8 to the high-value customers
Price of $5 to the low-value customers.
Discussion: When buying a new car, sales people discriminate
between high- and low-value customers. How do they do this?
Discussion: What can you do to defeat this?
14
Natural experiments
To gather information about the benefits and costs of a decision
you can run natural experiments.
Natural experiment example: A national restaurant chain
A regional manager wanted to test the profitability of a special
holiday menu
To do this, the menu was introduced in half the restaurants in
her region.
In comparing sales between the new menu locations and the
regular menu locations (the control group) the manager hoped to
isolate the effect of the holiday menu on profit.
15

Natural experiments (cont’d.)
This is a difference-in-difference estimator. The first difference
is before vs. after the introduction of the menu; the second
difference is the experimental vs. control groups
Difference-in-difference controls for unobserved factors that
can influence changes
The manager found that sales jumped during the holiday season
– but the increase was seen both in the control and experimental
groups—both increased by the same amount.
The manager concluded that the holiday menu’s popularity came
at the expense of the regular menu. So the holiday menu only
cannibalized the regular menu’s demand and didn’t attract new
customers to the restaurant.
16
Natural experiments (cont’d.)
Natural experiments can be useful in many different contexts.
When the FTC looked back at a 1998 gasoline merger in
Louisville, they used their own version of a difference-in-
difference estimator.
Three control cities (Chicago, Houston, and Arlington) were
used to control for demand and supply shocks that could affect
price.
The first difference was before vs. after the merger; the second
difference was Louisville prices vs. prices in control cities– this
allowed the FTC to isolate the effects of the merger and
determine its effect
17

1998 LouisGasoline Merger
18
Minimizing expected error costs
Sometimes, when faced with a decision, instead of focusing on
maximizing expected profits (benefits minus costs) it can be
useful to think about minimizing expected “error costs.”
This approach is helpful when one alternative would work well
only under certain conditions, and you are uncertain about
whether the conditions hold.
For example, “should we impose a carbon tax?”
If global warming is caused by human activity then a carbon tax
will help reduce it.
But if global warming is not caused by human activity, then a
carbon tax would only reduce economic activity and would not
cool the Earth.
19

Error costs (cont’d.)
The two global warming alternatives can be modeled by:
20
Type I error is the failure to tax when global warming (GW) is
caused by human activity.
The Type II error is the implementation of a carbon tax when
global warming (GW) is not caused by human activity.
The optimal decision is the one with the smaller expected error
costs, i.e. Tax if (1-p)*Cost(Type I) < p*Cost(Type II)
This type of analysis is especially useful for balancing the risks
associated with pricing errors (over- v. under-), e.g., for
airlines, hotels, cruise ships; as well as production errors (over
v. under)Carbon TaxNo TaxGW is caused by human activity
(p)0(p) x (error cost II)GW is not caused by human activity (1-
p)(1-p) x (error cost I)0
Risk versus uncertainty
Risk is how we characterize uncertainty about values that are
variable.
Risk is modeled using random variables.
Uncertainty is uncertainty about the about the distribution of
the random variables.
E.g., which probabilities should be assigned to the various
values the random variables can take?
This difference is critical in financial markets. Risk can be
predicted, priced and traded – people are comfortable with risk.
Dealing with uncertainty is much more difficult.
Mistaking risk for uncertainty can be a costly mistake

21
IndyMac: Risk vs. Uncertainty
Risk never went away, investors were just ignoring it
Black Swans & fat tails
I have nothing against economists: you should let them entertain
each others with their theories and elegant mathematics,
[But]…do not give any of them risk-management
responsibilities.
—Nassim Nicholas Taleb
22
Dealing with uncertainty
Uncertainty is unavoidable. So to cope with uncertainty in
decision making, gather more or better information.
Best Buy has used dispersed sets of non-experts to predict
future variables, such as a holiday sales rate.
Google uses internal prediction markets to generate demand and
usage forecasting.
The US Marines advise:
Because we can never eliminate uncertainty, we must learn to
fight effectively despite it. We can do this by developing
simple, flexible plans; planning for likely contingencies;

