ECO290E: Game Theory
Lecture 8
Games in Extensive-Form
Review of Midterm
• The definition of NE.
• Dominated strategy and NE.
• How to solve “Rock-Paper-Scissors”
game.
Definition of NE
• A Nash equilibrium is a combination of
strategies, denoted as s*, which satisfies
the following condition:
i, si
 i ( s )   i ( s , si )
*
*
i
• A Nash equilibrium is neither a strategy nor
a combination or payoffs.
Dominated strategy and NE
• If iterated elimination of strictly
dominated strategies eliminates all but
one combination of strategies, denoted
as s, then s becomes the unique NE of
the game.
• If a combination of strategies s is a NE,
then s survives iterated elimination of
strictly dominated strategies.
Review of Lecture 6
Price War
Monopolist
Entrant
In
Accommodat
e
-1
-1
Out
1
1
4
0
4
0
• There are two NE: (In, A) and (Out, PW)
• (Out, PW) relies on a non-credible threat.
Lessons
• Dynamic games often have multiple Nash
equilibria, and some of them do not seem
plausible since they rely on non-credible
threats.
• By solving games from the back to the
forward, we can erase those implausible
equilibria.
 Backward Induction
• This idea will lead us to the refinement of NE,
the subgame perfect Nash equilibrium.
Extensive Form Games
The extensive-form representation of a game
specifies the following 5 elements:
• The players in the game
• When each player has the move
• What each player can do at each of her
opportunities to move
• What each player knows at ---.
• The payoff received by each player for each
combination of moves that could be
chosen by the players.
Normal-Form Representation
• Every dynamic game generates a single
normal-form representation.
1
2 (L’,L’)
(L’,R’)
(R’,L’)
(R’,R’)
L
3,1
3,1
1,2
1,2
R
2,1
0,0
2,1
0,0
• A strategy for a player is a complete plan of
actions specifying a feasible action for the
player in every contingency.