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X-Machines for Agent-Based Modeling: FLAME Perspectives
TABLE 6.4: Difference between Nash equilibrium and evolutionary stable
state.
Nash Equilibrium
(John Forbes Nash) Game theory, explains a concept in a
game involving more than one player. If players have chosen
a certain strategy and no player will gain anything (in its
payoff) by changing its strategy, the players have attained
Nash equilibrium.
Evolutionary Stable State
(John Maynard Smith) Evolutionary game theory, for a
given set of behaviors (conserved over time), there must be
a profitable action in common, such that no other mutant
(or new) behavior enters the system at the time. In a game
description, if n-players are playing various strategies they
adopt one such strategy which is profitable to everyone,
such that no other new strategy can be adopted by any
player at that time.
6.6 Learning in an Iterated Prisoner’s Dilemma Game
The prisoner’s dilemma (PD) game is being used in game theory to depict
situations of competition or cooperation among players. The game is defined
as a non-zero sum game indicating that whenever one player benefits the other
player suffers penalties. The players do not have any knowledge of what the
other player might play thus this make it a non-cooperative game.
A classical form of the prisoner’s dilemma (PD) game is described.
Two suspects are arrested by the police. The police have insufficient
evidence for a conviction, and, having separated both prisoners, visit
each of them to offer the same deal. If one testifies (defects from the
other) for the prosecution against the other and the other remains silent
(cooperates with the other), the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both
prisoners are sentenced to only six months in jail for a minor charge. If
each betrays the other, each receives a five-year sentence. Each prisoner
must choose to betray the other or to remain silent. Each one is assured
that the other would not know about the betrayal before the end of the
investigation. How should the prisoners act? [150]
X-Machines for Agent-Based Modeling: FLAME Perspectives
TABLE 6.4: Difference between Nash equilibrium and evolutionary stable
state.
Nash Equilibrium
(John Forbes Nash) Game theory, explains a concept in a
game involving more than one player. If players have chosen
a certain strategy and no player will gain anything (in its
payoff) by changing its strategy, the players have attained
Nash equilibrium.
Evolutionary Stable State
(John Maynard Smith) Evolutionary game theory, for a
given set of behaviors (conserved over time), there must be
a profitable action in common, such that no other mutant
(or new) behavior enters the system at the time. In a game
description, if n-players are playing various strategies they
adopt one such strategy which is profitable to everyone,
such that no other new strategy can be adopted by any
player at that time.
6.6 Learning in an Iterated Prisoner’s Dilemma Game
The prisoner’s dilemma (PD) game is being used in game theory to depict
situations of competition or cooperation among players. The game is defined
as a non-zero sum game indicating that whenever one player benefits the other
player suffers penalties. The players do not have any knowledge of what the
other player might play thus this make it a non-cooperative game.
A classical form of the prisoner’s dilemma (PD) game is described.
Two suspects are arrested by the police. The police have insufficient
evidence for a conviction, and, having separated both prisoners, visit
each of them to offer the same deal. If one testifies (defects from the
other) for the prosecution against the other and the other remains silent
(cooperates with the other), the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both
prisoners are sentenced to only six months in jail for a minor charge. If
each betrays the other, each receives a five-year sentence. Each prisoner
must choose to betray the other or to remain silent. Each one is assured
that the other would not know about the betrayal before the end of the
investigation. How should the prisoners act? [150]