6博弈论第三讲_3 SPE 复旦大学 王永钦.ppt

Dynamic Games of Complete Information Yongqin Wang, CCES, Fudan Fall, 2007 2 Dynamic games of complete information Perfect information A player knows Who has made What choices when she has an opportunity to make a choice Imperfect information A player may not know exactly Who has made What choices when she has an opportunity to make a choice. 3 Subgame-perfect Nash equilibrium A Nash equilibrium of a dynamic game is subgame-perfect 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. 4 Find subgame perfect Nash equilibria: backward induction What is the subgame perfect Nash equilibrium? 5 Find subgame perfect Nash equilibria: backward induction What is the subgame perfect Nash equilibrium? 6 Bank runs (2.2.B of Gibbons) Two investors, 1 and 2, have each deposited D with a bank. The bank has invested these deposits in a long-term project. If the bank liquidates its investment before the project matures, a total of 2r can be recovered, where D r D/2. If bank’s investment matures, the project will pay out a total of 2R, where RD. Two dates at which the investors can make withdrawals from the bank. 7 Bank runs: timing of the game The timing of this game is as follows Date 1 (before the bank’s investment matures) Two investors play a simultaneous move game If both make withdrawals then each receives r and the game ends If only one makes a withdrawal then she receives D, the other receives 2r-D, and the game ends If neither makes a withdrawal then the project matures and the game continues to Date 2. Date 2 (after the bank’s investment matures) Two invest