Prove: If the boy-optimal matching and the girl-optimal matching turn out to be same for a set of preferences, there exists only one possible solution for stable matching.

"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $930,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.
The probability of a small box office earning $201,000 is 0.35. The probability of a medium box office of $1,590,000 is 0.45, and the probability of a large box office of $3,030,000 is 0.2.
Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $21,000 to get the novel evaluated by the movie critic.
The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.
If the movie will have a large box office, there is a 0.79 probability the critic will have a favorable opinion.
If the movie will have a medium box office, there is a 0.57 probability the critic will have a favorable opinion.
If the movie will have a small box office, there is a 0.15 probability the critic will have a favorable opinion.
Assume that Jay wants to maximize his expected monetary outcome. Enter the expected value of the preferred alternative. This includes whether or not to hire the movie critic and whether or not to go with the movie or network option."

"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $980,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.
The probability of a small box office earning $295,000 is 0.25. The probability of a medium box office of $1,210,000 is 0.49, and the probability of a large box office of $3,180,000 is 0.26.
Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $24,000 to get the novel evaluated by the movie critic.
The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.
If the movie will have a large box office, there is a 0.63 probability the critic will have a favorable opinion.
If the movie will have a medium box office, there is a 0.41 probability the critic will have a favorable opinion.
If the movie will have a small box office, there is a 0.11 probability the critic will have a favorable opinion.
Assume that Jay wants to maximize his expected monetary outcome. Enter the expected value of the preferred alternative. This includes whether or not to hire the movie critic and whether or not to go with the movie or network option."

The President P has been accused of colluding with Russian intelligence to tilt the election in his favor. Let g denote “how guilty” the President is of these charges. Assume g is either 1, 2, or 3, where 3 means “guilty as sin” and 1 means “not at all guilty.” Assume that g is chosen by nature and a voter V believes each value is equally likely (voters are pretty skeptical of politicians these days). A special counsel S has been appointed to investigate the accusation. If S is allowed to complete her work, she will learn the value of g and report it to the voter V . However, P might fire S before she is allowed to complete her work, in which case S cannot report anything to V . Assume that nature draws g, shows it to P, and then P decides whether to fire Ior not. If so, the “game” ends; if not, S reports g to V , and the game ends. Assume P ’s utility is ?1 times V ’s expectation of g at the end of the game (i.e., P is better off, the lower is the voter’s assessment of his guilt).

(c) Suppose all types except g = 1 fire S. What does V think is the expected value of g, given that S is fired? Is type g = 2 happy with that?

(d) Is it a perfect Bayesian equilibrium for all types to fire S? For type g = 1 not to fire S, and for the other types to fire S?

(e) Assuming P is rational, what should V conclude about g, if S is fired?

BUSINESS LAW QUESTION

1. If Charlie is being accused of battery, could this be a criminal trial, a civil trial, or both?

Both

Neither
Civil
Criminal

2. Dave is starting a new company making high-end hoodies and needs to find distributors to move his product. He doesn't have any agreements with any distributors at the moment.

His brother Johnny hates Dave and wants to destroy his business, so he goes to all the distributors in town and offers them $5,000 if they refuse to enter into any contract with Dave.

Johnny has committed the tort of tortious interference with contract - true or false?

3. Which of these would be a defense to a claim of defamation, if the plaintiff were NOT a public figure?

a. The defendant believed they were telling the truth.

b. The defendant made the allegedly defamatory statement while they were testifying in a murder trial.

c. The defendant is not a public figure.

d. The defendant did not want to hurt the plaintiff's reputation.

The Bill of Rights affords all accused persons of due process and the right to property. Many cases throught US history have been thrown-out of court because due process was not followed or because evidence was not properly acquired. In many cases, guilty persons have gone free because the police screwed-up the investigation. Do you think its right for a guilty person to go free because of a technicality? Or is upholding the Constitutional right to due process more important?

Kevin is accused by his employer of unauthorized access to a company computer. The employer pursues this as a private action. Which of the following are true about this dispute? Select all that apply.

A. Based on a shared relationship, like employer and employee

B. Requires evidence admissible in court

c. May require a third party to resolve the issue, like a mediator, judge, and/or jury D. May be resolved informally between the perpetrator and victim, or their legal representatives

d. The perpetrator is charged with breaking a law.

e.May be resolved informally between the perpetrator and victim, or their legal representatives