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In this exercise, we will show that in a three-player game a vector of strategies that makes use solely of strategies that are not dominated is not necessarily a perfect equilibrium. To do so, consider the following three-player game, where Player I chooses a row (T or B), Player II chooses a column (L or R), and Player III chooses a matrix (W or E).
(a) Find all the dominated strategies.
(b) Find all the Nash equilibria of this game.
(c) Find all the perfect equilibria of this game.
Find all the Bayesian Nash equilibria of this game. - Which of the Bayesian Nash equilibria are also perfect Bayesian equilibria? Why?
Solve for the Nash equilibrium in this game. Let's assume that the firms decide to collude and each to produce 50% of the total output? Is this collusion sustainable? What if they agreed on a different share of production? Explain
Imagine that there are three major network-affiliate television stations in Turlock, California: RBC, CBC, and MBC. - Find the set of rationalizable strategies in this game.
Suppose that there are four alternatives, w, x, y, and z. Find the top cycle set. Show, in particular, that z is in the top cycle set even though all committee members prefer w.
Explain how a person can choose freely, but his or her choices are caused by past events - Draw the causal tree for Newcomb's Problem when Eve cannot perfectly detect Adam's causal history.
At a 0.025 significance level using the critical value approach, test to see if the % error is higher than the industry standard. Clearly state your hypothesis and conclusions.
Radon levels in a house vary from week to week. In one house a sample of 8 weeks had the following readings for radon level ( in pCi/L): 1.9, 2.8, 5.7, 4.2, 1.9, 8.6, 3.9, 7.2
Which firm produces more in equilibrium? How do the quantities produced in equilibrium change if Firm 1 improves its technology, leading to a slightly lower
James is a rising ice hockey star. He is 19 years old and his future is looking very bright. He is very excited about being selected to play in a representative team and wants to do everything to maximise his chances of achieving this goal. He knows ..
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.
Find all the equilibria of the following two-player game.- What are all the subgames of the two-stage game?- Find all the subgame perfect equilibria of the two-stage game.
This is your exception category. In response to your classmates' posts, explain what circumstances would have to change to move a case from the rule category to the exception category, or vice versa.
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