Chapter 16: Bargaining
16.1 INTRODUCTION
This is Professor Luke Froeb and I am a co- author of
Managerial Economics: A Problem Solving Approach. This
video is designed to supplement Chapter 16: Bargaining.
You can think about bargaining in two complementary ways.
First is the strategic view, which analyzes bargaining as a game,
as in Chapter 15.
The other approach recognizes that bargaining doesn’t have
fixed rules, as do formal games, and looks at the alternatives to
agreement as key determinants of the type of bargains that can
be reached.
Both views offer useful advice on how to gain a bigger slice of
the proverbial pie. We begin with the strategic view.
16.2. GAME OF CHICKEN
I<SHOW GAME OF CHICKEN EQUILIBRIUM MODEL (BOOK P.
197)>
The movie Footloose tells the story of Ren McCormack, a
Chicago teen who moves to a small town where he finds
himself in a game of chicken against Chuck, the local bully. The
two drive tractors straight at one another, and the first one to
swerve loses, and gets labeled a “chicken.” The one who goes
straight gets the girl. If they both swerve, neither gets the girl,
but if they both go straight, they both end up in the hospital.
<<ILLUSTRATE THESE OUTCOMES IN THE FORMAL GAME WHEN
I SAY THEM>>
Pause the video and think intuitively about the equilibria of this
game. Remember equilibrium is where each party is doing the
best they can given what the other player is doing. ….. <<PUT
“PAUSE, FIGURE OUT THE EQUILIBRIA” ON SCREEN, AND LET IT
RUN FOR TEN SECONDS>>
<<SHOW GAME AND ILLUSTRATE THE TEXT>>
Ren
Go Straight Swerve
Chuck
Go Straight 0, 0
1,3
Swerve
2,2
1, 3
Both going straight is not an equilibrium because either party
could make themselves better off by swerving. Likewise, both
swerving is not an equilibrium because either party could make
themselves better off by going straight. If one goes straight and
the other swerves, then each player is going the best they can
given what the other is doing. We show these two equilibria in
this simultaneous move game.
OK, what do we learn by diagramming the game? Game theory
is silent about which equilibria we end up in. But we do learn
that the players would prefer one of the equilibria over the
other. The question that should immediately occur to you is
how can you manipulate the game so that you end up in your
preferred equilibrium? << ANIMATE BY POINTING ARROW
TOWARDS YOUR PREFERRED EQUILIBRIUM??>>
If Ren can figure out how to move first, or commit to a going
straight, then he turns this into a sequential game with a first
mover advantage. To see this, lets compute the “roll back”
equilibrium of the sequential move game.
.<<DRAW GAME TREE LIKE THE BARGAINING GAME BETWEEEN
MANAGEMENT AND LABOR, BUT OF THE GAME OF CHICKEN
ABOVE WITH REN MOVING FIRST. ILLUSTRATE THE ROLL BACK
EQUILIBRIUM OF THE GAME.>>
To do this, we start at the end, and analyze the second mover’s
incentives first. If Ren goes straight, and Chuck finds himself on
the bottom left branch of the tree, then Chuck does better by
swerving. We denote this by putting two lines through the
Straight option that is not going to be chosen by Chuck.
If Ren Swerves, and Chuck finds himself on the bottom right
branch of the tree, then Chuck does better by going straight.
We denote this by putting two lines through the Swerve option
that is not going to be chosen by Chuck.
OK, now that we know what Chuck will do, we can caluculate
Ren’s best move by looking ahead and reasoning back. If Ren
goes straight, Chuck will serve, and Ren receives 3. But if Ren
swerves, Chuck goes straight, and Ren gets only 1. We denote
this by putting two lines through the Swerve option on the
upper branch of the tree that is not optimal for Ren.
The equilibrium path of the game is Ren going straight and
Chuck swerving. We denote this with a thick solid line.
<<ANIMATE THE PATH>>
Now we show you what happens in the movie. Watch how Ren
commits to going straight, which is equivalent to moving first.
<<SHOW CLIP FROM MOVIE WHERE REN COMMIITS TO GOING
STRAIGHT AND CHUCK SWERVES: 1:30—2:15 of
https://www.youtube.com/watch?v=pwGQDtC-h18. Note that
this movie has been remade so if you think it works better in
the new version, use it.>>
16.3. Bargaining as a Strategic Game
<<DRAW REDUCED FORM GAME WHERE PARTIES SPLIT 100,
NOT 200, AND ANIMATE THE TEXT BELOW BY USING ARROWS
TO POINT AT THE RELEVANT PART OF THE TABLE>>
OK, lets do the same analysis for a bargaining game between
management and labor, bargaining over how to split a pie of
size 100. Each can bargain hard, or accommodate. If both
bargain hard, then they do not reach agreement, and each
earns zero. If both accommodate, each earns 50. If one
bargains hard and the other accommodates, the one who
bargains hard gets 75 while the one who accommodates gets
25. <<ANIMATE THE PAYOFFS AS I SAY THEM>>
This bargaining game has the same logical structure as the
game of chicken. Note that accommodate, accommodate is
not an equilibrium because either party could do better by
bargaining hard. Likewise, (bargain hard, bargain hard) is not
an equilibrium because either party could do better by
accommodating. The two equilibria are for one to bargain
hard, and the other to accommodate.
