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(Cohesion in legislatures) The following pair of games is designed to study the implications of different legislative procedures for the cohesion of a governing coalition. In both games a legislature consists of three members. Ini- tially a governing coalition, consisting of two of the legislators, is given. There are two periods. At the start of each period a member of the governing coalition is randomly chosen (i.e. each legislator is chosen with probability 1 ) to propose a bill, which is a partition of one unit of payoff between the three legislators. Then the legislators simultaneously cast votes; each legislator votes either for or against the bill. If two or more legislators vote for the bill, it is accepted. Otherwise the course of events differs between the two games. In a game that models the current US legislature, rejection of a bill in period t leads to a given partition dt of the pie, where 0 dt 1 for i = 1, 2, 3; the governing coalition (the set from which i 2 the proposer of a bill is drawn) remains the same in period 2 following a rejection in period 1. In a game that models the current UK legislature, rejection of a bill brings down the government; a new governing coalition is determined randomly, and no legislator receives any payoff in that period. Specify each game precisely and find its subgame perfect equilibrium outcomes. Study the degree to which the governing coalition is cohesive (i.e. all its members vote in the same way).
If so, find a payoff function consistent with the information. If not, show why not. Answer the same questions when, alternatively, the decision-maker prefers the lottery.
Determine the expression for the number of customers served at each cart. (Recall that Cart O gets the customers between O and x, or just x, while Cart 1gets the customers betv.reen x and l, or 1 - x.)
What are the lower and upper specifications limits (a, b) such that only 2.5% of the pistons ring would exceed the limits. What is the power of the test if the true mean shifts by one standard deviation?
A certain tennis player makes a successful first serve 75% of the time. Assume that each serve is independent of the others. If she serves 5 times, what's the probability she gets:
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.
Find the Nash revision strategies for Ann and Bob which form a SGPNE with the δ identified in part (a) - Verify that the strategies found in part (b) do form a SGPNE
An injection molding machine produces golf tees that are 20.0% nonconforming. Using the normal distribution as an approximation to the binomial, find the probability that, in a random sample of 360 golf tees, 65 or less are nonconforming. Show you..
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.
How many female offspring does a normal organism produce? How many male offspring? Use your answers to ?nd the number of grandchildren born to each mutant and to each normal organism.
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?
What is the dominant strategy and describe the Nash equilibrium or Nash equilibria, Why did they do this? Do you think that Sun Resorts cares about how many airlines will serve the island? Explain.
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
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