Game Theory and Social
Simulation
Gilberto Câmara, Earth System Science Center, INPE
Licence: Creative Commons By Attribution Non Commercial Share Alike
http://creativecommons.org/licenses/by-nc-sa/2.5/
Acknowledgments for using previous material
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Martin Nowak (Harvard University, USA)
Francisco C. Santos (Université Libre de Bruxelles, Belgium)
Craig Callender (Philosophy, Univ California San Diego, USA)
Ana Aguiar (INPE, Brazil)
Tiago Carneiro (Federal University of Ouro Preto, Brazil)
Guy Brasseur (NCAR, USA)
Game Theory
GT is an analytical tool for social sciences that is used to model
strategic interactions or conflict situations.
Strategic interaction: When actions of a player influence payoffs to
other players
Game Theory
Explanation: What is the game to be played?
Prediction: What outcome will prevail?
Advice or prescription: Which strategies are likely to yield good results
in which situations?
Where can we use Game Theory?
Any situation that requires us to anticipate our rival’s response
to our action is a potential context for GT.
Economics, Political science, Biology
What is a Normal Form Game?
Players: list of players
Strategies: all actions available to all players
Payoffs: a payoff assigned to every contingency (every possible
strategy profile as the outcome of the game)
John Kennedy and Nikita Khrushchev
Modeling two-party games
Payoffs for each player depend on actions of both
Two possible strategies: A party cooperates when he performs
value-increasing promises, and defects when he breaches
Modeling choice in non-cooperative games
Player 2
Cooperate
Cooperate
Player 1
Defect
Defect
Player 1
Both cooperate cooperates,
Player 2 defects
Player 1
defects, Player
2 cooperates
Both defect
Silvio Santos e o jogo do “Sete e Meio”
Dois jogadores se enfrentam na TV.
Se dois jogarem “meio”, cada um ganha R$ 14 mil.
Se um jogar “sete” e o outro “meio”, o primeiro ganha R$ 112
mil e outro não ganha nada
Se os dois jogarem “sete”, não ganham nada.
Prisoners’ Dilemma
Two suspects are caught and put in different rooms (no
communication). They are offered the following deal:
1. If both of you confess, you will both get 3 years in prison
2. If you confesses whereas the other does not, you will get 1
year and the other gets 5 years in prison .
3. If neither of you confess, you both will get 2 years in prison.
The “chicken game”
“Rebel without a cause”
Two persons drive their cars towards a cliff. They must stop or both may
die in the fall. The one that stops first will be called a "chicken," meaning a
coward.
The hawk-dove game (== chicken game)
Two individuals compete for a resource (In biological terms, its value increases in the
Darwinian fitness of the individual who obtains the resource)
Hawk
Initiate aggressive behaviour, not stopping until injured or until one's
opponent backs down.
Dove
Retreat immediately if one's opponent initiates aggressive behaviour.
Maynard Smith and Price, "The logic of animal conflict“ (Nature, 1973 )
The hawk-dove game (== chicken game)
Encyclopedia Britannica
The stag-hunt game: conflict between safety
and social cooperation
Two hunters want to kill a stag. Success is uncertain and, if it comes,
require the efforts of both. On the other hand, either hunter can forsake
his partner and catch a hare with a good chance of success.
The stag-hunt game: conflict between safety
and social cooperation
C
D
C
10,10
0,6
D
6,0
5,5
Rousseau, in A Discourse on Inequality:
“If it was a matter of hunting a deer, everyone well realized that he must
remain faithful to his post; but if a hare happened to pass within reach of
one of them, we cannot doubt that he would have gone off in pursuit of it
without scruple..."
Generalizing...
Cooperation requires at least two individuals:
A: the one providing cooperation (DONOR)
B: the one benefiting from cooperation (RECEIVER)
Donor has a cost c to cooperate
and confers a benefit b to other
player
C
D
C
b–c
-c
D
b
0
you
Payoff matrix
other
Terminology
Player 2
T = Temptation to defect
R = Reward for mutual cooperation
P = Punishment for mutual defection
S = Sucker's payoff
Generalizing...
Payoff matrix
R: mutual cooperation
other
P: mutual defection
C
D
C
R(1)
S(-c)
D
T(b)
P(0)
S : sucker’s payoff
T : temptation to defect
you
Taking R = 1 and P = 0
Generalizing...
Payoff matrix
R: mutual cooperation
opponent
P: mutual defection
C
D
C
1
S
D
T
0
S : sucker’s payoff
T : temptation to defect
you
Taking R = 1 and P = 0
Different ordering -> Different tensions
greed
C D
C R S
D T P
fear
Chicken game
T >1 > S > 0
Stag-hunt game
1>T > 0 > S
Prisoner’s dilemma
T >1 > 0 > S
(Macy&Flache, PNAS 2002)
Spatial Prisioner´s Dillema
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Nowak and May considered a large lattice with each cell occupied
by one player. The players engage in one round of the Prisoner’s
Dilemma game against each of their neighbors.
Afterward, the next generation is formed: each cell is taken over by
a copy of the highest-scoring strategy within the neighborhood.