developing standing operating procedures; and fostering
initiative among subordinates.
23
Risk versus uncertainty
Part of the housing crisis can be attributed to an error in
translating uncertainty to risk through a mathematical formula
created by David Li.
The formula was designed to measure the correlation between
returns of various assets that made up collateralized debt
obligations (CDOs).
But there was uncertainty about how one asset’s failure would
related to that of another asset. There was also a lack of
historical data about relationships among the underlying assets.
Li’s solution was to use past credit default swap (CDS) pri ces
as an indication of correlation returns (clever but imperfect).
CDS data came from a time when housing prices were on the
rise, and the correlation changed during a period of decreasing
prices.
Nearly everyone was using this formula, and… we’ve seen how
it all turned out
24
Telecom Firm

Sell directly to large customers
(.20) × $30 + (.80) × $130 = $110
Sell only through dealers
(.60) × $100 + (.40) × $130 = $112
Distributors leave
(probability = .20)
Firm profit = $30
Distributors stay
(probability = .80)
Firm profit = $130
Large customers leave
(probability = .60)
Firm profit = $100
Large customers stay
(probability = .40)
Firm profit = $130
Entrant
Enter
(.50) × $60 + (.50) × $-40 = $10
Stay Out
(.50) × $0 + (.50) × $0 = $0
Incumbent prices high
(probability = .50)
Entrant profit = $60
Incumbent prices low
(probability = .50)
Entrant profit = $-40
Incumbent prices high
(probability = .50)
Entrant profit = $0
Incumbent prices low
(probability = .50)
Entrant profit = $0
Pricing Decision

Price High
(.50) × $5 + (.50) × $0 = $2.50
Price Low
(.50) × $2 + (.50) × $2 = $2
Get high-value customer
(probability = .50)
Profit = $5
Get low-value customer
(probability = .50)
Profit = $0
Get high-value customer
(probability = .50)
Profit = $2
Get low-value customer
(probability = .50)
Profit = $2
Bargaining
16
PowerPoint Slides
© Luke M. Froeb,
Vanderbilt 2014
CHAPTER
Strategic view of bargaining: model as either a simultaneous-
move or sequential-move game.
A player can gain bigger share of the “pie” by
changing a simultaneous-move game into a sequential- move
game with a ﬁrst-mover advantage;
or by
committing to a position.
Credible commitments (threats) are difficult to make because

they require players to commit to a course of action against
their self-interest. Thus, the best threat is one you never have to
use.
2
The strategic view of bargaining focuses on how the outcome of
bargaining games depends on who moves ﬁrst and who can
commit to a bargaining position, as well as whether the other
player can make a counteroffer.
The non-strategic view of bargaining focuses on the gains and
alternatives to agreement to determine the outcome of
barganing.
Main insight: The gains from agreement relative to the
alternatives to agreement determine the terms of any agreement.
Anything you can do to increase your opponent’s relative gains
from reaching agreement or to decrease your own will improve
your bargaining position.
3
continued
1: NBA
In summer 2011, National Basketball Assc. owners were
negotiating with the players’ union over how to split revenues

Union wanted 57%, owners only offered 50%
Owners locked out the players, cancelling the start of the season
After months of legal threats and lost revenue, players finally
accepted owners’ initial offer
4
2: Texaco
In 1985, Texaco was found guilty by a Texas jury for
interfering with Pennzoil’s attempt to buy Getty Oil.
Texaco was fined $10.5 billion, but appealed the verdict and
began negotiating with Pennzoil.
In 1987, Texaco filed for bankruptcy. Pennzoil was then unable
to seize control of Texaco’s assets.
Texaco was also freed from the responsibility to pay interest
and dividends.
One year later Texaco and Pennzoil settled the case, with
Texaco having to pay only $3 billion. Texaco successfully used
bankruptcy to reduce its liability by over 70%
This chapter examines bargaining, and strategies to improve
your bargaining position, like those used by Bear Stearns and
Texaco .
5
Introduction: Bargaining
There are two complementary ways to look at bargaining:
the strategic view analyzes bargaining using the tools of game
theory (ch 15). Bargaining can be viewed as either a
simultaneous-move game with two equilibria or a sequential-
move game, where one player gains an advantage by committing
to a position.
the non-strategic view acknowledges that real life negotiations
don’t have fixed rules as formal games do. This view postulates
that the alternatives to agreement determine the terms of
agreement, regardless of the rules of the negotiating game.

