Introduction to Bargaining

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Introduction to Bargaining

• PL SC 379R
• Lecture 1

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Conflict as Bargaining

• Pure conflict is quite rare (Complete
  extermination/genocide)
• More often, states in conflict are trying to
  divide some good and cant agree on how the split
  should be made
• Bargaining is the process by which states come to
  an agreement on how to divide a good and may
  include discussions, threats, displays of force,
  or even war
• The bargaining process occurs in a state of
  anarchy(?)

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Some terms

• Bargaining is always strategic
• We assume actors are rational and therefore can
  rank preferences over outcomes
• Actors wish to avoid war because it is ex-post
  inefficient, and therefore will try using
  deterrence , or compellence
• One way of thinking about these types of
  interactions is game theory

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Game Theory

• Game theory is a way of using mathematical logic
  to model interactions between 2 or more players
• Simplest games are 2x2
• We will also use extensive form games

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Prisoners Dilemma
P2
Cooperate Defect
Cooperate
P1
Defect
6
Prisoners Dilemma
P2
Cooperate Defect
Cooperate
P1
Defect
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Prisoners Dilemma
P2
Cooperate Defect
Cooperate
P1
Defect
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Prisoners Dilemma

• No matter what P2 does, P1 is better off
  defecting. No matter what P1 does, P2 is better
  off defecting
• As long as each player can cheat, defect will
  be the dominant strategy. Therefore cooperation
  seems impossible in this game
• Bargaining obstacle how do states overcome this
  lack of trust and make agreements?

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Chicken
P2
Cooperate Defect
Cooperate
P1
Defect
10
Chicken
P2
Cooperate Defect
Cooperate
P1
Defect
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Chicken

• The game of chicken has no dominant strategy
• If P2 defects, P1 would rather cooperate. If P2
  cooperates, P1 would rather defect
• Bargaining obstacle If P1 wants to win, she
  must convince P2 that she is going to defect.
  But P2 will also be trying to convince P1 that he
  will defect

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PD Extensive Form
(5,5) (0,8) (8,0) (1,1)
C
P2
C
D
P1
C
D
P2
D
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Backwards Induction
(5,5) (0,8) (8,0) (1,1)
C
P2
C
D
P1
C
D
P2
D
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Backwards Induction
(5,5) (0,8) (8,0) (1,1)
C
P2
C
D
P1
C
D
P2
D
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Some important points

• Because actors are strategic, they do not always
  try to obtain their most preferred outcome.
  Rather, they try to obtain the most preferred
  outcome they believe is possible
• In order for a conflict to be resolved peacefully
  two things must occur
• A settlement must be found that all actors prefer
  to fighting
• A way must be found to make the agreements
  self-enforcing

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War is ex-post inefficient

• States would always be better off avoiding war
  because fighting entails costs
• If states knew ahead of time what settlement
  would be reached at the end of a war, both would
  be better off simply making this agreement
  without fighting
• There should always be a settlement that both
  sides prefer to war

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Expected Utility

• Before we can understand why there is always a
  settlement preferable to war we need a tiny
  little bit of math.
• Expected Utility
• p(win)u(win) p(loss)u(loss)
• So lets say two people are sharing a pie 50/50.
  One of the pie-eaters is thinking about starting
  a fight to get the rest of the pie. If he wins
  he gets the whole pie (if he gets beat up he gets
  nothing), and he estimates he has about a 60
  chance of winning
• .601 .400 .60
• Will he fight?
• Yes, unless there are some costs involved (bloody
  knuckles, loss of a friend, etc.)

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Bargaining Space (Fearon)
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Bargaining Space

• Any agreement that both sides prefer to war is
  referred to as bargaining space. Because costs
  are involved with fighting, there should be
  bargaining space in ALL situations
• So why do states ever fight????

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Why states fight

• Issue indivisibility. Splitting up a pie is
  easy, but what if we were bargaining over an
  ipod? What types of all or nothing examples
  exist between states?
• Private Information. Actors have incentives to
  lie about a variety of things. Genuine
  disagreements (apart from lies) may also exist
• Impossible to commit not to fight in the future.
  A state may choose to fight now because it fears
  having to fight later

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Bluffing

• If states hope to deter other states by using
  threats, the ultimate goal is to not have to
  carry the threat out. Therefore
• Leaders have incentives to bluff
• If P1 makes a threat, P2 must decide whether P1
  will carry out the threat, or whether he will
  back down. What P2 does depends on what he
  believes P1s type to be
• Game tree

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Audience Costs

• A player may signal his intentions by invoking
  costly signals
• If a (democratic) leader makes a public threat
  and then backs down, how does he appear to his
  (voting) public? What is likely to happen to
  such a leader?
• Audience Costs
• How else might states lock themselves into
  carrying out a certain action (chicken)?

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Honest Disagreements

• Each state may honestly believe that it is the
  stronger state and would win an eventual war
  (WWI)
• States may disagree about what is more important
  to victory (offensive power vs. defensive power)
• States may have different expectations about what
  will achieve victory (killing lots of the enemy
  vs. dragging the fight out into a long and costly
  process)

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Bargaining Reputation

• How a player acted in the past may indicate how
  she is likely to act in the future
• Outside observers When P1 and P2 are bargaining,
  one or both may be concerned about how P3 will
  interpret events
• Future bargaining P1 may be concerned with the
  way P2 interprets events because they will inform
  future bargaining situations

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Future conflicts

• Leaders may decide a conflict over some issue is
  inevitable, and may decide that in the future
  their relative capabilities will decline. They
  may therefore choose to fight now rather than
  fight (or make large concessions later)
• How can states lock themselves into a course of
  non-violence in the future (prisoners dilemma)?