1. PRISONER’S DILEMMA BERK EROL
«to confess or not to confess»»
13/12/2016

2. GAME THEORY
The study of mathematical models of conflict and cooperation between intelligent rational decision-makers.
Mainly used in economics & business, political science, biology, psychology, philosophy, computer science & logic.
Umbrella term for the science of logical decision making in humans, animals, and computers.
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3. GAME TYPES Cooperative / Non-cooperative Symmetric / Asymmetric
A game is cooperative if the players are able to form alliances.
Symmetric / Asymmetric
In a symmetric game, payoffs depend only on the other strategies not on the players.
Zero-sum / Non-zero-sum
In zero-sum games, a player benefits only at the equal expense of others.
Simultaneous / Sequential
In sequential games, players have some prior knowledge about earlier actions.
Perfect information / imperfect information
A game is one of perfect information if all players know all previous moves of others.
Others
Combinatorial, infinitely long, discrete/continuous, differential, population, pooling games
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4. PRISONER’S DILEMMA
Shows why two completely "rational" individuals might not cooperate, even if it appears that it is in their best interests to do so.
Characteristics: non-cooperative, symmetric, non-zero-sum, simultaneous, imperfect information.
It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950.
Albert W. Tucker formalized the game with prison sentences payoffs and named it, "prisoner's dilemma".
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5. FORMAL PRESENTATION
Two members of a criminal gang are arrested and imprisoned.
No communication between them (imperfect information).
Lack of sufficient evidence.
Simultaneously, the prosecutors offer each prisoner a bargain.
Each prisoner have 2 opportunities: cooperate or betray
Prisoner B cooperates
Prisoner B betrays
Prisoner A cooperates
Each serves 1 year
Prisoner A: 3 years Prisoner B: goes free
Prisoner A betrays
Prisoner A: goes free Prisoner B: 3 years
Each serves 2 years
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6. GENERALIZED FORM R: cooperation reward P: punishment payoff
T: temptation payoff
S: sucker’s payoff
T > R > P > S
Cooperate
Betray
R, R
S, T
T, S
P, P
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7. R > P T > R and P > S So the dilemma is
For the overall situation, mutual cooperation is superior to mutual defection.
T > R and P > S
From an individual perspective, rational outcome is defection.
So the dilemma is
Mutual cooperation yields a better outcome but it is not rational at the individual level.
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8. ITERATED PRISONER’S DILEMMA
The same two players play more than once in succession and they remember previous actions of their opponent and change their strategy accordingly.
Requires: 2R > T + S
To prevent alternating cooperation and defection giving a greater reward than mutual cooperation.
The Evolution of Cooperation (1984) by Robert Axelrod
Tournament of the N step prisoner’s dilemma (with N fixed) for which he invited academic colleagues to devise computer strategies.
Winning strategy in Axelrod’s tournament: Tit for Tat
Cooperate on the first iteration then repeat the opponent’s last action.
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9. NECESSARY CONDITIONS FOR A SUCCESSUL STRATEGY BY AXELROD
Nice (optimistic)
Not defect before its opponent does.
Retaliation
Not always cooperation but also sometimes retaliation.
Forgiving
Fall back to cooperating if the opponent does not continue to defect.
Non-envious
Not striving to score more than the opponent.
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10. REFERENCES https://en.wikipedia.org/wiki/Prisoner's_dilemma
dilemma/