【正文】 is 1 if player 1 plays H and player 2 plays HT June 10, 2021 73347 Game TheoryLecture 15 6 Nash equilibrium in a dynamic game ? We can also use normalform to represent a dynamic game ? The set of Nash equilibria in a dynamic game of plete information is the set of Nash equilibria of its normalform ? How to find the Nash equilibria in a dynamic game of plete information ? Construct the normalform of the dynamic game of plete information ? Find the Nash equilibria in the normalform June 10, 2021 73347 Game TheoryLecture 15 7 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 10, 2021 73347 Game TheoryLecture 15 8 Subgame ? A subgame of a game tree begins at a nonterminal node and includes all the nodes and edges following the nonterminal node ? A subgame beginning at a nonterminal node x can be obtained as follows: ? remove the edge connecting x and its predecessor ? the connected part containing x is the subgame 1, 1 Player 1 Player 2 H T 1, 1 H T Player 2 H T 1, 1 1, 1 a subgame June 10, 2021 73347 Game TheoryLecture 15 9 Existence of subgameperfect Nash equilibrium ? Every finite dynamic game of plete and perfect information has a subgameperfect Nash equilibrium that can be found by backward induction. June 10, 2021 73347 Game TheoryLecture 15 10 Backward induction: illustration ? Subgameperfect Nash equilibrium (C, EH). ? player 1 plays C。 ? player 2 plays E if player 1 plays C, plays H if player 1 plays D. Player 1 C D Player 2 E F 3, 0 2, 1 Player 2 G H 1, 3 0, 2 June 10, 2021 73347 Game TheoryLecture 15 11 Multiple subgameperfect Nash equilibria: illustration ? Subgameperfect Nash equilibrium (D, FHK). ? player 1 plays D ?