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Two players are to divide $2,000 between them. The utility functions of the players are the amounts of money they receive: u1(x) = u2(x) = x. If they cannot come to agreement, neither of them receives anything.
For the following cases, describe the bargaining game derived from the given situation, in utility units, and find its Nash solution of the game.
(a) Given any division which the players agree upon, the first player receives his full share under the agreed division, and the second player pays a tax of 40%.
(b) Repeat the situation in the previous item, but assume that the second player pays a tax of 60%.
(c) The first player pays a tax of 20%, and the second pays a tax of 30%.
In the following two-player zero-sum game, find the optimal behavior strategies of the two players. (Why must such strategies exist?)
Find the set of Nash equilibria of this game.- Prove that the set of correlated equilibria of this game is the convex hull of the set of Nash equilibria.
Advanced Micro Devices declared a 10 percent price raise for certain advanced microprocessors, used primarily in video games. The processors will sell for about $1,000 compared to Intel's $950 price.
You randomly call friends who could be potential partners for a dance. You think that they all respond to your requests independently of each other, and you estimate that each one s 7% likely to accept your request. Let X denote the number of call..
What are the pure-strategy Bayesian Nash equilibria of this game? - Which of the Bayesian Nash equilibria that you found in (a) are perfect Bayesian equilibria?
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.
Does this game have a subgame perfect Nash equilibrium? - Do you think any one of the players has a strategy that guarantees him a win (a payoff of 2)?
Construct a belief space in which the described situation is represented by a state of the world and indicate that state.
A scooter factory runs three assembly lines, A, B, and C. 98.9% of line A's scooters pass inspection, while only 97.8% of line B's scooters and 98.5% of line C's scooters pass inspection.
According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected.Referring to the information, the average of all the sample proportions of customers who will mak..
Represent this game in the extensive and normal forms. - Find the pure-strategy Nash equilibria of this game. - Calculate the mixed-strategy Nash equilibria and note how they depend on x.
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?
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