GAME THEORY
Introduction , Human behavior
What is Game Theory ?
■ Game Theory is a way of thinking
about strategic interactions between
self-interested people
■ And also How those interactions
should be structured
What do I mean to play a
game?
■ Sets of actions that players can take
and after everybody has chosen what
they are going to do in the game, there
is some result where everybody feels a
level of happiness
The Prisoner's Dilemma
■ Two members of a criminal gang are
arrested and imprisoned. Each prisoner
is in solitary confinement with no means
of communicating with the other.
Simultaneously, the prosecutors offer
each prisoner a bargain. Each prisoner is
given the opportunity either to: betray
the other by testifying that the other
committed the crime, or to cooperate
with the other by remaining silent.
The offer is:
■ If A and B each betray the other, each
of them serves 2 years in prison
■ If A betrays B but B remains silent, A
will be set free and B will serve 3 years
in prison (and vice versa)
■ If A and B both remain silent, both of
them will only serve 1 year in prison
(on the lesser charge)
So what would you do if you
were one of these criminals?
Would you betray?
I will give you a piece of paper.
Write letter ‘D’ if you would
betray and ‘C’, otherwise.
Nash Equilibrium
■ Neither player has an incentive to
change strategy, given the other
player’s choice
■ The life story of game theorist and
mathematician John Nash was turned
into the biopic A Beautiful Mind
■ Here, regardless of what the other
decides, each prisoner gets a higher
reward by betraying the other
("defecting")
■ Mutual defection is the only
strong(pure) Nash equilibrium in the game
■ Since both "rationally" decide to defect,
each receives a lower reward than if both
were to stay quiet
More Details
■ Rational behavior among players
 Players have a common interest to make the
payoff as large as possible, but
 Players have competing interests to maximize
their own payoff.
 A player’s rational decisions require anticipating
rivals’ responses
 These expectations are not perfect, so
uncertainty is a necessary feature of games
Player types
■ Optimists (20 percent), who always go for
the highest payoff, hoping the other
player will coordinate to achieve that goal;
■ Pessimists (30 percent), who act
according to the opposite assumption;
■ The Envious (21 percent), who try to score
more points than their partners;
■ The trustful (17 percent), who always
cooperate.
■ The remaining 12 percent appeared to
make their choices completely at random.
Question
■ Is there a game with no (pure) Nash
equilibrium?
■ In sequential games, where players
know each other's previous behavior
and have the opportunity to punish
each other, what is dominant strategy?
Sequential Games
■ In sequential games, where players
know each other's previous behavior
and have the opportunity to punish
each other, defection is the dominant
strategy as well.
Sequential Games (cont’d)
■ If the game is played exactly N times
and both players know this, then it is
always game theoretically optimal to
defect in all rounds. The only
possible Nash equilibrium is to always
defect.. The same applies if the game
length is unknown but has a known
upper limit.