Structured negotiation reduces stress and removes the guess work

1. Presentation by:
Alexander Carter-Silk
THE SCIENCE OF NEGOTIATION
IPTC Group

2. Game Theory: Its all bunkum !
• John Von Neuman Mini Max Strategies
• John Nash Nobel Prize for Mathematics
• Spence – “ Signalling”
• Joseph Stilling Insurance Behaviour”
(screening)
• Leonid Hurwicz Nobel Prize for economics
• Erik Maskin Nobel Prize
• Roger Myeson Nobel Prize
• Schelling
“In the British 3g Telecoms Auction, Ken Binmore devised a
games strategy which parted the telco’s from $35bn, it was
described by Newsweek as the most ruthlessly effective
strategy ever deployed in an auction….”

3. Game Strategies
• The Cortez Strategy
• Solomon's Dilemma
• Prisoner’s dilema
• Battle of the Sexes
• Chicken Zero Sum game
• Rousseau the Hunter’s Paradox
• The Tragedy of the Commons

4. Ordinal Values & Revealed Preferences
• Does transparency always produce the
optimal outcome?
• Threats and Brinkmanship
• Contracts
• Reputation
• Cutting off communication
• Moving in steps
• Screening
• Team work and alliances
• Negotiating Agents

5. TERMINOLOGY
THE GAME:
OPTIMAL PAYOFF:
RATIONAL SELF INTEREST V. ALTRUISMS:
IMPERFECT KNOWLEDGE PERCEPTION v. KNOWLEDGE
CO-OPERATIVE v. NON-CO-OPERATIVE:
UTILITY PREFERENCE AND INDIFFERENCE:
ORDINAL VALUES & THE CHAIN OF INEQUALITIES
THE NASH EQUILIBRIUM :
DOMINANT STRATEGIES NON-DOMINANT STRATEGIES
UNCERTAIN OR IMPROBABLE:

6. CO-OPERATE OR DEFECT
• There are two players, Row and Column.
• Each has two possible moves,
• “cooperate” or “defect,” corresponding, respectively,
to the options of remaining silent or confessing.
• For each possible pair of moves, the payoffs to Row and
Column
• R is the “reward” payoff that each player receives if
both cooperate.
• P is the “punishment” that each receives if both
defect.
• T is the “temptation” that each receives if he alone
defects and
• S is the “sucker” payoff that he receives if he alone
cooperates.

7. Chain of Inequalities
Symmetric 2×2 PD With Ordinal Payoffs
In its simplest form the PD is a game described by the payoff matrix:
D/C = 4/1 C= the sucker bet
C D
DD = 1/1
DD =The wasteland
C R, R S, T
CC = 2/2
D T, S P, P CC = Non-optimal for both
parties but better than DD
satisfying the chain of inequalities:
PD1) T>R>P>S
Temptation, Reward, Punishment, Sucker

8. Game 1: Co-operate or Dominate?
• There is a prize of £1,500.00 to share between
the three teams within one minute all of the
teams must reach agreement
• Three participants have one minute to reach
their optimal conclusion
• The participants must not communicate their
desired or optimal pay-off
• Each individual should work towards his/her
optimal payoff.
• If no agreement is reached, the participants
share the payout, if no agreement is reached
each participants get nil (The worst outcome)

9. The Hunter’s Paradox
Stag Bison Rabbit
Stag 3 0 1
3
0 0
Bison 0 3 1
0
0 3
Rabbit 0 0 1
1 1 1

10. Dominant Strategy
• The worst outcome (non optimal) is that there is no
agreement.
• If my choice is less than the aggregated desired payoffs of
the other two participants then I can achieve my pay off by
making an open bid
• Assuming uneven payoff aspirations by other participants
each greater than 500 any bid above 0 is a strategy achieves
better than the worst payoff.
• With an opening bid of anything above 500 the opposing
parties must assume that the bid is irrational.
• Multiple parties create co-operation amongst groups
(contracts) to improve the probability of an optimal outcome.
• Multiple games which limits the scope for aggression/
defection by the minority.

11. Game 2 Strategies for Co-Operation
• Each of the participant must choose a number
between 1 and 100,
• The number chosen must the same as that
chosen by the other participants.
Each participant must consider the choice
which each of the others will choose.
That choice must be one which each of the
other participants can rationally consider to be
the most likely to be chosen by a group which
are determined to co-operate.

