Flashcards in 05 - Dynamic Games of Complete Information Deck (10)

Loading flashcards...

1

## 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).

2

## 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

3

## How do subgame perfect Nash equilibrium (SPNE) and NE relate?

### Every SPNE is a Nash equilibrium, but the reverse need not hold

4

## 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.

5

## 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.

6

## 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.

7

## 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.

8

## 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.

9

## 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).

10