Lecture 8

Question 1

define a subgame

Answer 1

part of the extensive form, it is a collection of nodes and branches that satisfies three properties

Question 2

what are the three properties that satisfy subgame?

Answer 2

starts at a single decision node; contains every successor to this node; if it contains any part of an information set, then it contains all the nodes in that information set

Question 3

How does SPNE coincide with backward induction in games with perfect information?

Answer 3

SPNE applies to any game with extensive form (perfect or imperfect information), but also provides predictions of games of imperfect information

Question 4

Define subgame perfect nash equilibrium

Answer 4

pair of strategies is SPNE if the strategies, when confined to any subgame of the original game, have the players playing a nash equilibrium within that subgame

Question 5

what does the fact that an SPNE strategy profile is one that forms a NE in every subgame imply?

Answer 5

implies that in a SPNE we require not only nash equilibrium of the original game, but also an equilibrium for further points that characterize subgames (even points that won’t be reached).

Question 6

In games of perfection information.. with respect to SPNE…?

Answer 6

the set of SPNE coincide with those found via backward induction. If payoffs are all distinct, then there exists a unique SPNE