12. Game 3: Best Response
• Each participant is to pick a number
between 0 and 100 there is a £100 prize
for the player whose number is closest to
half the other person’s number.
• Some possible dominant strategies
– 50
– 25
– 12.5
–0
• What number will you choose and why?

13. Predictable behaviour Screening
• There are three types of credit card borrower Max
Payers Revolvers and Deadbeats
• The task was to devise a strategy (dominant) which
screened out max payers and dead beats
• The answer was the transfer balance option why?
– The Revolvers don’t pay interests
– The Deadbeats have no intention of paying back
– The max payers benefit from zero interest on
balances and rare the most profitable
• The strategy has screened out the undesirable card
holders.

14. Rational v Altruistic
• Two parties begin with equal positions (Ordinal
symmetry) an altruistic strategy will provide a
better pay off for than a strategy of RATIONAL
SELF INTEREST
• One party begins with and Altruistic Strategy and
the other with a RATIONAL SELF INTEREST, the
party employing the RATIONAL SELF INTEREST
will usually dominate.

15. RATIONAL V. IRRATIONAL
• When one party is motivated by a desire to
defeat the opponent rather than minimise risk
or optimise payoff
• The probability of success is increased (the
willingness to take the risk of losing).
• The IRRATIONAL dominates the
RATIONAL

16. Probability and Lottery Litigation!
• For any given “state”, there is exists a finite
number of outcomes.
• Some of those outcomes are “unlikely”
• For any given “utility” for each player there is a
probability that one or more strategies will
dominate.
• For any number of players with given
combinations of utility and a given number of
games there are a limited number of outcomes
which are possible

17. The Bridge: Deterrent or Provocation
• Two cars approach a narrow bridge from
opposite directions only one may pass at a
time. This requires one car to wait. If both
cars enter the bridge simultaneously neither
may pass.
• If the cars alternate then both pass but one
must wait.
• If both drivers value time (t) equally then
either both will lose time or one must act
“altruistically” and let the other pass. Both
improve, but the one who has acted
altruistically gets a less than optimal
outcome.
”

18. Compromise or Co-Operate
• Compromise is not an option it serves neither party,
aggression might succeed but now it risks being
matched with aggression in which case neither party
optimises his out come.
• Both parties do better if one acts altruistically aggression
is rewarded, one party must give up his “rational self
interest.
• With equal ordinal values and a zero sum game one
party must give way to achieve a Nash equilibrium.
• There are two equilibriums A gives way to B and B gives
way to A the alternative is the worst outcome for both.

19. Perception: Rational v Irrational
• The Defender’s perceives that he has a
defensible but not impenetrable position
• The Aggressor has an inferior position or force.
• The Defendant’s perception of the Aggressor's
tenacity and commitment is material in his (the
Defender’s) decision to defend or concede

20. Cortez
• The Spanish Conqueror Cortez landed in Mexico
with a small group of soldiers. To demonstrate that
he was committed to victory or nothing, he burnt
his ships (no retreat)the Aztecs walked away from
the fight.
• Knowledge and perception are not necessarily
the same
• The Incas rationalised that if Cortez were willing to
fight to the last man, then the best outcome (the
dominant strategy) would be to surrender rather
than face much greater losses inflicted by an
implacable enemy

21. Threats and Promises
• The best strategic response to a threat of a
worst outcome will depend not upon any
assessment as to whether the worst
outcome=most likely outcome but whether it
is perceived that the threat will be carried out.
• Is the outcome a zero sum game.
• If it is not a zero sum game is there more
than one possible outcome which represents
an equilibrium out come.

22. Threats and Promises
• Clarity Certainty
– Distinguish between compelling and
punishing
– Object of a threat is to change behaviour
– Object of promise is to reward an optimal
outcome
– Is the threat credible.
– Earlier performance is rewarded
– Threat Late performance is punished.
• Risk proportionate to the threat, increasing the
risk. Change the threat or change the rules of
the game

23. Multiple Games – Infinite Games
• If the first game is repeated, several times the dynamics change. The
altruistic party will learn that he always loses and may therefore adopt a
learnt behaviour strategy.
• Thus
– Move 1 = P1 Cooperates P2 Defects (and crosses the bridge)
– Move 2 = P1 Defects P2 also Defects and his outcome is less than it
was in move 1.
– Move 3 = P1 Defects again P1 Co-operates he passes second but
does better than he did in move 2
– Move 4 = Two possible nodes P1 Defects (this leads to P2 defecting
or P1 co-operates and P2 learns that alternate co-operation defection
strategies are not ideal but give the best outcome

24. Multiple Finite Games
• The game proceeds much as our previous example except the
probability of co-operation now changes. Assume a finite
number of games N such that for (N-1) the probability of co-
operation decreases.
• In this game the party who wishes to optimise his position will
consider defecting as the number of games counts down. This
party knows;
– He cannot rely on co-operation from the other party as the
temptation of increasing the optimal outcome exceeds the
probable benefit of co-operation.
– Each party has increased his “utility” from co-operation
throughout the “game” and therefore his propensity for risk
is increased towards the end of the games. The highest
probability on the last move is that both parties will defect
– The increased probability of defection towards the end of
the game decreased the effect of “learnt” behaviour.

