Game Theory and Social Simulation

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Game Theory and Social Simulation

• Gilberto Câmara, Earth System Science Center, INPE

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Acknowledgments for using previous material

• 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)

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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

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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?

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Where can we use Game Theory?

• Any situation that requires us to anticipate our
  rivals response to our action is a potential
  context for GT.
• Economics, Political science, Biology

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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
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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

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Modeling choice in non-cooperative games
Player 2
Cooperate Defect
Cooperate Both cooperate Player 1 cooperates, Player 2 defects
Defect Player 1 defects, Player 2 cooperates Both defect
Player 1
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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.
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Prisoners Dilemma

• Two suspects are caught and put in different
  rooms (no communication). They are offered the
  following deal
• If both of you confess, you will both get 3 years
  in prison
• If you confesses whereas the other does not, you
  will get 1 year and the other gets 5 years in
  prison .
• If neither of you confess, you both will get 2
  years in prison.

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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.
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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 )
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The hawk-dove game ( chicken game)
Encyclopedia Britannica
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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.
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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..."
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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
you
Payoff matrix
other
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Terminology
Player 2
T Temptation to defect R Reward for mutual
cooperation P Punishment for mutual defection
S Sucker's payoff
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Generalizing...
Payoff matrix
R mutual cooperation P mutual defection
S suckers payoff T temptation to
defect
other
you
Taking R 1 and P 0
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Generalizing...
Payoff matrix
R mutual cooperation P mutual defection
S suckers payoff T temptation to
defect
opponent
you
Taking R 1 and P 0
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Different ordering -gt Different tensions
greed fear
Chicken game Stag-hunt game
Prisoners dilemma
T gt 1 gt S gt 0
1 gt T gt 0 gt S
T gt 1 gt 0 gt S
(MacyFlache, PNAS 2002)
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Spatial Prisioners Dillema

• Nowak and May considered a large lattice with
  each cell occupied by one player. The players
  engage in one round of the Prisoners 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.