Personality Enhancement Program (PEP I

Infinity Business School

Personality Enhancement Program
(PEP I)
Neeraj Batra / Session 01

PEP I Infinity Business School

Prisoners Dilemma
Imagine Angie & Bert Caught In A Theft
Separated By The Police To Seek Confession
The Police Motivate Defection With Leniency
The Theoretical Options Can Be:
They both co-operate with each other (i.e don’t confess)
This is referred as (C,C)

One of them co-operates,the other defects (i.e rats on the other)
This is referred as (C,D)

They both rat on each other, i.e they both defect
This is referred as (D,D)


Prisoners Dilemma

If The Punishment Matrix (also called the Payoff) is as follows:

DC (0,10) means the first guy gets 0 years,the second guy 10 years
CC (1,1) means each of them gets 1 year
DD (4,4) means each of them gets 4 years
CD (10,0) means the first guy gets 10 years,the second guy 0 years
This is referred to as the Payoff Matrix
In Order of Preference For Each Of Them DC > CC > DD > CD
Defection Is Thus A Dominant Strategy in The Prisoners Dilemma
In A Symmetrical Game the Equilibrium Lies at DD
Nash's Equilibrium


Key Terminology in Prisoners Dilemma

DC is called the Temptation Payoff : The payoff for taking the
temptation to Defect on your partner

CC is called the Reward or Mutual Payoff : The payoff for co-
operating with your partner

DD is called the Punishment Payoff : The payoff for defecting on your
partner who defects similarly

CD is called the Suckers Payoff : The payoff for cooperating when
your partner is defecting
Symmetric Games are games in which the order of the players
action does not cause any dynamic change in the payoff matrix



Prisoners Dilemma

Lets Look At The Payoff Matrix For Angie & Bert

Option 1 Option 2 Option 3 Option 4

Angie C D C D
Bert C D D C
Angies Punishment (Payoff) 1 4 10 0
Berts Punishment (Payoff) 1 4 0 10
Total Punishment (Payoff) 2 8 10 10


The Rational Choice

In the traditional prisoners dilemma, the exasperating conclusion
any rational prisoner faces is that there is really no choice but to
defect. Considering what the other person might do, for each case,
your best option (less time in jail) is to defect. Of course, your
partner comes to the same conclusion. The net result is a situation
that is inferior to the situation you would get if both cooperated.


PEP I Outcomes & Strategies
Various Infinity Business School

Theoretically you can draw up 24 Payoff Matrices of various ranking
combinations for a 2 x 2 game.
However only 6 Payoff Matrices would make logical sense to exist. These
are as follows:

1 CC > CD > DC > DD Co-operation is better
2 CC > DC > CD > DD Co-operation is better
3 CC > DC > DD > CD Tit for Tat works : Stag Hunt Strategy
4 DC > CC > CD > DD Reverse Strategy is better: Chicken
5 DC > CC > DD > CD Defection Works: Prisoners Dilemma
6 DC > DD > CC > CD Defection works best: Deadlock Strategy

Out of the above, only 3,4,5 & 6 qualify for any strategy in which
Defection gives better results. Thus either DC > CC or DD > CD or both
must happen otherwise there is no incentive to defect.
Clearly Payoff matrices 1 and 2 are out in this case


The Variants of Prisoners Dilemma

1 STAG is PD with Reward reversed
CC > DC > DD > CD
with Temptation payoff
CHICKEN is PD with Punishment
2 DC > CC > CD > DD
reversed with Sucker payoff

3 DC > CC > DD > CD This is the Prisoners Dilemma

DEADLOCK is PD with Punishment
4 DC > DD > CC > CD
reversed with Rewards payoff



The Chicken Strategy

Angie and Bert are driving cars
Coming from opposite directions
One who swerves first is the chicken.
Best payoff is:
DC > CC > CD > DD



The Stag Strategy
There are two hunters & 2 games:
A RABBIT AND A DEER.
Chances of getting the deer independently:
NEXT TO ZERO
The deer meat will be shared :
75:25 in favour of one who snare the deer
CO-OPERATION  50:50 TO EACH.

Best payoff is
CC > DC > DD > CD



Common Examples from real life

The Fire:
A club has a fire, and all rush for the exits, preventing the exit of
anyone; as a result, all perish.

