Test 1

Question 0

Coordinate for battle of the sexes

Answer 0

O opera B baseball
BB 4,3
OB 1,1
BO 2,2
OO 3,4

Question 1

Coordinates for chicken

Answer 1

C= swerve n= not swerve
CC 3,3
CN 2,4
NN 1,1
NC 4,2

Question 2

Prisoner’s Dilemma

Answer 2

C don't tell N tell
CC 3,3 
NC 4,1
CN 1,4 
NN 2,2

Question 3

Dominant strategy

Answer 3

A common best response for both strategies of the other player

Question 4

Nash equilibrium

Answer 4

A strategy profile for which neither player gains by unilaterally switching strategies

Question 5

2 dom strategies = how many Nash equilibriums?

Answer 5

1

Question 6

1 dominant strategy = how many Nash equilibriums?

Answer 6

1

Question 7

0 dominant strategies = how many Nash equilibrium?

Answer 7

0 or 2

Question 8

What is paradoxical about Prisoner’s Dilemma?

Answer 8

They both have a CBR of N and N but strategy profile NN doesn’t have the best outcome since it is ranked 2,2

Question 9

Winning strategy for player 1 in nim(m,n)

Answer 9

If m is not a variable of n+1. First move reduce running sum to a multiple of n+1. Subsequent moves respond to j with (n+1)-j

Question 10

Player twos winning strategy in Nim(m,n)

Answer 10

If m is a multiple if n+1 respond to j with (n+1)-j

Question 11

Player ones winning strategy in RNim(m,n)

Answer 11

If m is not a variable of one more than n+1. First move reduce running sum to a multiple of one more than n+1. Respond to j with (n+1)-j

Question 12

Winning strategy for player two in RNim(m,n)

Answer 12

If m is a multiple of one more than n+1 respond to j with (n+1)-j

Question 13

ChooseNim winning strategy

Answer 13

Player one only! Choose a number for m that is not a multiple of (n+1)

Question 14

What does TFGWT stand for

Answer 14

Totally finite games without ties

Question 15

Five properties of TFGWT

Answer 15

1 there are two players, player I and player II, who move alternately with player I going first
2 no randomizing mechanisms are used
3 whenever a play ends, exactly one winner exists
4 each play ends after finitely many moves
5 at any moment, in any play, tyre at only finitely many options for a legal next move.

Question 16

Strategy in TFGWT

Answer 16

A set of rules that specify a single move for every partial play leading up to turn

Question 17

Winning strategy

Answer 17

A strategy that makes it impossible for a play to lose a play of the game by following the rules

Question 18

Sub tree

Answer 18

The part if a tree containing a node with all the nodes hanging from that node

Question 19

Play

Answer 19

A legal sequence of moves hat begins before anyone has moved and ends when the game is over

Question 20

Branch

Answer 20

The sequence of nodes of a winning strategy

Question 21

Fork

Answer 21

The different strategy results coming from a node

Question 22

Pigeonhole Principle finite version

Answer 22

If we have n amount of items to put into m bins and n>m then at least one bin will have more than one object.

Question 23

Pigeonhole principle infinite version

Answer 23

If we have infinitely many object and finite many bns, some bins will have infinitely many objects,

Question 24

Konig’s Infinity Lemma

Answer 24

No tree can satisfy the following three:
1 every fork of t is finite in width
2 every branch of T is finite in length
3 T has infinitely many nodes altogether

Question 25

Variants of KIL

Answer 25

Variant 1- every tree satisfying both 1 and 2 violates 3

Variant 2 every tree satisfying both1 and 3 violates 2

Question 26

What are the bins in the applying PHP to prove KIL

Answer 26

Subtrees

Question 27

Zermelo’s Theorem

Answer 27

For every TFGWT, either player I or player II has the winning strategy