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What is the difference between Nash equilibrium and Pareto Efficiency. Can you give me an example where Nash equilibrium is not Pareto Optimal?

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Nash Equilibrium (N.E) is a general solution concept in Game Theory. N.E is a state of game when any player does not want to deviate from the strategy she is playing because she cannot do so profitably. So, no players wants to deviate from the strategy that they are playing given that others don't change their strategy. Thus, it is a mutually enforcing kind of strategy profile.

'Pareto optimality' is an efficiency concept. So no state will be Pareto Optimal if, at least one of the players can get more payoff without decreasing the payoff of any other player. There are many many examples of Nash Equilibria which are not pareto optimal. The most famous example could be the N.E in prisoner's dilemma.

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