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Assignment
Here is an opportunity to convert either a missing homework or a homework on which you received a "check minus" into a "check." What I want you to do is to apply the concepts of game theory to a real world situation. Here is what I want you to do:
1. Find a newspaper article describing a real world strategic situation, or think of a strategic situation that occurs in your life. You can even take a strategic situation from a movie or TV show.
2. De?ne a game (either normal-form or extensive-form) that models the situation. You might have to simplify the situation or make up reasonable payo? numbers.
3. Solve the game for its Nash equilibrium (or SPNE, PBE, etc.) and brie?y discuss.
The writeup should be about 2-4 pages, and please be neat when you are drawing the payo? matrix or game tree.
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.
Employee absences can seriously affect productivity. In one country, employees are absent from work an average of 2.6 weeks of the 52-week work-year.
In an extensive-form game with perfect recall, is every Nash equilibrium part of a sequential equilibrium?- That is, for every Nash equilibrium σ∗ does there exist a belief system μ that satisfies the property that (σ∗, μ) is a sequential equilibriu..
Give an example of an extensive-form game in which player i has perfect recall and there is a mixed strategy σiwith more than one behavior strategy equivalent to it.
Describe this situation as an extensive-form game, where the root of the game is a chance move that determines with equal probability whether the contractor was negligent or not.
What are the Nash equilibria under the assumption that the police do not ticket anyone? - What are the Nash equilibria under the assumption that the police ticket everyone who travels more than 70?
How many twbgames are then: in this game (excluding the game itself)? b. Write down the strategies of the two players. c. Find all pure strategy subgame perfect Nash equilania.
Find all the assignments in the core of the n-player game in which every player ranks the houses in the same way.
What is the set of Nash equilibria for k m? For k = m = 1, is the game the same (except for the names of the actions) as any considered so far in this chapter?
Describe this situation as a two-player strategic-form game.- Prove that the only equilibrium in this game is that given by both chains selecting the location x =1/2 .
Write a brief description of a game in which you have participated, entailing strategic moves such as a commitment, threat, or promise and paying spe cial attention to the essential aspect of credibility.
Construct a belief space in which the described situation is represented by a state of the world and indicate that state.
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