1. GAME THEORY

2. Game Theory - Introduction
 The decision-making process in situations where
outcomes depend upon choices made by one or
more players.
 The word "game" describes any situation
involving positive or negative outcomes
determined by the players' choices and, in some
cases, chance.

3. Game Theory - Evolution
 1921 - Emile Borel, a French mathematician, published
several papers on the theory of games using poker as an
example.
 1928 - John Von Neumann published his first paper on
game theory in 1928, is made it popular.
 1944 – Theory of games and Economic Behavior by John
von Neumann and Oskar Morgenstern is published.
 1950 – Prisoner‟s Dilemma is introduced, introducing the
dominant strategy theory.
 1953 – Solution to non-cooperative games was provided
with the evolution of the Nash Equilibrium.
 1970 – Extensively applied in the field of biology with the
development of „evolutionary game theory‟.
 2007 – Used in almost all the fields for decision making
purposes, including the software to track down the
terrorists.

4. Game Theory - Assumptions
 Each player is rational, acting in his self-interest;
 The players' choices determine the outcome of
the game, but each player has only partial control
of the outcome;
 Each decision maker has perfect knowledge of
the game and of his opposition;

5. Game Theory - Classification
 Single Player v Multi Player Games
 Co-operative v Non-Cooperative Games
 Symmetric v Asymmetric Games
 Zero-sum v Non-Zero-sum Games
 Simultaneous v Sequential Games
 Perfect Information v Imperfect Information

6. Single Player Game – Games
against Nature
 The outcome and the player‟s payoff depends on both
his chosen strategy and the “choice” made by a totally
disinterested nature.
 A Game Against Nature part of what is generally
called decision theory (rather than game theory)
because there is only one player who makes a
rational choice and is interested in the outcome.

7. Multi Player Games - Examples
 Prisinor‟s Dilemma
 Travellers‟ Dilemma
 Battle of the Sexes
 Diners‟ Dilemma
 Rock, Paper, Scissors!!!

8. Prisoners‟ Dilemma
 Both the prisoners are more likely to defect
irrespective of what the other prisoner does, even
though it gets them a sub-optimal output.
 If they were allowed to communicate and reach a
consensus, then they could have reached the optimal
output.
Prisoner B stays silent Prisoner B confesses
(cooperates) (defects)
Prisoner A stays silent Prisoner A: 1 year
Each serves 1 month
(cooperates) Prisoner B: goes free
Prisoner A confesses Prisoner A: goes free
Each serves 3 months
(defects) Prisoner B: 1 year

9. Battle of the Sexes
 A couple had agreed to meet in the evening but
had not agreed on the venue and cannot
communicate now.
 They can either go to the opera or the football
match.
 Their pay-off matrix can be Football by –
Oper given
a
Opera 3,2 1,1
Football 0,0 2,3

10. Diners‟ dilemma
 It is a n-person‟s prisoners‟ dilemma.
 A group of individuals go out to dine together.
 They agree that they will split the cheque equally
between them.
 Each individual must now decide whether to order
the cheaper dish or the expensive one.
 It is presumed that the exensive dish is better
than the cheaper ones but the price differential is
not justified.

11. Diners‟ dilemma - Consequences
 Each individual reasons that the expense which
they add to their bill while ordering the more
expensive item is very low.
 Hence, they justify the cost to experience the
improved dining experience.
 However, each individual reasons similarly, and
thus they all end up paying for a more expensive
dish.
 By assumption, this is worse than each of them
ordering and paying for the cheaper dish.

12. Rock, Paper, Scissors!!!
 It is a two-player zero-sum game.
 No matter what a person decides, the
mathematical probability of his winning, drawing,
or losing is exactly the same.
 The dominant strategy to this game seems to
exists, which is why the same person end up in
the merit roll of the championships held around
the world every year.
Child 2
rock paper Scissors
rock 0,0 -1,1 1,-1
Child 1 paper 1,-1 0,0 -1,1
scissors -1,1 1,-1 0,0

13. Travellers‟ Dilemma
 Case designed by Dr. Kaushik Basu in 1994.
 Each traveller can value there belongings for
anything between $2 and $100.
 They will be reimbursed the lower value of the
two claims.
 The lower claimant will be rewarded with
additional $2 while the higher claimant will be
charged $2.

14. Travellers‟ Dilemma - Paradox
 The rational strategy for the travellers would be to
claim the lower value, i.e. $2.
 In reality, people chose $100, which resulted
them in being better-off financially.
 This experiment rewards people for deflecting
from the Nash Equilibrium and act non-rationally.
 This has led people to question the practicality of
the game theory.
 Subsequently, the idea of „super-rationality‟ was
developed under this, which stated that under
pure strategies $100 is the optimal solutioin for
the problem.

15. Strategies
 Dominant Strategy – a strategy which dominates
irrespective of what the other player does.
 Maximax Strategy – The player looks to maximize the
maximum pay-off that he may stand to gain from the
game.
 Minimax Strategy – The player looks to maximize the
minimum payoff that he receives.
 Collusion – When both players decide to co-operate to
maximise their total output.
 Tit for tat – A player reacts to the opponents actions by
following it, i.e deflection followed by deflection.
 Backward Induction – The player derives his strategies by
working the most likely strategy of his opponent and then
working backwards.
 Markov Strategy – A strategy through which a player
decides his actions based only on his present
state, ignoring the past states.

16. Nash Equilibrium
 It is a solution concept of a game involving two or
more players, in which each player is assumed to
know the equilibrium strategies of the other
players, and no player has anything to gain by
changing only his own strategy unilaterally.
 If each player has chosen a strategy and no
player can benefit by changing his or her strategy
while the other players keep theirs
unchanged, then the current set of strategy
choices and the corresponding payoffs constitute
a Nash equilibrium.
 It does not necessarily mean the best pay-off for
all the players involved although it might be
achieved as is the case with cartels.

17. Bibliography
 www.economist.com
 www.kaushikbasu.org
 www.wikipedia.com
 www.stanford.edu