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Rationalizable actions in a public good game:-
(More difficult, but also more interesting.) Show the following results for the variant of the game in Exercise in which contributions are restricted to be nonnegative.
a. Any contribution of more than wi/2 is strictly dominated for player i.
b. If n = 3 and w1 = w2 = w3 = w then every contribution of at most w/2 is rationalizable. [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.]
c. If n = 3 and w1 = w2 3 then the unique rationalizable contribution of players 1 and 2 is 0 and the unique rationalizable contribution of player 3 is w3. [Eliminate strictly dominated actions iteratively. After eliminating a contribution of more than wi/2 for each player i (by part a), you can eliminate small contributions by player 3; subsequently you can eliminate any positive contribution by players 1 and 2.]
An instructor claims the average time to take a statistics test is more than 39 minutes. If a sample of 33 students took 43 minutes, is the instructor's claim true? Test at the 0.05 level.
Each party's prefer- ences are represented by the expected number of votes it gains. Formulate this situation as a strategic game and find its mixed strategy equilibria.
What is the profit-maximizing output level xM? What is the profit-maximizing price pM - In absence of recurring fixed costs, what is the monopolist's profit?
Draw this game's extensive-form tree for k = 5. - Use backward induction to find the subgame perfect equilibrium.- Describe the backward induction outcome of this game for any finite integer k.
For multiple sclerosis patients we wish to estimate the mean age at which the disease was first diagnosed. We want a 90% confidence interval that is 8 years wide. If the population variance is estimated to be 85 from previous research, how large a..
Do you think farmers collected more or less hay once this law was established and do you think Iceland's prosperity improved because of good neighbors?
Now consider the variant in which each player, on her turn, has the additional option of shooting into the air. Find the subgame perfect equilibria of this game when pA pB. Explain the logic behind A's equilibrium action.
Each player in any given match can condition her action on whether she was the first to suggest getting together. - Assume that for any given player the probability of being the first is one half. Find the ESSs of this game.
Which is better for the IS manager to employ and why?
Describe the circumstances under which you should use ANOVA instead of t tests, and explain why t tests are inappropriate in these circumstances. Find a peer-reviewed article that reflects these circumstances, describe the research conducted (i.e...
Critical Thinking: Suppose you and a friend each take different random samples of data pairs (x,y) from the sample population. Assume the samples are the same size.
Assume that c is an integral number of cents and that α > c + 1. Is (c, c) a Nash equilibrium of this game? Is there any other Nash equilibrium?
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