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Let i be a player with perfect recall in an extensive-form game and let bi be a behavior strategy of player i.
Suppose that there is a strategy vector σ-i of the other players such that ρ(x; bi, σ-i) > 0 for each leaf in the game tree.
Prove that there exists a unique mixed strategy σi equivalent to bi.
A finite lot of 40 digital watches includes 30% nonconforming units. Using the hypergeometric distribution, what is the probability that a sample of 6 will contain 3 nonconforming watches? Show your work.
Show that every such contribution is a best response to a belief that assigns probability one to each of the other players' contributing some amount at most equal to w/2.
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 lottery requires that you select six different numbers from the integers 1 to 49. Write a Java program that will do this for you and generate five sets of six numbers as a result.
Suppose you have been offered chance to participate in a Treasure Hunt game whose rules are as follows. There are 3-colored boxes: red, green and yellow.
A worker faces a review every year. He prefers to spend time making if he will be reviewed; otherwise he would prefer to use time somewhere else.
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?
Show that for any p ∈ [0, 100], there is a Nash equilibrium of the game in which an agreement is reached at this price. Describe the equilibrium strategy profile and explain.
Consider now an evolutionary game where what evolves are not strategies in a one-shot game but strategies in a repeated game without discounting
A market research firm conducts studies regarding the success of new products. The company is not always perfect in predicting the success.
A simple game is a game in coalitional form, with transferable utility,- Show that the core of any simple game can be characterized in terms of its set of veto players.
A null hypothesis is that the average pulse rate of adults is 70. For a sample of 64 adults, the average pulse rate is 71.8. A significance test is done and the p-value is 0.02. What is the most appropriate conclusion based on α of 0.05?
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