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An exchange game
Each of two individuals receives a ticket on which there is an integer from 1 to m indicating the size of a prize she may receive. The individuals' tickets are assigned randomly and independently; the probability of an individual's receiving each possible number is positive. Each individual is given the option to exchange her prize for the other individual's prize; the individuals are given this option simultaneously.
If both individuals wish to exchange then the prizes are exchanged; otherwise each individual receives her own prize. Each individual's objective is to maximize her expected monetary payoff. Model this situation as a Bayesian game and show that in any Nash equilibrium the highest prize that either individual is willing to exchange is the smallest possible prize.
Find 95% confidence intervals for the proportion of Tyson packages with contamination and the proportion of Perdue packages with contamination (use 3 decimal places in your answers).
In the game of roulette, a player can place a $8 bet on the number 33 and have a 1/38 probability of winning. If the metal ball lands on 33, the player gets to keep the $8 paid to play the game and the player is awarded an additional $280.
Formulate this situation as a strategic game and find all its mixed strategy equilibria. (First argue that in every equilibrium B assigns probability zero to the action of allocating one division to each pass.
Select one analytic technique and discuss a potential application in your childcare profession. Be specific about your choice and how it applies to your profession.
Construct a 95% confidence interval estimate for the population mean price for two movie tickets, with online service charges, large popcorn, and two medium soft drinks, assuming a normal distribution.
A scooter factory runs three assembly lines, A, B, and C. 98.9% of line A's scooters pass inspection, while only 97.8% of line B's scooters and 98.5% of line C's scooters pass inspection.
Manuel is a high school basketball player. He is a 70% free throw shooter. That means his probability of making a free throw is 0.70. What is the probability that Manuel makes his first free throw on his fifth shot?
Write the payoff vectors corresponding to the equilibria of these games to reveal a pattern. - Can you tell to what the payoff vector of the T-stage game converges as T becomes large?
What is the normal-form representation of this game? - What is the best-response function for each party? - What is the pure-strategy Nash equilibrium? Is it unique?
Construct a 3 x 3 game in which there is only one Nash equilibrium in pure strategies and the vector of payoffs in this equilibrium is "worse" than some other vector of payoffs in the game.
What is the smallest value of T for which it possible for B and b to be played in the first play of the game, in a subgame perfect equilibrium
Employee absences can seriously affect productivity. In one country, employees are absent from work an average of 2.6 weeks of the 52-week work-year.
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