25. Imperfect Knowledge
• If both parties have different states of knowledge then their
propensity to defect or co-operate are different and the probability of
any particular outcome occurring is skewed.
• The party with the greater knowledge will not necessarily
increase his reward from the game.
• One can express this variation as
• OPPOSITION >INDIFFERENCE<PREFERENCE
• If P1 knows that P2 has a pressing desire to cross the bridge at all
costs he may enforce co-operation but in the sequence P1 before
P2. P2 needs to cross the bridge but recognises that getting across
the bridge more slowly gives him a better outcome than ending in a
DEFECT/DEFECT scenario.
• Unless P2 knows P1’s preference the probable outcome is skewed
against the party with the dominant preference and P1’s strategy will
dominate.

26. Prisoners Dilemma –
Tanya and Cinque have been arrested for robbing the Hibernia
Savings Bank and placed in separate isolation cells. Both care
much more about their personal freedom than about the welfare of
their accomplice. A clever prosecutor makes the following offer to
each.
“You may choose to confess or remain silent.
If you confess and your accomplice remains silent I will drop all
charges against you and use your testimony to ensure that your
accomplice does serious time.
Likewise,
If your accomplice confesses while you remain silent, they will go
free while you do the time.
If you both confess I get two convictions, but I'll see to it that you
both get early parole.
If you both remain silent, I'll have to settle for token sentences on
firearms possession charges. If you wish to confess, you must
leave a note with the jailer before my return tomorrow morning.”

27. Rational Self Interest
• The “dilemma” faced by the prisoners here is that, whatever
the other does, each is better off confessing than remaining
silent. But the outcome obtained when both confess is worse
for each than the outcome they would have obtained had both
remained silent.
• In a multi-player generalizations model familiar situations in which it is
difficult to get rational, selfish agents to cooperate for their common good.
• When multiple games are played with multiple the PD (Prisoners
Dilemma) is weakened because groupings can develop where one or
more opponents moves to co-operate can be anticipated…The social
network develops….
• The “co-operative outcome is generally only obtainable where every player
violates rational self interest

28. The Art of War (Sun Tzu 500BC)
• Only fight a battle you can win.
• Aggression is only a viable option when one has overwhelming force
against a vulnerable opponent
• In the absence of overwhelming force manoeuvrability and position is
critical.
• Know your opponent, identify his weaknesses, without knowledge you
cannot manoeuvre safely.
– Seek knowledge; Even casual conversation will reveal valuable
intelligence
– Take the initiative; Remove the opponents key arguments early,
often considered the art of deception.
– Plan the surprise; Make a conscious decision when to play a key
card
– Gain relative superiority; Making the equal unequal, identify the
opponents perceptions and change them
– Be flexible; Accept that as negotiations develop positions change
adapt to them change and absorb

29. Observations
• In a single game, the highest probability is that Rational
Self Interest will succeed over Altruism. (the aggressor
will dominate the game).
• In a multiple game the party with the greatest demand
for a specific outcome is actually WEAKER than the
party with no strong dominant preferences.
• Indifference leads to equal probability of highly beneficial
outcomes but equally leads to the potential for poor utility
returns.
• In multi-game scenarios it is most probable that the
parties will weakly dominate on alternate moves and that
sequential co-operation will occur leading to less than
optimal outcomes for both parties.
• In games with imperfect knowledge and different
preferences solving for the optimal strategy may depend
on third party forces.

30. Creating Co-operation Agreements
• In a multiplayer situations contracts will be formed, these may
be enduring or may change.
• Example: I an office the partners are trying to decide whether
to buy a piece of artwork. You are strongly pro purchase and
ranged against you have people with the following preferences.
– Strongly preferential (want to buy)
– Highly opinionated and strongly preferential against
– Strongly Opposed
– Indifferent
– Wavering
• Which group of people represent your best allies and why?

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