The Concert:
At a concert, Amit stands on his toes to see the performer better. The
person behind Amit is forced to stand, and the effect ripples
throughout the auditorium. Soon all are standing, and no one has a
better view than they would have had in a sitting position, except that
now they must stand versus sit.




Ragging:
No one likes being ragged. You get butterflies when you visit
college on the first day. However you were ragged as a fresher.
Thus, you must act the senior for retribution and to maintain
“tradition” and ragging continues indefinitely.

Steroids:
Athlete A uses steroids, which gives him a competitive advantage.
Other athletes are forced to use steroids to retain parity. As a result,
no athlete is given a competitive advantage, but all are subjected to
the hazards of steroids.




Free Email:
A leading provider of email services starts providing free email to
gain market share and very soon so does everyone else leaving
neither with a competitive advantage. Soon all email service
providers go belly up.

Cell Phone Operators:
A cell phone operator cuts the pulse rate to pull new subscribers,
almost thereafter so does all his competitors thereby bringing all rates
down and poaching each others clients. Ultimately each company
swaps each others clients but none are better off in number than
before leaving them greatly poorer.




Celebrity Endorsements:
A leading soft drink manufacturer uses the heart throb hero to promote
their cola over a competitor, very soon the competitor gets another hero
to do the same. The heroes are paid Rs 10 Mn each leaving both
companies that much poorer.



Prisoners Dilemma
Business Example – Zero Sum Game

Here is an example of a zero-sum game. It is a very simplified
model of price competition. Assume two Cola companies have a
fixed cost of Rs 5 Mn per period, regardless whether they sell
anything or not. We will call the companies Pepsi and Coke, just to
take two names at random.

The two companies are competing for the same market and each
firm must choose a high price (Rs 20 per bottle) or a low price
(Rs10 per bottle). Here are the rules of the game:



Prisoners Dilemma

1) At a price of Rs20, 500,000 bottles can be sold for a total revenue of Rs10
Mn
2) At a price of Rs10, 1,000,000 bottles can be sold for a total revenue of Rs
10 Mn
3) If both companies charge the same price, they split the sales evenly
between them.
4) If one company charges a higher price, the company with the lower price
sells the whole amount and the company with the higher price sells
nothing.
5) Payoffs are profits -- revenue minus the Rs 5 Mn fixed cost.



Prisoners Dilemma

Here is the payoff table for these two companies

Payoff Table

Pepsi
Price Rs.10 Rs.20
Rs.10 0,0 5 Mn, -5Mn
Coca cola
Rs.20 -5 Mn, 5 Mn 0,0



Prisoners Dilemma

This is a zero-sum game.For two-person zero-sum games, there is a
clear concept of a solution. The solution to the game is the maximum
criterion -- that is, each player chooses the strategy that maximizes her
minimum payoff. In this game, Coke’s minimum payoff at a price of
Rs10 is zero, and at a price of Rs20 it is –5 Mn, so the Rs10 price
maximizes the minimum payoff. The same reasoning applies to Pepsi,
so both will choose the Rs10 price.

Here is the reasoning behind the maximum solution: Coke knows that
whatever it loses, Pepsi gains; so whatever strategy it chooses, Pepsi
will choose the strategy that gives the minimum payoff for that row.
Again, Pepsi reasons conversely.



Prisoners Dilemma
Price Competition Example
Think of two companies selling "bottles" at a price of one, two, or three rupees
per bottle. The payoffs are profits -- after allowing for costs of all kinds -- and
are shown in the table below. The general idea behind the example is that the
company that charges a lower price will get more customers and thus, within
limits, more profits than the high-price competitor.

Table (Payoff in Mns)
Pure Life Bottles
P=1 P=2 P=3
P=1 0,0 50,-10 40, -20
Green
P=2 -10,50 20, 20 90, 10
Bottles
P=3 -20,40 10, 90 50, 50



Prisoners Dilemma
Price Competition Example

We can see that this is not a zero-sum game. Profits may add up to
100, 20, 40, or zero, depending on the strategies that the two
competitors choose. We can also see fairly easily that there is no
dominant strategy equilibrium.

Green Bottles company can reason as follows: if Pure Life Bottles
were to choose a price of 3, then its best competitive price is 2, but
otherwise Green Bottles best price is 1 , thus there is no dominant
strategy.