If you can increase your opponent’s relative gain, or decrease
your own, you can gain a bigger share of the pie.
By declaring (or threatening) bankruptcy, Bear Stearns and
Texaco were able to improve their bargaining “position”, i.e.,
by changing the alternatives to agreement, they changed the
terms of agreement.
6
Bargaining: a simultaneous-move game
Example: Wage negotiations
Management and labor are bargaining over a fixed sum of $200
million
Two possible strategies are available to each player: “bargain
hard” or “accommodate.”
If both bargain hard, no deal is reached. Neither side gains.
If both accommodate, they split the gains from trade.
If one player bargains hard and the other accommodates, then
the player who bargains hard takes 75% of the “pie”
7
Bargaining: a simultaneous game (cont.)
There are two equilibria for this game
Management prefers the lower-left equilibrium
Labor prefers the upper-right.
This bargaining game has the same structure as a game of
“chicken”
Each party can gain by committing to a position, which turns it
into a sequential game
8
Bargaining: a sequential-move game
In sequential-move bargaining the first “player” makes an offer

that the second “player” can accept or refuse.
Again to analyze a sequential-move game look ahead and reason
back.
The first-mover “looks ahead and reasons back” to determine
the how her rival will react to each possible move. Then the
first-mover can determine the consequences of each possible
move.
In this case, the sequential-move games present a “first-mover
advantage,” i.e., by moving first a player can gain an advantage.
Using the same wage negotiation example, we can look at
sequential-move bargaining and first-mover advantage.
9
Bargaining game: first-mover advantage
Management “wins” by moving first and making a low offer
10
Bargaining game: first-mover advantage
Union can change the outcome by credibly committing to strike
if a low offer is made
11
Sequential-move bargaining (cont.)
Because the management has the first-mover advantage, it is in
their best interest to make a low offer, and it is in the union’s
best interest to accept that offer.
However, if the union can effectively threaten to strike (in such
a way that the management believes them) they can change the
outcome of the game despite management’s first-mover
advantage.
Credible threats are hard to make because they require the union

act against its self interest.
If management doesn’t believe the threat, the union might
actually have to follow through on the threat.
So, again, the best threat is one you never have to use.
12
Non-strategic View of Bargaining
The outcome in strategic bargaining “games” is dependent on
the rules of the game, but in real life, the rules are not always
clear.
John Nash proved that any reasonable outcome to a bargain
would maximize the product of the bargainers’ surplus.
This is known as an “axiomatic” or “non-strategic” view of
bargaining.
In this view, the gains from bargaining relative to the
alternatives to bargaining, determine the terms of any bargain.
This view also teaches that to increase your bargaining power,
you can increase your opponent’s gain from reaching agreement
or decrease your own.
If your rival has more to gain by agreeing, he becomes more
eager to reach agreement, and accepts a smaller share of the
surplus.
13
Non-strategic view (cont.)
Nash’s axiomatic approach:
[ S1(z) – D1 ] x [ (S2(z) – D2 ] , where:
z is the agreement
S1(z) is the value of the agreement to player 1 (sub 2 for player
two)
D1 is “disagreement value,” or pay-off if no agreement is
reached, for player 1 (sub 2 for player two)
So player 1’s gain from agreement is (S1(z) – D1)
14

Non-strategic view (cont.)
For example, two brothers are bargaining over a dollar.
If no agreement is reached, neither participant gains.
If they reach an agreement (z)
Player one, the older brother, has a surplus of z
Player two, the younger brother, has a surplus of 1 – z
Nash’s solution is for them to “split” the gains from trade, i.e.,
{½, ½} is the axiomatic solution.
But, now the older brother receives a $0.50 bonus for “sharing
nicely,” and the total gain rises from $1.00 to $1.50
The Nash bargaining outcome is for the brothers to split to total
gains – each receiving $0.75, meaning the older brother
effectively shares half of his bonus.
By increasing the first player’s gain to reaching agreement, he
becomes more eager to reach agreement, and “shares” his gain
with his brother.
15
Bonuses for agreement
Giving a bonus for reaching agreement is similar to incentive
compensation schemes used by many companies.
When salespeople are offered bonuses it increases their
eagerness to reach agreement and this induces them to accept
“weaker” agreements.
So giving salespeople such a bonus driven incentive will lead to
lower prices when they negotiate with customers.
(This concept will be further addressed in chapter 20)
16
Alternatives to agreement
Nash’s bargaining solution incorporates the effect of
alternatives to agreement on the agreement itself. This creates

