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(Silverman's game) Each of two players chooses a positive inte- ger. If player i's integer is greater than player j's integer and less than three times this integer then player j pays $1 to player i. If player i's integer is at least three times player j's integer then player i pays $1 to player j. If the integers are equal, no payment is made. Each player's preferences are represented by her expected monetary payoff. Show that the game has no Nash equilibrium in pure strategies, and that the pair of mixed strategies in which each player chooses 1, 2, and 5 each with probability 1 is a mixed strategy Nash equilibrium. (In fact, this pair of mixed strategies is the unique mixed strategy Nash equilibrium.)
Find all Nash equilibria in pure strategies in the following non-zero-sum games. Describe the steps that you used in finding the equilibria.
Assume you are one of two manufactures of tennis balls. Both you and your competitor have zero marginal costs. Total demand for tennis balls is
What is the probability of no off-the-job accidents during a one-year period (to 4 decimals)?
Suppose the maximum risk value for a particular client is 0.4. What is the optimal allocation of investment funds among stocks, bonds, mutual funds and cash? What is the annual rate of return and the total risk for the optimal portfolio?
Little Kona is a small coffee corporation that is planning entering a market dominated through Big Brew. Each corporation's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price.
A pizza delivery service delivers to a campus dormitory. Delivery times follow a normal distribution with a mean of 20 minutes and a standard deviation of 4 minutes. Find the delivery time that 20% of all deliveries are less than?
Suppose you are a potential entrant into a market that previously has had entry blocked through the government. Your market research has estimated that the market demand curve for industry is
What is the probability that Marie will be ranked number one after this year? What is the probability that Marie will win all 4 games this year against Jan?
the following game matrix shows the strategies and payoffs to sony and philips as they choose what connection
a) what is the probability that a randomly selected scooter passed inspection? b) what is the probability that if a randomly selected scooter did not pass inspection, it came from assembly line B?
Planning Parenthood, a national organization that assists teenage mothers with pregnancy, estimates that approximately 37% of the women coming into the center had contracted a sexually transmitted infection. They wish to plan a study to obtain a m..
What is the mean of the sampling distribution of the difference between means?
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