Flashcards in Test 1 Deck (28)

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## Coordinates for chicken

###
C= swerve n= not swerve

CC 3,3

CN 2,4

NN 1,1

NC 4,2

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## Coordinate for battle of the sexes

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O opera B baseball

BB 4,3

OB 1,1

BO 2,2

OO 3,4

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## Prisoner's Dilemma

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C don't tell N tell

CC 3,3

NC 4,1

CN 1,4

NN 2,2

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## Dominant strategy

### A common best response for both strategies of the other player

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## Nash equilibrium

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

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## 2 dom strategies = how many Nash equilibriums?

### 1

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## 1 dominant strategy = how many Nash equilibriums?

### 1

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## 0 dominant strategies = how many Nash equilibrium?

### 0 or 2

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## What is paradoxical about Prisoner's Dilemma?

### 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

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

### 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

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## Player twos winning strategy in Nim(m,n)

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

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## Player ones winning strategy in RNim(m,n)

### 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

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

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

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## ChooseNim winning strategy

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

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## What does TFGWT stand for

### Totally finite games without ties

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## Five properties of TFGWT

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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.

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## Strategy in TFGWT

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

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## Winning strategy

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

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## Sub tree

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

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## Play

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

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## Branch

### The sequence of nodes of a winning strategy

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## Fork

### The different strategy results coming from a node

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## Pigeonhole Principle finite version

### 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.

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## Pigeonhole principle infinite version

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

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## Konig's Infinity Lemma

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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

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## Variants of KIL

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

Variant 2 every tree satisfying both1 and 3 violates 2

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## What are the bins in the applying PHP to prove KIL

### Subtrees

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