Nash equilibria in entry game Two Nash equilibria (In, Accommodate >(Out, Fight does the second nash equilibrium make sense? Non-creditable threats a Limitation to the normal form representation Incumbent Accommodate Fight 1 0 0 Challenger Out 2二1 2 1 2
Nash equilibria in entry game Incumbent Accommodate Fight Challenger In 2 , 1 0 , 0 Out 1 , 2 1 , 2 21 ◼ Two Nash equilibria ➢ ( In, Accommodate ) ➢ ( Out, Fight ) ◼ Does the second Nash equilibrium make sense? ◼ Non-creditable threats ◼ Limitation to the normal form representation
Remove nonreasonable nash equilibrium Subgame perfect Nash equilibrium is a refinement of Nash equilibrium It can rule out nonreasonable Nash equilibria or non-creditable threats We first need to define subgame
Remove nonreasonable Nash equilibrium ◼ Subgame perfect Nash equilibrium is a refinement of Nash equilibrium ◼ It can rule out nonreasonable Nash equilibria or non-creditable threats ◼ We first need to define subgame 22
Su ogame A subgame of a game Player 1 tree begins at a nonterminal node and H T includes all the nodes and edges following the Player 2 Player 2 nonterminal node A subgame beginning at H T H a nonterminal node x can be obtained as follows 1,-11,-1 1,1 remove the edge connecting x and its predecessor the connected part a subgame containing x is the subgame
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 23 -1, 1 Player 1 Player 2 H T 1, -1 H T Player 2 H T 1, -1 -1, 1 a subgame
Subgame: example Player2众 Player 1 E Player 1 C D G 3,1 Player 2 F 2,0 Player 1 G H 3,1 Player 1 G H 1,2 0,0
Subgame: example 24 Player 2 E F Player 1 G H 3, 1 1, 2 0, 0 Player 1 C D 2, 0 Player 2 E F Player 1 G H 3, 1 1, 2 0, 0 Player 1 G H 1, 2 0, 0
Subgame-perfect Nash equilibrium A Nash equilibrium of a dynamic game is subgame-perfect if the strategies of the Nash equilibrium constitute a Nash equilibrium in every subgame of the game Subgame-perfect Nash equilibrium is a Nash equilibrium
Subgame-perfect Nash equilibrium ◼ A Nash equilibrium of a dynamic game is subgame-perfect if the strategies of the Nash equilibrium constitute a Nash equilibrium in every subgame of the game. ◼ Subgame-perfect Nash equilibrium is a Nash equilibrium. 25