BARGAINING AND BARGAINING TACTICS

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BARGAINING ANDBARGAINING TACTICS

• Topics 10-11

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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.

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Example of Bargaining Situations

• (a) General bargaining situations players have
• 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
• (d) (Small) child-parent bargaining
• (e) Buyer-seller (e.g., of a house) bargaining
• (f) Labor-management collective bargaining
• (g) The first Berlin Crisis (blockade and
  airlift), 1948
• (h) The second Berlin Crisis (leading to Berlin
  Wall), 1959-61 gt
• (i) 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

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Checkpoint Charlie, Berlin, October 1961
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Checkpoint Charlie, Berlin, November 10, 1989
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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

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Pre-Play Communications

• P1 can send messages that
• project an image of P1 to P2, or
• convey to P2 P1s (claimed) image of P2.
• P1 can project an image that suggests P1 is
  crazy, irrational, emotional, and uncalculating
  and generally that P1 doesnt 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, self-defeating, irrational behavior
• (b) P1 get into his car (apparently)
  stumble-down drunk

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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. Ks 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 dont think
  youre mad. (But can you be sure Im not mad
  remember my shoe-thumping and other erratic
  behavior?)

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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 P1s
  car is crash-proof, 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 dont even want any
  dessert so you cant 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.

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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.

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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
  P2s 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 wont 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 wont ask for it again.
• (k) Hitler at Munich

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Pre-Play Communications (cont.)

• P1 conveys the impression that he believes P2s
  preferences are such that C2 is as good as W2 and
  that giving in is therefore P2s dominant
  strategy, so P1 can safely stand firm.
• (b) P1 conveys the impression that he believes
  that P1 doesnt care if he is revealed to be
  chicken.
• (e) The seller conveys impression that he
  believes that the buyers reservation price is
  high.
• (e) The buyer conveys impression that he
  believes that the sellers reservation price is
  lower.
• (f) The union conveys impression that it
  believes that management can easily pay higher
  wages.

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A Different Prime Minister Projecting a Different
Image
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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 P1s 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 P2s incentive to give in.

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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).

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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) cant retreat and must
  either fight (stand firm) or be killed or
  captured.

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Strategic Moves Reducing L2 (cont.)

• (f) Union leaders arouse expectations among
  members (If we dont 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 doesnt want concede to his bargaining
  power is enhanced if he can say I sorry, but my
  hands are tied if I make this concession, Ill
  never be able to get the treaty we both want
  ratified by the Senate
• two-level games and the Schelling Conjecture

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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) JFKs 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.

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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?

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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.

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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).

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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.
• P1 appoints an instructed agent to negotiate with
  P2 the agent has no authority to make
  substantial concessions and cannot communicate
  with P1
• P1 locks his steering wheel in the straight
  ahead position and throws key out the window.

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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
• If you move in to capture us and/or free the
  hostages, we will kill the hostages.
• It may also sustain their compellent threat
  against the authorities
• 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?
• 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.

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Post-WWII Germany
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Irrevocable Commitment (cont.)

• 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.

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The Ultimate Trip Wire A Doomsday Machine

• (h) The US (or SU) might install a Doomsday
  Machine that would automatically destroy the
  world if SUs (or USs) 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.

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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)
• P1 decomposes the execution of his threat to
  inflict punishment on P2 (i.e., the threat is
  carried out gradually)
• To sustain a compellent threat, the hostage
  holders announce they will kill one hostage a day
  until authorities give in to their demands.
• 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).

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Post-WWII Germany
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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.

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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 dont 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.

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Threat That Leaves Something Chance (cont.)

• 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.
• 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)
• 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
• a substantial risk of escalation leading to
  general (even nuclear) war (that neither the US
  nor the SU could confidently control ).

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Threat That Leaves Something Chance (cont.)

• 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.

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Threat That Leaves Something Chance (cont.)

• 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.