some sound bargaining advice:
To improve your own bargaining position, increase your
opponent’s gain from reaching agreement, S2(z) – D2, or reduce
your own gain from reaching agreement, S1(z) – D1.
When you increase your opponent’s gain in agreement, you
make him more willing to agree.
Reducing your own gain makes you less willing to compromise
and helps to improve your position.
17
How Nash’s view differs from strategic
The strategic view of bargaining places a greater emphasis on
timing and commitment in determining the outcome of the
game.
With the labor/management example, the union’s commitment
to strike, or management making the first move, changes the
equilibrium of the game.
But neither action changes the gains of the agreement so neither
would affect the Nash bargaining outcome.
The Nash bargaining outcome incorporates the idea that if you
decrease your own gain to agreement you become a better
bargainer.
EXAMPLE: the best time to ask for a raise is when you have
another attractive offer waiting for you, you have less to gain
by reaching agreement. Your bargaining position improves.
This is similar to the idea of “opportunity cost.” The
opportunity cost of staying at your current job is giving up the
new offer; if the new job pays more, you’re costs (bottom line)
go up.
18
Improving a Bargaining Position
Discussion Question: When is the best time to buy a car?
Hint: Remember, car salesmen are generally paid a commission

for the sales they make.
Discussion Question: How can mergers or acquisitions improve
bargaining power?
19
Merger bargaining example
A Managed Care Organization (MCO) markets its network to an
employer
Network value is $100 if it contains either one of two local
hospitals
But the value rises to $120 if it contains both
And there is no value without at least one of the hospitals
The gain to the MCO from adding either of the hospitals to its
network when it already has the other is $20
Nash bargaining solution predicts this is evenly split
So, each hospital gets $10 for joining the MCO
But if the hospitals merge and bargain together,
The MCO can no longer drop one of the hospitals, so the gain
from striking a bargain with the merged hospital is the full $120
The gain is evenly split in the Nash bargaining solution
The merged hospitals thus receive $60, a post-merger gain of
$40
20
Health care mergers
In Rhode Island in 2003, Blue Cross Blue Shield (BCBS, the
health insurance company covering state employees) hired
PharmaCare to provide pharmaceutical services.
PharmaCare created a network of retail pharmacies willing to
sell drugs to state employees at discounted rates.
The previous contract had allowed employees to buy from any
pharmacy but was considerably more expensive.
In the new PharmaCare contract, 4 retail pharmacies were
excluded from the plan. These 4 firms lobbied RI legislature to

include them in the new plan and offered to provide the same
discounted price but PharmCare declined their request to join.
Pharmacare maintained that allowing the other stores to join
would eliminate the savings generated by having a restricted
network. PharmaCare’s bargaining position would deteriorate.
Many politicians, though, like “freedom-of-choice” bills that
would open any pharmacy willing to meet the negotiated prices.
21
Title?
Under the 2002 CHAOS (Create Havoc Around Our System)
plan, flight attendants threatened to either stage a mass walkout
for several days or to strike individual flights of Midwest
Express, with no advance warning to either customers or
management.
Midwest Express reacted by cancelling all flight attendant
vacation, and threatened to lock out any employee who
participated in the strike
Flight attendant union promised funding from its strike fund to
support any attendant who ended up locked out.
The biggest strength of the union’s threat was that it could be
effective without full implementation.
The threat of random strikes was enough to push passengers to
other airlines.
After 30 days of CHAOS, the union successfully negotiated a
new contract.
22
Management
Union
low offer generous offer
acceptstrike
0 , 0 150 , 50 50 , 150
acceptstrike

0 , 0
Management
Union
low offer generous offer
strike
0 , 0 50 , 150
acceptstrike
0 , 0

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