Chapter-8 - Chapter 8: Sequential Games Kidnapping game Do...

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Chapter 8: Sequential Games Kidnapping game 1 4 2 2 5 3 4 1 3 5 Release Release Kill Kill Guy Guy Guy Vivica Do not pay ransom Pay ransom Guy Vivica Do not kidnap Kidnap Perfect information: all the information sets are singleton.
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Strategy Strategy is a complete plan: specify action for each information set. Guy’s strategy: whether to kidnap; if kidnap and ransom, whether to kill; if kidnap and no ransom, whether to kill. Strategy is a complete plan: specify action for each information set. Guy’s strategy: whether to kidnap; if kidnap and ransom, whether to kill; if kidnap and no ransom, whether to kill.
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Vivica (kin of victim) 3,5 Guy (kidnapper) Pay ransom Do not pay ransom Do not kidnap / Kill / Kill Do not kidnap / Kill / Release Do not kidnap / Release / Kill Do not kidnap / Release / Release Kidnap / K 4,1 2,2 1,4 5,3 ill / Kill Kidnap / Kill / Release Kidnap / Release / Kill Kidnap / Release / Release Strategic Form
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Nash Equilibrium Five Nash equilibria. -( Kidnap/Release/Kill, Pay ransom ) Do not kidnap/Kill/Kill, Do not pay ransom ) Do not kidnap/Kill/Release, Do not pay ransom ) Do not kidnap/Release/Kill, Do not pay ransom ) Do not kidnap/Release/Release, Do not pay ransom ) Five Nash equilibria. Kidnap/Release/Kill, Pay ransom ) Do not kidnap/Kill/Kill, Do not pay ransom ) Do not kidnap/Kill/Release, Do not pay ransom ) Do not kidnap/Release/Kill, Do not pay ransom ) Do not kidnap/Release/Release, Do not pay ransom )
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Non-credible Threat Consider Nash equilibrium ( Do not kidnap/release/Kill, Do not pay ransom ). According to the strategies, Vivica’s decision node is not reached. Guy does not kidnap simply because Vivica does not pay ransom. Is Vivica’s threat credible, is she bluffing? - Suppose Guy plays kidnap. - Vivica knows that Guy will kill if ransom is not paid, so it is optimal for her to pay ransom. Consider Nash equilibrium ( Do not kidnap/release/Kill, Do not pay ransom ). According to the strategies, Vivica’s decision node is not reached. Guy does not kidnap simply because Vivica does not pay ransom. Is Vivica’s threat credible, is she bluffing? - Suppose Guy plays kidnap. - Vivica knows that Guy will kill if ransom is not paid, so it is optimal for her to pay ransom.
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No Bluffing The only convincing equilibrium is ( Kidnap/Release/Kill, Pay ransom ). Nash equilibrium only requires actions are optimal for the decision nodes that are reached over the course of equilibrium play . To kill Nash equilibrium involving with non-credible threat, we strengthen the concept of Nash equilibrium. Subgame perfect Nash equilibrium : For a game of perfect information, a strategy profile is a subgame perfect Nash equilibrium if, at each decision node, it assigns an action that maximizes a player's payoff. The only convincing equilibrium is ( Kidnap/Release/Kill, Pay ransom ).
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This note was uploaded on 07/17/2008 for the course ECON 601 taught by Professor Yang during the Spring '08 term at Ohio State.

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Chapter-8 - Chapter 8: Sequential Games Kidnapping game Do...

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