BARGAINING
AND
BARGAINING TACTICS
Topics #10-11
A Generalized Chicken Game
• Bargaining tactics may be used by P1 to induce P2 to “Give In,”
– so that P1 can safely “Stand Firm.”
– Obviously P2 can use similar tactics.
• Some bargaining situations (like the Game of Chicken) are
essentially symmetric, but others clearly are not,
– e.g., hostage holders vs. authorities.
Example of Bargaining Situations
(a) General bargaining situations: players have
–
–
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
a common interest in reaching an agreement but
conflicting interests with respect to what particular agreement to
reach.
An actual chicken game
A hostage-holding situation
(Small) child-parent bargaining
Buyer-seller (e.g., of a house) bargaining
Labor-management collective bargaining
The first Berlin Crisis (blockade and airlift), 1948
The second Berlin Crisis (leading to Berlin Wall), 1959-61 =>
The Cuban Missile Crisis (1962)
–
In his speech of October 22, 1962, President Kennedy declared that “our
unswerving objective” is to get Soviet missiles removed from Cuba.
(j) The general U.S.-S.U. cold war conflict and nuclear balance
(k) Other international conflicts
Checkpoint Charlie, Berlin, October 1961
Checkpoint Charlie, Berlin, November 10, 1989
Credible Commitment
• P1 somehow makes an credible commitment to stand firm.
– The first player to make a credible commitment to “stand
firm” wins.
– If it is possible to make such a commitment,
• it is essential to disclose this to the other player
immediately,
• before he can make a similar commitment.
• Realistically, it is impossible to make such an absolute and
irrevocable commitment.
• Therefore attention focuses on tactics (pre-play
communications and strategic moves) that enhance the
credibility of commitments.
– Schelling, Arms and Influence, Chapter 2, “The Art of
Commitment”
Pre-Play Communications
• P1 can send messages that
• project an image of P1 to P2, or
• convey to P2 P1’s (claimed) image of P2.
– P1 can project an image that suggests P1 is crazy,
irrational, emotional, and uncalculating and generally that
P1 doesn’t understand the risks of standing firm.
– This has been called the “rationality of irrationality” or “the
political uses of madness” [Daniel Ellsberg]
• (a) P1 tries to appear to be a “force of nature,” so the
only reasonable response by P2 is to give in and
minimize damage.
• (a) P1 exhibits (apparently) erratic, emotional, selfdefeating, irrational behavior
• (b) P1 get into his car (apparently) stumble-down
drunk
Pre-Play Communications (cont.)
– (c) terrorists, escaped prisoners, and most criminals have an inherent
bargaining advantage over the authorities in this respect
– (d) the child throws a deliberate temper-tantrum [“strategic
screaming”]
– (g) Mr. K’s [Soviet leader Nikita Khrushchev] “shoe-thumping” and
other incidents
– Note: such tactics can be dangerous, as they give P2 an incentive to
engage in preventive or pre-emptive action.
• P1 attributes rationality (and perhaps cowardice) to P2,
claiming P2 understands the risks of standing firm
– (g) Mr. K to JFK: “only a madman would fight a nuclear war over
Berlin – and I don’t think you’re mad. (But can you be sure I’m
not mad — remember my “shoe-thumping” and other erratic
behavior?)”
Pre-Play Communications (cont.)
• Messages designed to influence the perceived (not the actual)
values of payoffs W, C, L, or P.
– P1 can convey the impression that he regards P1 is not so bad,
so maybe P1 is no worse than L1, which implies that P1 believes
that standing firm is a dominant strategy (and thereby compels
P2 to give in).
• (b) P1 claims that his car is crash-proof.
•
•
•
•
•
– Note: P1 does not have to persuade P2 that P1’s car is crashproof, only that P1 believes that it is crash-proof.
(c) The hostage holders claim that martyrdom is a ticket to
heaven (so P may really be their best outcome, not worst).
(d) The child says “I don’t even want any dessert [so you can’t
make me eat my vegetables].”
(e) The buyer/seller hides the fact that he is very anxious to
buy/sell.
(f) The union/company releases a report purporting to show that
they can readily survive a long strike/lockout.
(j) P1 releases a study showing that his civil and other defensive
preparations are so effective that P1 can survive nuclear war.
Pre-Play Communications (cont.)
• P1 can convey the impression that he regards L1 as worse
than it really is, so again maybe P1 is no worse than L1,
which again implies that P1 believes that standing firm is a
dominant strategy (and thereby compels P2 to give in).
– (b) P1 claims that he believes that to be revealed as “chicken” is
a fate worse than death.