Prisoners Dilemma
Games with Multiple Nash Equilibria
Two crisp manufacturers (LAYS and KOOL) have to choose prices for their
packs. There are three possible prices: Rs 8 (LOW), Rs 10 (MED) or Rs 12 (HI).
The audiences for the three prices are 50 Mn, 30 Mn, and 20 Mn, respectively. If
they choose the same prices they will split the audience for that market equally,
while if they choose different prices, each will get the total customer base for
that price band. Market shares are proportionate to payoffs. The payoffs (market
shares) are in the Table below:
Table (Market Shares)
KOOL
LOW MED HI
LOW 20, 25 50, 30 50, 20
LAYS MED 30, 50 15, 15 30, 20
HI 20, 50 20, 30 10, 10


Prisoners Dilemma

You should be able to verify that this is a non-constant sum game, and that
there are no dominant strategy equilibria. If we find the Nash Equilibria by
elimination, we find that there are two of them -- the upper middle cell and
the middle-left one, in both of which one station chooses LOW and gets a
50 market share and the other chooses MED and gets 30 (Hint: These have
the highest total payoff). But it doesn't matter which company chooses
which format.

It may seem that this makes little difference, since
• the total payoff is the same in both cases, namely 80
• both are efficient, in that there is no larger total payoff than 80



Prisoners Dilemma

There are multiple Nash Equilibria in which neither of these things
is so. But even when they are both true, the multiplication of
equilibria creates a danger. The danger is that both stations will
choose the more profitable LOW format -- and split the market,
getting only 25 each! Actually, there is an even worse danger that
each station might assume that the other station will choose LOW,
and each choose MID, splitting that market and leaving each with a
market share of just 15.



Prisoners Dilemma

More generally, the problem for the players is to figure out which
equilibrium will in fact occur. In still other words, a game of this
kind raises a "coordination problem:" how can the two companies
coordinate their choices of strategies and avoid the danger of a
mutually inferior outcome such as splitting the market? Games
that present coordination problems are sometimes called
coordination games.
From this point of view, we might say that multiple Nash
equilibria provide us with a possible "explanation" of coordination
problems. That would be an important positive finding, not a
problem!



Prisoners Dilemma
Multiple Players: The Queuing Game

Many of the "games" that are most important in the real world
involve considerably more than two players.

In this sort of model, we assume that all players are identical,
have the same strategy options and get symmetrical payoffs. We
also assume that the payoff to each player depends only on the
number of other players who choose each strategy, and not on
which agent chooses which strategy.



Prisoners Dilemma
As usual, let us begin with a story. We suppose that six people are
waiting at the ration queue, but that the clerks have not yet arrived at
the counter to serve them. Anyway, they are sitting and awaiting their
chance to be called, and one of them stands up and steps to the office
to bribe and be the first in the queue. As a result the others feel that
they, too, must bribe to get ahead in the queue, and a number of people
end up bribing when they could all have been honest.



Prisoners Dilemma
Here is a numerical example to illustrate a payoff structure that might lead to
this result. Let us suppose that there are six people, and that the gross payoff
to each passenger depends on when she is served, with payoffs as follows in
the second column of Table X. Order of service is listed in the first column.
Table X
Order served Gross Payoff Net Payoff
First 20 18
Second 15 13
Third 13 11
Fourth 10 8
Fifth 9 7
Sixth 8 6


Prisoners Dilemma

The Gross payoffs are however before the bribe. There is a two-point
bribe reduction for a participant. These net payoffs are given in the
third column of the table.
Those who do not bribe are chosen for service at random, after those
who stand in line have been served. If no-one bribes, then each person
has an equal chance of being served first, second, ..., sixth, and an
expected payoff of 12.50 In such a case the aggregate payoff is 75.
But this will not be the case, since an individual can improve her
payoff by bribing, provided she is first in line. The net payoff to the
person first in line is 18 >12.5, so someone will get up and bribe.



Prisoners Dilemma

This leaves the average payoff at 11 for those who remain. Since the
second person in line gets a net payoff of 13, someone will be better off
to get up and bribe for the second place in line.
third person in line gets a net payoff of 11, someone will be better off
to get up and bribe for the third place in line.
fourth person in line gets a net payoff of 8, which is less than the
payoff of 9, there is no further incentive for anyone to bribe the clerks
and we reach the game’s Nash’s equilibrium.



