Flashcards in 05 - Dynamic Games of Complete Information Deck (10)
What is a subgame of an extensive-form game?
a) begins at a decision node D that is a singleton information set,
b) includes all the decision and terminal nodes following D in the game tree (but no other nodes), and
c) does not cut any information sets (i.e., if a decision node ˜D follows D, then all other nodes in the information set containing ˜D must also follow D).
What is a subgame perfect Nash equilibrium (SPNE)?
A strategy profile σ in an extensive-form game is a subgame perfect Nash equilibrium (SPNE) if it induces a Nash equilibrium in every subgame
How do subgame perfect Nash equilibrium (SPNE) and NE relate?
Every SPNE is a Nash equilibrium, but the reverse need not hold
In a finite game of perfect information, when is a strategy profile subgame perfect?
In a finite game of perfect information, a strategy profile is a SPNE if and only if it is a Nash equilibrium that can be derived through backwards induction.
What does Zermelo’s Theorem imply about subgame perfect Nash equilibria?
Every finite game of perfect information has a pure-strategy SPNE. Moreover, if no player has the same payoffs at any two terminal nodes, then there is a unique SPNE.
How does a subgame perfect Nash equilibrium look like?
A subgame perfect Nash equilibrium is a strategy profile: it specifies actions for every information set in the game tree.
How does a subgame perfect outcome look like?
A subgame perfect outcome describes the path from the initial node to the terminal node that is reached when SPNE strategies are played.
How do Backwards Induction (BI) and SPNE relate?
SPNE generalizes backwards induction (BI): whenever BI applicable, SPNE and BI equivalent, but SPNE also applies to
(i) imperfect information and
(ii) infinite-horizon games.
How does the one-shot deviation principle help to identify SPNE?
In the above class of extensive-form games for T < 1, a strategy profile s* = (s*1, ..., s*n) is an SPNE if and only if for every player i, there is no profitable one-shot deviation from s*i .
Idea of proof:
-> If there is a profitable one-shot deviation, there is a profitable deviation in some subgame, contradicting SPNE.
-> Suppose there is a profitable deviation; however complicated it is, there is a last subgame where itdeviates (BI intuition).