– (c) The hostage holders reveal that they believe that they are
already under a death sentence (e.g., for prior criminal
convictions).
– (e) The buyer conveys the impression that his “reservation
price” (the highest price he would actually be willing to pay) is
lower than it actually is.
– (e) The seller conveys the impression that his “reservation
price” (the lowest price he would actually be willing to take) is
higher than it actually is.
– (f) The company reveals that it believes it would go out of
business of it gave in to union wage demands.
Pre-Play Communications (cont.)
• P1 tries to persuade P2 that C2 is as good as W2, so that P2
will believe that giving in is P2’s dominant strategy, and that
P1 can therefore safely stand firm.
– (a) P1 assures P2 that “this is my last demand” — it is not costly for
you to give in and it won’t set a precedent for the future [but see
below on reputation effects].
– (c) Child to parent: “Let me have this treat just this once — I won’t
ask for it again.”
– (k) Hitler at Munich
Pre-Play Communications (cont.)
• P1 conveys the impression that he believes P2’s preferences
are such that C2 is as good as W2 and that giving in is therefore
P2’s dominant strategy, so P1 can safely stand firm.
– (b) P1 conveys the impression that he believes that P1
doesn’t care if he is revealed to be “chicken.”
– (e) The seller conveys impression that he believes that
the buyer’s reservation price is high.
– (e) The buyer conveys impression that he believes that
the seller’s reservation price is lower.
– (f) The union conveys impression that it believes that
management can easily pay higher wages.
A Different Prime Minister Projecting a
Different Image
Strategic Moves
A strategic move actually changes the payoff values W, C, L, or P.
• P1 changes actual payoff values for P2 so that “giving in” is
more attractive (perhaps even dominant) for P2.
– P1 takes actions to increase the value C2, i.e., makes concessions to P2.
• Note: a problem with this strategic move is that, not only are the
concessions (presumably) coming out of P1’s pocket (reducing the
value C1), but also that P1 may look too anxious to avoid P1, so that it
seems safer for P2 to stand firm and aim to get W2.
– P1 takes actions to increase the value of L2, e.g.,
– to provide P2 with a “graceful exit” [“no invasion” pledge in
Cuban Missile crisis]
– to avoid seeking “unconditional surrender” [Allied WWII war
goals?]
– to promise to treat surrendering forces humanely, etc.,
• thereby
– making giving in more palatable to P2,
– which makes it safer for P1 to stand firm,
– further reinforcing P2’s incentive to give in.
Strategic Moves (cont.)
• P1 changes actual payoff values for himself so that “standing
firm” is evidently more attractive (and perhaps actually
dominant) for P1.
– P1 must take care that such changes are evident to P2.
– P1 visibly takes actions that increase the value of P1 (i.e.,
make mutual disaster less disastrous for himself).
• (b) P1 actually puts effective safety devices in his car.
• (e) The buyer/seller looks around for other willing sellers/buyers.
• (f) The union builds up strike fund or enters into swap agreement
with other unions.
• (f) The company builds up inventories.
• (j) The U.S. (or S.U.) actually invests in a massive civil defense
program (or ABM system).
Strategic Moves (cont.)
• Less obviously and more perversely, P1 visibly takes actions
that reduce the value of L1 (making it most costly for P! to
“give in”).
• Sometimes “weakness can be [bargaining] strength.”
– (b) P1 brings all his friends (and maybe enemies too) to
watch the chicken game.
– (c) Given numerous hostages, the hostage holders kill
one or a few (but definitely not all) of them,
• so that they must expect a worse penalty if they give in and
are captured.
• [The hostage holders are also “decomposing their threat.”]
• (k) P1 “burns his bridges behind him,” so that he (or his
soldiers) can’t retreat and must either fight (“stand firm) or
be killed or captured.
Strategic Moves: Reducing L2 (cont.)
• (f) Union leaders arouse expectations among members (“If
we don’t get you a 20% wage boost, you should kick us out of
office”)
• (g) U.S. puts lightly armed 5,000 troops in Berlin.
– Also see below on “trip wires” and “the threat that leaves something
to chance.”
• (k) Israel builds settlements on West Bank, so that it
becomes more difficult for them to make future territorial
concessions
• (k) The U.S. President is negotiating a treaty with another
country, which makes a demand the President doesn’t want
concede to: his bargaining power is enhanced if he can say “I
sorry, but my hands are tied; if I make this concession, I’ll
never be able to get the treaty we both want ratified by the
Senate
• “two-level games” and the “Schelling Conjecture”
Strategic Moves: Reputation Effects
• One move of this type is especially important: P1 can invest
his long-term reputation in the outcome of the present
bargaining situation,
• thereby (greatly) reducing the value of L1, possibly to the point
that L1 is worse than P1.
