國外博弈論課件lecture(15)(已修改)
2024-10-31 13:57 本頁面
【正文】 June 13, 2021 73347 Game TheoryLecture 18 1 Dynamic Games of Complete Information Dynamic Games of Complete and Imperfect Information June 13, 2021 73347 Game TheoryLecture 18 2 Outline of dynamic games of plete information ? Dynamic games of plete information ? Extensiveform representation ? Dynamic games of plete and perfect information ? Game tree ? Subgameperfect Nash equilibrium ? Backward induction ? Applications ? Dynamic games of plete and imperfect information ? More applications ? Repeated games June 13, 2021 73347 Game TheoryLecture 18 3 Today’s Agenda ? Review of previous class ? Tariffs and imperfect international petition ( of Gibbons) ? Repeated games June 13, 2021 73347 Game TheoryLecture 18 4 Information set ? Gibbons’ definition: An information set for a player is a collection of nodes satisfying: ? the player has the move at every node in the information set, and ? when the play of the game reaches a node in the information set, the player with the move does not know which node in the information set has (or has not) been reached. ? All the nodes in an information set belong to the same player ? The player must have the same set of feasible actions at each node in the information set. June 13, 2021 73347 Game TheoryLecture 18 5 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. ? A subgame of a game tree ? begins at a singleton information set (an information set containing 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 13, 2021 73347 Game TheoryLecture 18 6 Example Player 1 L R Player 2 L’ R’ 2, 2, 0 Player 2 L’ R’ 3 L” R” 3 L” R” 3 L” R” 3 L” R” 1, 2, 3 3, 1, 2 2, 2, 1 2, 2, 1 0, 0, 1 1, 1, 2 1, 1, 1 June 13, 2021 73347 Game TheoryLecture 18 7 Tariffs and imperfect international petition ( of Gibbons) ? Two identical countries, 1 and 2, simultaneously choose their tariff rates, denoted t1, t
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