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21.08.2017

Nash Equilibrium

Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. A game may have multiple Nash Equilibria or none at all.

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It is considered one of the most important concepts of Game Theory, which attempts to determine mathematically and logically the actions that participants of a game should take to secure the best outcomes for themselves. The reason why Nash Equilibrium is considered such an important concept of Game Theory relates to its applicability. The Nash Equilibrium can be incorporated into a wide range of disciplines, from economics to the social sciences.

Lecture 4 - 7-(Game Theory) - Subgame Perfect Equilibrium (7-43)

Every player wins because everyone gets the outcome they desire. If no one changes his strategy, then the Nash Equilibrium is proven. For example, imagine a game between Tom and Sam. The outcome A, A represents a Nash Equilibrium. In this game, two criminals are arrested and each is held in solitary confinement with no means of communicating with the other. The prosecutors do not have the evidence to convict the pair, so they offer each prisoner the opportunity to either betray the other by testifying that the other committed the crime or cooperate by remaining silent.

If both prisoners betray each other, each serves five years in prison. If A betrays B but B remains silent, prisoner A is set free and prisoner B serves 10 years in prison, or vice versa.

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If each remains silent, then each serves just one year in prison. The Nash equilibrium in this example is for both players to betray each other.

Pooling equilibrium

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