– “If I give in on the issue, everyone will expect me to give on other
issues, so it is clearly in my long-term interests to stand firm now, even
if that means getting the worst payoff P1 in the short-run.”
– Such reputation effects may be powerful even if P1 does not
deliberately enhance them.
– Reputation effects make a “this is my last demand” ploy by P2 less
likely to succeed.
• (b) If P1 plays chicken regularly (and his future opponents are
watching) while P2 does not, P1 cares more about his reputation
and has the stronger incentive to stand firm, and P1 knows this.
• (h) JFK’s speech of 10/22/62: Soviet offensive missiles in Cuba
“cannot be accepted by this country if our courage and our
commitments are ever to be trusted again by either friend or foe.”
The “Last Clear Chance” to Avoid
Mutual Disaster
• Consider the game of “Discrete Chicken” displayed below.
– It is played sequentially (with perfect information).
– The players move in alternating terms.
– At each move, a player has two choices:
• advance one additional (“discrete”) step toward the other player (i.e.,
continue to “drive straight”), or
• to stop advancing (or step off the board, in any event to “swerve”).
– The payoffs are the same as in standard “2 x 2 Chicken.”
• What will happen?
The “Last Clear Chance” (cont.)
• Nothing dramatic will happen -- the game is perfectly safe
(unless one of the players is entirely irrational).
• The winner of the game is determined not by skill or by
nerves of steel but by these two factors:
• which player moves first, and
• whether the number n of discrete steps (boxes) between the
players at the outset is odd or even.
– If n is odd (as below), the first moving player wins
– If n is even, the second moving player wins.
The “Last Clear Chance” (cont.)
• These two factors determine which player has the “last clear chance” to
avoid mutual disaster (see Schelling, Arms and Influence, pp. 44ff).
– Note that “Sequential Chicken” (Topic #6, last slide) has n = 1 = odd, so the
first mover has the advantage.
• Note also that “real chicken” is a “continuous” game,
– i.e., the cars do not advance towards one another in discrete alternating
steps.
– Thus it is unclear who has the “last clear chance” to avoid collision,
• which is what make the game dangerous and a test of nerves
• Note also that that the “Classic 2x2 Game of Chicken” payoff matrix is
discrete,
– i.e., players a single choice to either “drive straight” or “swerve.”
– What makes this dangerous is simultaneous (rather than sequential) choice.
• Lesson: in a bargaining situation each player may try to displace onto the
other player the “last clear chance” to avoid mutual disaster (by “giving
in”).
Strategic Moves: Irrevocable Commitment
• A strategic moves may actually and irrevocably commit P1 to
stand firm, by eliminating “giving in” as a feasible option.
• See Schelling, Arms and Influence, Chapter 2 [“The Art of Commitment”]
and
• Dixit and Nalebuff, Chapter Six (“Credible Commitments.”)
– Such an irrevocable commitment displaces clearly onto P2 the “last
clear chance” to avoid mutual punishment by giving in.
– It is of course very important for P1 to make sure that P2 sees what P1
has done.
(a) P1 appoints an instructed agent to negotiate with P2; the agent has no
authority to make substantial concessions and cannot communicate with
P1
(b) P1 locks his steering wheel in the “straight ahead” position and throws
key out the window.
Irrevocable Commitment (cont.)
•
The Hostage-Holding Game: The bargaining power of the hostage
holders derives from the fact that they can kill the hostages.
– This fact sustains their deterrent threat against the authorities:
•
–
It may also sustain their compellent threat against the authorities:
•
–
If you move in to capture us and/or free the hostages, we will kill the
hostages.
If you do not release our comrades from prison (or whatever their
demand is), we will kill the hostages.
But if and when the hostage holders carry out this threat, they lose
all of their bargaining power, and the authorities can move in and
capture them
•
so will they really carry out the threat?
(c) The hostage holders can rig up a trip-wire system that is visible to the
authorities, such that an attempt by authorities capture them or free the
hostages will trigger an automatic killing of the hostages.
–
This can sustain the hostage holders’ deterrent threat but not their
compellent threat.
Post-WWII Germany
Irrevocable Commitment (cont.)
(g) U.S. troops in West Berlin served a “trip-wire” function:
– If the Soviets were to attack West Berlin and kill or
capture the U.S. soldiers, U.S. decision makers would be
politically compelled to dispatch reinforcements to West
Berlin and thereby risk general war.