Prisoners Dilemma

The total payoff is 69, far less than the 75 that would have been the
total payoff if, somehow, the bribing could have been prevented.
Two people are better off -- the first two in line -- with the first gaining
an assured payoff of 5.5 above the uncertain average payoff she would
have had in the absence of queuing and the second gaining 0.5. But the
rest are worse off. The third person in line gets 12, losing 1.5; and the
rest get average payoffs of 9, losing 3.5 each. Since the total gains
from bribing are 6 and the losses 12, we can say that, in one fairly
clear sense, bribing is inefficient.



Prisoners Dilemma

We should note that it is in the power of the authority (the ration, in this
case) to prevent this inefficiency by the simple expedient of not
respecting the bribe and increasing transparency of queuing. If the
clerks were to ignore the bribe and, let us say, pass out lots for order of
service at the time of their arrival, there would be no point for anybody
to bribe, and there would be no effort wasted by queuing (in an
equilibrial information state).
This is a representation of an asymmetrical model of Prisoners
dilemma.



Prisoners Dilemma
The Marketing Game

4 Companies play for market share by Co-operating on pricing i.e. Do
Not Undercut Competitors Vs Defecting Undercut Competitors. The
Payoff Matrix for the Game is as follows.:

Round 01 :
(4Cs 12,12,12,12)
(2Cs, 2Ds 10,15)
(4Ds 9, 9, 9, 9)
(3Cs, D 10,10,10,20)
(C, 3Ds 10,12)


Prisoners Dilemma
The Marketing Game

Round 03 :
(4Cs 12,12,12,12)
(2Cs, 2Ds 11,11)
(4Ds 11,11,11,11)
(3Cs, D 11,10)
(C, 3Ds 12,10)

Round 05 :
(C & D Combination) 12,14
All Cs 13 each
All Ds 11


Prisoners Dilemma
Some other points

A+B =A+B+A’B’ (Synergy Effect)
Example Wolves Pack : Hunting/Opec

Nash’s Equilibrium is the point where neither player can
unilaterally improve his position any further.

In most one round games DD is the Nash’s Equilibrium



Prisoners Dilemma
Some other points

To increase rounds or “lengthen the shadow of future” there are several
techniques used such as : Arms control (phased destructions)

To get Co-operation phased extension of country loans by IMF

In intense cardinal payoffs co-operation can be given huge payoffs e.g. if
China adheres to the WTO guidelines it gets an MFN status

Anti-dumping duties is another effective way of discouraging defection



Prisoners Dilemma
Some other points

Improving communication and information exchange can increase co-
operation

By reducing transaction costs/inefficiencies co-operation can be
institutionalized (Payoff matrix) History plays a key role in the key
players strategy.

Trust plays a key role in key players strategy

The payoff matrix plays a key role in key players strategy



Prisoners Dilemma

THE FOUR RULES

Rule No 1 : THE GOLDEN RULE
DO UNTO OTHERS AS YOU WOULD HAVE
THEM DO UNTO YOU
(Repay Even Evil With Forgiveness- Jesus Christ)
(BUT If You Repay Evil With Kindness, With What
Will You Repay Kindness?)



Prisoners Dilemma

THE FOUR RULES

Rule No. 2: THE SILVER RULE

DO UNTO OTHERS WHAT YOU WOULD NOT
HAVE THEM DO UNTO YOU
(Martin King Luther/Mahatma Gandhi)
(Principle of Non Co-operation)



Prisoners Dilemma

The Four Rules

Rule No. 3: THE BRONZE RULE
DO UNTO OTHERS AS THEY DO UNTO YOU
(Repay Kindness With Kindness, Evil With Justice -
Confucius)
LEX TALIONIS PRINCIPLE
What Happens To Two Wrongs Don’t Make A Right ?


PEP I
PEP I

Prisoners Dilemma

The Four Rules
Rule No. 4 : THE IRON RULE
DO UNTO OTHERS AS YOU LIKE BEFORE THEY DO
UNTO YOU
(The Power Rule, Provided You Can Get Away With It)
Leads to Inconsistency : Suck Up to those Above, Exploit
Those Below


Personality Enhancement Program (PEP I

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