ECO290E: Game Theory
Lecture 10
Examples of Dynamic Games
Review of Lec. 8 & 9
• A strategy in a dynamic game is a
complete plan of actions, i.e.,
specifying what she will do in every her
information set.
• Dynamic games may have many Nash
equilibria, but some of these may
involve non-credible threats or
promises. The subgame perfect Nash
equilibria are those that pass a
credibility test.
SPNE
• A subgame perfect Nash equilibrium
(SPNE) is a combination of strategies in
a extensive-form which constitutes a
Nash equilibrium in every subgame.
 Since the entire game itself is a
subgame, it is obvious that a SPNE is a
NE, i.e., SPNE is stronger solution
concept than NE.
Existence of NE
• Since any dynamic game has a (unique)
normal-form representation, at least
one NE exist as long as a game is finite,
i.e., finite number of players and
strategies.
• If some of the paths in the game tree
involve infinite stages (information set),
then the corresponding normal-form
game is no longer finite.
 The dynamic game may not have a NE!
Existence of SPNE
• Any finite dynamic game also has a SPNE,
since each subgame is finite and thereby
must have at least one NE.
• To find a SPNE, first identify all the smallest
subgames that contain the terminal nodes,
and then replace each such subgame with
the payoffs from one of Nash equilibria.
• The next step is to solve the second smallest
subgames given these truncated payoffs.
• Working backwards through the tree in this
way yields a SPNE!
Other Examples
• To be completed.