1.) Consider the discrete Bertrand game described in the Oligopoly lecture notes/video. According to the rules of this game each student selects a number from the set {0,1,2, 3, 4, 5, 6, 7, 8, 9, 10} and is randomly matched with another student. Whoever has the lowest number wins that amount in dollars and whoever has the high number wins zero. In the event of ties, each student receives half their number in dollars. What number would you select if you played this game in our online class? Explain your reasoning.
2.) Continue to consider this discrete Bertrand model, but now assume that each student has a constant cost of 5 that is deducted from all payoffs. So whoever has the low number wins their number, minus 5. Whoever has the high number loses 5 total. In the event of a tie, each student wins an amount equal to their number divided by two, then minus five. Find any Nash equilibria in this game. Explain your reasoning. Hint: It is perfectly fine for both players to have losses in equilibrium! There are more than 1 Nash equilibria.
In: Economics
In: Physics
In sports betting, sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for this spread. For example, if Team A is favored by 5 points, and wins the game by 7 points, then a bet on Team A is a winning bet. However, if Team A wins the game by only 3 points, then a bet on Team A is a losing bet. Suppose that in games, the margin of victory for the favored team relative to the spread is approximately normally distributed with a mean of negative 1.0 point and a standard deviation of 11 points. Complete parts (a) through (c) below. (a) What is the probability that the favored team wins by 6 or more points relative to the spread?
In: Statistics and Probability
In C++
Write the definition for following methods of List data structure.
5. pushFront – The function appends an element in the list at the front. The operation increases the number of elements in the list by one.
6. pushback - The function appends an element in the list at the end. The operation increases the number of elements in the list by one.
7.popFront - The function returns and then removes an element in the list from the front. The operation decreases the number of elements in the list by one.
8.popBack - - The function returns and then removes an element in the list from the end. The operation decreases the number of elements in the list by one.
In: Computer Science
In a lottery game a player chooses four digits (digits can repeat, for instance 0, 2, 0, 2 is a valid choice) and bet $1 that all four of them will arise in the four digit number drawn from the lottery. It isn’t necessary that the order will be the same: if a player selects 2, 6, 7, 8 the selection of 8, 2, 7, 6 means he won. Player gets $200 if he wins.
1. What is the probability of winning?
2. What is the probability mass function of X, the net earnings in one game?
3. What are the mean and standard deviation of net earnings?
In: Statistics and Probability
In a lottery game a player chooses four digits (digits can repeat, for instance 0, 2, 0, 2 is a valid choice) and bet $1 that all four of them will arise in the four digit number drawn from the lottery. It isn’t necessary that the order will be the same: if a player selects 2, 6, 7, 8 the selection of 8, 2, 7, 6 means he won. Player gets $200 if he wins.
1. What is the probability of winning?
2. What is the probability mass function of X, the net earnings in one game?
3. What are the mean and standard deviation of net earnings?
In: Statistics and Probability
Alex Edmans, the London Business School professor at the start of the video, identified a “Happy Worker Premium.” This is a signal to investors that this company has a better chance of producing higher profits due to worker satisfaction. According to the text, job performance is comprised of three factors where motivation (or job satisfaction) is only one factor. What are the other two factors of job performance and how can those two factors be improved if found lacking?
Aaron Hurst, author of the Purpose Driven Economy says that CEOs offer perks as a sign of confidence the company is successful when what managers should be doing is listening to what workers really want, rather than the company giving the workers what the company thinks they want. Which process-based perspective of motivation theory does this imply – equity theory or expectancy theory?
Aaron Hurst says that a study out of Yale shows that intrinsic motivation and rewards are more important than extrinsic motivation and rewards. Mr. Hurst also says when companies offer many extrinsic motivators, like ping-pong tables or yoga sessions, they may have negative consequences rather than positive consequences. What do you think Mr. Hurst means by this statement?
In: Economics
Why is this java code reaching a deadlock and how to I fix it without serializing the code (i.e. I don't want to do not have the Girl authenticate the Boy then have the Boy authenticate the Girl)?
import java.applet.*;
import javax.swing.*;
import java.awt.*;
import java.awt.event.*;
// Attempt at a simple handshake. Girl pings Boy, gets confirmation.
// Then Boy pings girl, get confirmation.
class Monitor {
String name;
public Monitor (String name) { this.name = name; }
public String getName() { return this.name; }
// Girl thread invokes ping, asks Boy to confirm. But Boy invokes ping,
// and asks Girl to confirm. Neither Boy nor Girl can give time to their
// confirm call because they are stuck in ping. Hence the handshake
// cannot be completed.
public synchronized void ping (Monitor p) {
System.out.println(this.name + " (ping): pinging " + p.getName());
p.confirm(this);
System.out.println(this.name + " (ping): got confirmation");
}
public synchronized void confirm (Monitor p) {
System.out.println(this.name+" (confirm): confirm to "+p.getName());
}
}
class Runner extends Thread {
Monitor m1, m2;
public Runner (Monitor m1, Monitor m2) {
this.m1 = m1;
this.m2 = m2;
}
public void run () { m1.ping(m2); }
}
public class DeadLock {
public static void main (String args[]) {
int i=1;
System.out.println("Starting..."+(i++));
Monitor a = new Monitor("Girl");
Monitor b = new Monitor("Boy");
(new Runner(a, b)).start();
(new Runner(b, a)).start();
}
} |
In: Computer Science
Problem 4. What is the probability that a five card poker hand contains at least one ace?
Problem 5. What is the probability that a five card poker hand contains two pairs? (two of each of two different kinds, and a fifth card of a third kind)
Problem 6. Suppose that 100 people enter a contest and that different winners are selected at random for first, second, and third prizes. What is the probability that Michelle wins one of these prizes if she is one of the contestants?
Problem 7. Find the probability of winning the lottery by selecting the correct six integers between 0 and 50, where the order in which the integers are selected does not matter.
Problem 8. What is the probability that a die never comes up an even number when it is rolled six times?
Problem 9. In roulette, a wheel with 38 numbers is spun. Of these, 18 are red, and 18 are black. The other two numbers, which are neither black nor red, are 0 and 00. The probability that when the wheel is spun it lands on any particular number is 1/38.
a. What is the probability that the wheel lands on a red
number?
b. What is the probability that the wheel lands on a black number
twice in a row?
c. What is the probability that the wheel lands on 0 or
00?
d. What is the probability that in five spins the wheel never lands
on either 0 or 00?
Problem 10. (Challenge) Which is more likely: rolling a total of 9 when two dice are rolled or rolling a total of 9 when three dice are rolled?
In: Statistics and Probability
Game theory: Consider a sealed-bid auction in which the winning bidder pays the average of the two highest bids. Assume that players have valuations v1 > v2 > … > vn, that ties are won by the tied player with the highest valuation, and that each player’s valuation is common knowledge.
a. Is there any Nash equilibrium in which the two highest bids are different? If there is, give an example. If there is not, prove that no such equilibrium exists.
b. Is there any Nash equilibrium in which a player other than the one with the highest valuation wins? If there is, give an example. If there is not, prove that no such equilibrium exists.
c. Will bidding more than one’s own valuation be weakly dominated in this auction? Will bidding one’s own valuation exactly be weakly dominated? Will bidding less than one’s own valuation be weakly dominated?
d. What is the highest possible winning bid in any Nash equilibrium of this game? What is the lowest possible winning bid in Nash equilibrium?
In: Economics