Chapter-4 - Chapter 4: Nash Equilibrium Chicken Game...

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Chapter 4: Nash Equilibrium Chicken Game - Two cars facing each other in duel-like fashion. - Cars come hurtling towards one another: each driver decides whether to avoid a collision or hang tough. This game is played by movie executives, nation leaders, … Chicken Game - Two cars facing each other in duel-like fashion. - Cars come hurtling towards one another: each driver decides whether to avoid a collision or hang tough. This game is played by movie executives, nation leaders, … Driver 2 Driver 1 2,2 1,3 3,1 0,0 Swerve Hang tough Swerve Hang tough
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Nash Equilibrium Neither player has a strictly dominated strategies. John Nash – Beautiful Mind Nash equilibrium uses a different way to pin down players’ belief about others. Neither player has a strictly dominated strategies. John Nash – Beautiful Mind Nash equilibrium uses a different way to pin down players’ belief about others. 1. Players are rational : Each player's strategy maximizes his payoff given his beliefs as to the strategies used by the other players. 2. Beliefs are correct : Each player's beliefs as to the strategies used by the other players coincide with the actual strategies used by those players. 1. Players are rational : Each player's strategy maximizes his payoff given his beliefs as to the strategies used by the other players. 2. Beliefs are correct : Each player's beliefs as to the strategies used by the other players coincide with the actual strategies used by those players.
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Nash Equilibrium A strategy profile is a Nash equilibrium if each player’s strategy maximizes his or her payoff given the strategies used by the other players. Defined: With n players, then there are n conditions. All players are simultaneously doing their best, or playing best responses to others’ strategies. The strategy profiles under Nash equilibrium are stable: each player is content to do what she is doing given what everyone else is doing. With n players, then there are n conditions. All players are simultaneously doing their best, or playing best responses to others’ strategies. The strategy profiles under Nash equilibrium are stable: each player is content to do what she is doing given what everyone else is doing.
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Chicken Game Is ( tough, tough ) a Nash equilibrium? - Given player 1 plays tough , player 2’ best response is to play swerve . Not a NE. Is ( swerve, swerve ) a Nash equilibrium? - Given player 1 plays swerve , player 2’s best response is to play tough . Not a NE. Is ( tough, swerve ) a Nash equilibrium? - Given player 1 plays tough , player 2’s best response is swerve . Player 2 has no incentive to deviate. - Given Player 2 plays swerve , player 1’s best response is to play tough . Player 1 has no incentive to deviate.
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Chapter-4 - Chapter 4: Nash Equilibrium Chicken Game...

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