Lecture 3-Centipede-game.pdf - HE3002 Game Theory Lecture 3 Dynamic Games of Complete Information(The Centipede Game(Semester 1 AY 2019\/20 1\/3 The

Lecture 3-Centipede-game.pdf - HE3002 Game Theory Lecture 3...

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HE3002: Game Theory Lecture 3: Dynamic Games of Complete Information (The Centipede Game) (Semester 1, AY 2019/20) 1 / 3
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The Centipede Game: Backstory Money currently inside Bag X: Money currently inside Bag Y: Initially, Bag X contains $2; Bag Y is empty. $2 $0 2 / 3
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The Centipede Game: Backstory Money currently inside Bag X: Money currently inside Bag Y: $2 $0 Payoff of P 1 : Payoff of P 2 : P 1 Out 2 0 Player 1 can choose “Out” by taking one of the bags, leaving the other to Player 2. Clearly, if Player 1 is choosing “Out”, he will take Bag X, leaving Bag Y to Player 2. Therefore, if Player 1 chooses “Out”, he get $2, whereas Player 2 gets $0. The game ends immediately whenever a player chooses “Out”. 2 / 3
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The Centipede Game: Backstory Money currently inside Bag X: Money currently inside Bag Y: Payoff of P 1 : Payoff of P 2 : P 1 Out 2 0 In Alternatively, Player 1 can choose “In” and pass the turn to Player 2. Every time a player chooses “In”, a third party puts $1 into each bag. = $3 $1 2 / 3
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The Centipede Game: Backstory Money currently inside Bag X: Money currently inside Bag Y: Payoff of P 1 : Payoff of P 2 : P 1 Out 2 0 In $3 $1 Out P 2 1 3 Now, it is Player 2’s turn to choose. Player 2 can choose “Out” and take the more valuable Bag X, leaving Bag Y to Player 1. Therefore, if Player 2 chooses “Out”, he get $3, whereas Player 2 gets $1, and the game ends. 2 / 3
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The Centipede Game: Backstory Money currently inside Bag X: Money currently inside Bag Y: Payoff of P 1 : Payoff of P 2 : P 1 Out 2 0 In Out P 2 1 3 In Alternatively, Player 2 can choose “In”, pass the turn back to Player 1, and let the two bags grow by $1 each again. = $4 $2 2 / 3
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The Centipede Game: Backstory Money currently inside Bag X: Money currently inside Bag Y: Payoff of P 1 : Payoff of P 2 : P 1 Out 2 0 In Out P 2 1 3 In $4 $2 Out P 1 4 2 Now, it is Player 1’s turn to choose again. He can choose “Out” and take the more valuable Bag X, leaving Bag Y to Player 2.
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