國外博弈論課件lecture(17)-資料下載頁
2024-10-19 13:59本頁面
【正文】 ? We first need to define subgame June 11, 2021 73347 Game TheoryLecture 16 22 Subgame ? A subgame of a dynamic game tree ? begins at a singleton information set (an information set contains a single node), and ? includes all the nodes and edges following the singleton information set, and ? does not cut any information set。 that is, if a node of an information set belongs to this subgame then all the nodes of the information set also belong to the subgame. June 11, 2021 73347 Game TheoryLecture 16 23 Subgame: illustration 1 I E 0, 0 2 B A 1, 1 1 2 R D , K, K R D R D 2 K, K K, K a subgame a subgame Not a subgame June 11, 2021 73347 Game TheoryLecture 16 24 Subgameperfect Nash equilibrium ? A Nash equilibrium of a dynamic game is subgameperfect if the strategies of the Nash equilibrium constitute or induce a Nash equilibrium in every subgame of the game. ? Subgameperfect Nash equilibrium is a Nash equilibrium. June 11, 2021 73347 Game TheoryLecture 16 25 Find subgame perfect Nash equilibria: backward induction 1 I E 0, 0 2 B A 1, 1 1 2 R D , K, K R D R D 2 K, K K, K a subgame a subgame ?Starting with those smallest subgames ?Then move backward until the root is reached One subgameperfect Nash equilibrium ( IR, AR ) June 11, 2021 73347 Game TheoryLecture 16 26 Find subgame perfect Nash equilibria: backward induction 1 I E 0, 0 2 B A 1, 1 1 2 R D , K, K R D R D 2 K, K K, K a subgame a subgame ?Starting with those smallest subgames ?Then move backward until the root is reached Another subgameperfect Nash equilibrium ( ED, BD ) June 11, 2021 73347 Game TheoryLecture 16 27 Summary ? Dynamic game of plete and imperfect information ? Subgame perfect Nash equilibrium ? Backward induction ? Next time ? Bank runs ( of Gibbons) ? Tariffs and imperfect international petition ( of Gibbons) ? Reading lists ? Sec AC of Gibbons
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