– So the Soviets knew that a military move against West
Berlin (which would certainly be successful, even with
U.S. troops there) would carry a real risk of general war.
– On the other hand, if all U.S. troops had been stationed in
West Germany (rather than West Berlin), the U.S. would
have to make the decision that would risk general war in
the event of a Soviet move on West Berlin.
The Ultimate Trip Wire: A “Doomsday Machine”
(h) The US (or SU) might install a
“Doomsday Machine” that would
automatically destroy the world
if SU’s (or US’s) missiles ever
strike US (or SU) territory.
– Herman Kahn proposed such a
“Doomsday Machine” as a thought
experiment, exemplifying
• a perfect “Type I Deterrent” but
highly flawed otherwise (and not
just morally).
– In the Dr. Strangelove movie, the SU
installs such machine
• but makes the mistake of not
immediately announcing what it
has done.
Strategic Moves to Avoid the “Last Clear
Chance” Dilemma
(a) P1 makes a pre-emptive commitment (to deter P2 from
making his own irrevocable commitment)
(a) P1 “decomposes” the execution of his threat to inflict
punishment on P2 (i.e., the threat is carried out gradually)
(c) To sustain a compellent threat, the hostage holders
announce they will kill one hostage a day until authorities give
in to their demands.
(e) A strike or lockout is really the decomposed execution of a
threat,
–
–
because collective bargaining continues as each side inflicts gradually
increasing punishment on the other.
Remember the Dollar Auction Game (from Topic #2, Playing Games).
Post-WWII Germany
The Berlin Blockade and Airlift, 1948-49
• The Soviets placed barricades and
soldiers across the roads and
railway lines leading from West
Germany to Berlin, thereby
– forcing (they thought) the western
Allies to choose between capitulation
or shooting their way through the
barricades and
– they (correctly) anticipated that the
Allies would not be willing to start
shooting.
• The creative (and costly but
ultimately successful) western
response was the airlift,
– which forced the Soviets to acquiesce
or to start shooting down Allied
planes, and
– the Allies (correctly) anticipated that
the Soviets would not be willing to
start shooting.
A “Threat That Leaves Something Chance”
• See Schelling, Arms and Influence, Chapter 3 (“The
Manipulation of Risk”).
• This means that P1 says to P2:
– If you don’t give in, I may or may not carry out my threat
to inflict mutual punishment on us — but whether it is
carried out or not will be determined, not by my own
choice (I know that I will always have an incentive to
renege on carrying out my threat), but by a chance
mechanism that I am now setting in motion.
• It is more credible
– that P1 will set such a random mechanism going than
– that P1 would deliberately chose to carry out a mutually
punitive threat.
Threat That Leaves Something Chance (cont.)
(c) To sustain a compellent threat, a single hostage holder with a
single hostage (for whom a decomposed threat is not
feasible) announces the following:
–
–
–
–
–
he will put one bullet in his gun,
spin the bullet chamber,
aim the gun at the hostage, and
pull the trigger, and
repeat this process once a day until the authorities give in to his demands.
(g) U.S. troops in West Berlin more realistically served as a trip
wire that would generate (in the event of a Soviet move on
West Berlin)
(g) not the certainty of escalation leading to general (even nuclear) war (an
outcome the U.S. would be extraordinarily reluctant to choose deliberately)
but rather
(h) a substantial risk of escalation leading to general (even nuclear) war (that
neither the US nor the SU could confidently control ).
Threat That Leaves Something Chance (cont.)
(j) One (of many) drawbacks of a “doomsday machine” is that it
is totally unforgiving in the event of accidental missile firings;
– perhaps a doomsday machine should trigger a random
mechanism that would destroy the world with some
positive probability much less than 1.
– Of course, if the doomsday machine were tested in some
accidental incident and if it did not destroy the world [to
the huge relief of everybody, including the side that
installed it], the other side might speculate as to whether
the whole thing is a bluff.
Threat That Leaves Something Chance (cont.)
(k) Probably the best simple model of intense international
conflict is Discrete Chicken with this added element:
– In each move, players can either stay where they are or
advance or retreat in discrete steps.
– Between the moves of each player, “Nature” uses a
random device to decide whether to blow up the world,
where the probability that Nature will blow up the world
•
•
•
is zero if the players remain at opposite ends of the board,
increases as the players get closer to one another, and
is at a maximum (but still less than certainty) if the players collide (i.e.,
occupy the same position on the board).
– Note that neither has the “last clear chance” to avoid
blowing up the world.