We know from studying the game of chicken that if one of the
players can move first, or commit to bargaining hard, then she
can capture the lion’s share of the gains from trade. We show
this in the sequential game here where Management moves
first and captures a bigger share of the gains from trade.
<<AGAIN, CHANGE THE NUMBERS SO YOU ARE SPLITTING 100,
AND MAKE THE TWO LINES BIG SO THAT THEY ARE EASILY
SEEN, AND THICKEN AND ANIMATE THE EQUILIBRIUM PATH OF
THE GAME.>>
Management
low offer
generous offer
Union
strike
accept
0,0
150 , 50
strike
0,0
accept
50 , 150
Committing to a position, or moving first is more difficult than it
sounds because it forces you to ignore counter-offers that
would be otherwise profitable to accept. For example, the
father of one of my coauthors always buys a car by bringing in a
check filled out for the amount that he wants to pay, and tells
the salesman he has five minutes to accept the offer, or he is
walking out the door. If the salesman believes that this is a
credible take-it-or-leave-it offer, he will accept the offer. It
usually works. But sometimes, the salesperson tries to make a
counteroffer, so the dad has to walk out.
16.4 THE NON-STRATEGIC VIEW OF BARGAINING
The strategic view bargaining follows from the assumption that
bargaining can be modeled as a game. However, few
bargaining situations follow well defined rules, so an alternate
view is derived from what we call the axiomatic or non strategic
view of bargaining, again developed by John Nash.
Informally, Nash’s theory simply states that two players
involved in a bargaining game will split the net gains from trade
between the two of them.
To make this concrete imagine that Tina and Becky are trying to
decide whether to quit their jobs and start a restaurant. Tina
has a relatively good job, making $30,000 each year (after
taxes), but Becky makes only $20,000. Obviously, Tina is more
reluctant to quit her job than Becky.
So Becky tries to convince her by promising more of the share
of the profit. If restaurant will make $100,000 profit, how will
the profit be split between them?
We illustrate the non-strategic answer in the picture below. If
they both agree, they earn $100k. If they cannot reach
agreement Tina earns $30 and Becky earns $20. These are
sometimes known as the “disagreement values” or
“alternatives to agreement.” <<DRAW TINA ON LEFT WITH 30
TO THE LEFT OF HER AND TINA ON THE RIGHT WITH 20 TO THE
RIGHT OF HER. PUT 100K IN THE MIDDLE OF THE TWO
PLAYERS.>>
The net gains from reaching agreement are 100-20-30=50. So
the two “split” the 50 and each earns 25 above what she would
have earned without the agreement. So Tina earns 55=30+50/2
and Becky earns 45=20+50/2.
Now imagine that Becky’s father offers to give her $10,000 to
help support the restaurant. How does this affect the
bargaining? This raises the net gains to reaching agreement
from $50 to $60, which means that Tina earns 60=30+60/2 and
Becky earns 50=20+60/2. Essentially, the extra 10,000 is split
between the two players because it makes Becky more eager to
reach agreement, so she ends up giving half of it away through
a bigger share to Tina. <<ILLUSTRATE>>
OK, what do we learn by looking at bargaining this way. First,
we learn that the alternatives to agreement determine the
terms of agreement. Since Tina had a better alternative, she
gets a bigger share than Becky.
In fact, if Tina can make her outside alternative better, she can
earn an even bigger share of the gains from trade. Similarly, if
Tina can make Becky’s outside alternative worse, she can earn a
bigger share of the gains from trade.
<<SCREEN TEXT: To improve your own bargaining position, you
must either increase your opponent’s gain or reduce your own
gain from reaching agreement.>>
In other words, each player’s willingness to compromise
determines his bargaining position. The greater the
foreseeable gain, the more willing he is to compromise, and the
weaker his bargaining position will be.
16.5. Conclusion
Bargaining can be approached from a strategic viewpoint or a
nonstrategic viewpoint.
So which should we use to analyze games. Here is the standard
professor cop-out, “it depends.” If you can