Perspective
For this line, identify the slope and the y-intercept.
y=-1/3x+2
Slope=-1/3
y-intercept=2
What does it mean for a strategy to be strictly dominant and what does it mean for a strategy to be strictly dominated.
A strategy is strictly dominant if it gives you a higher payoff than any of your other options, no matter what choices the other players make.
A strategy is strictly dominated if there is another strategy available to you that always gives you a higher payoff, no matter what choices the other players make.
True or False:
A Directed and Weighted graph only has arrows.
False, also numbers associated with the edge.
In a regular 2 player game associated with Game Theory, what are Player 1's Pure strategies and what are player 2's Pure Strategies.
Player 1: A,B,C
Player 2: X,Y,Z
Let u=(2,-1), v=(1,2), and w=(3,0) Calculate the following.
-2u+3v+w=?
(2,8)
Write the sample space for the following experiment.
A fair 6-sided dice rolled once.
1,2,3,4,5,6
Create a graph with a degree sequence of:
{1,2,2,3,4}
Will check on white board if correct.
What is the Greedy Coloring Algorithm?
The Greedy Coloring Algorithm is a fast, step-by-step way to color a graph's nodes so that no two connected nodes share the same color.
It works by going through the nodes one by one and assigning each node the very first available color that its neighbors aren't already using.
It is called "greedy" because it makes the easiest choice right now without planning ahead, which means it is quick but doesn't always use the absolute fewest colors possible.
Find the equation of line that is parallel to the line y=2x+3 and goes through the origin.
y=2x
Write the sample space for the following experiment.
A fair coin flipped 3 times in a row.
HHH, TTT, TTH, HHT, HTH, THH, HTT, THT.
Draw a tree with 6 vertices, in which one has a degree of 6.
Impossible.
If you were to centrally project an x=1 graph and make it a x=2 graph instead what would happen to the shape in the graph
It gets 2x bigger.
Consider the line in 3D space that goes through the points (-1,4,1) and (2,5,1)
Calculate a parameterization of the line.
Hint: u+tv
(-1,4,1)+t(3,1,0)
Fill in the following payoff metric for GT 2. Produce a game that has the following 2 properties,
(A,X) and B,X) are the only 2 pure Nash equilibriums and the social welfare of (A,Z) is 13.
will check on board (multiple possible solutions)
Create a tree with 6 vertices and exactly 2 leaves.
Will check on board.
Answer all of the following questions correctly using true or false
1.Every tree is bipartite
2.Every cyclic graph is bipartide
3.If a graph has a chromatic number n, then so does every subgraph of that graph
1. True
2. False
3. False
A building is 50ft tall. You are standing 150 away from the tree and you are centrally project the building onto a canvas 3 ft away, How tall is the image of the building on the canvas?
How far away do you need to be from the tree so that it appears to be 3 ft tall on the canvas?
Must answer both questions correctly for points.
1ft
50ft
On problem Game Theory 1 find all of the following.
1.All Dominance Relations
2.Strictly Dominated Strategies
3.Strictly Dominant Strategies
1. C>A, C>B, Y>X, Y>Z
2. A, B, X, Z
3. C, Y
Complete the following problem in which v, e, and f are the number of vertices, edges, and faces in a drawing of a graph without edge crossings.
k2,4
v=6
e=8
f=4
DS:2,2,2,2,4,4
Suppose G is a connected planar graph with 330 vertices and 650 edges. If G were drawn without any edge crossings, into how many regions' would G divide the plane? In other words, how many faces does G have?
322 faces