Find all pure strategy bayesian nash equilibria for game

Assignment Help Game Theory

Reference no: EM131252424

Separating Equilibrium: Consider the entry game described in exercise. Is it true that in this game any separating perfect Bayesian equilibrium imposes unique beliefs for the incumbent in all information sets?

Exercise
Entry (again): The market for widgets has an incumbent firm. The total value of having 100% of the market is 10, which the incumbent receives if no one enters. A potential entrant arrives, and it can be one of two types: tough (T ) or weak (W). A weak entrant can choose one of three options: small entry (S), big entry (B), or exit (X). A tough entrant can choose only between S or B (it is inconceivable that it would choose X). There is no cost for a tough entrant to enter at any level. However, it costs a weak entrant 6 to enter at any level. Exiting costs nothing to the entrant. The entrant knows his type, but the incumbent knows only the prior distribution: Pr{T }= 1/2.

In response to any level of entry, the incumbent can choose to accommodate (A) or fight (F). Accommodating an entrant imposes no costs. Independent of the entrant's type, accommodating small entry gives the incumbent 60% of the market and the entrant 40%, while accommodating big entry gives the incumbent 40% of the market and the entrant 60%.

Fighting a tough entrant increases the incumbent's market share by 20% (relative to accommodating) but imposes a cost of 4 on the incumbent. Fighting a weak entrant that chose S increases the market share of the incumbent to 100% but imposes a cost of 2 on the incumbent. Fighting a weak entrant that chose B increases the market share of the incumbent to 100% but imposes a cost of 8 on the incumbent.

a. Draw this game in extensive form.

b. Using a matrix representation, find all the pure-strategy Bayesian Nash equilibria for this game.

c. Which one of the Bayesian Nash equilibria is preferred by the incumbent? Can it be supported as a perfect Bayesian equilibrium?

d. Find all the perfect Bayesian equilibria of this game.

Reference no: EM131252424

Questions Cloud

Monitor and ensure good performance : How would you monitor and ensure good performance from your bastion host?

What are the pure strategy bayesian nash equilibria : 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?

Describe operational risks and their sources : why cyber security exists and how it benefits the society, describe operational risks and their sources.describe product liability and the role of the government in acquisition and procurement of cyber security products and services.

What issues are most important to your opponent : What issues are most important to your opponent? (List 5 in order of importance) What is your opponent's BATNA? Reservation Price? Target? What are your opponent's sources of power?

Find all pure strategy bayesian nash equilibria for game : Draw this game in extensive form. - Using a matrix representation, find all the pure-strategy Bayesian Nash equilibria for this game.

Are women really more emotional than men : Are women really more emotional than men? Defend your answer based on the available research. This will require you to cite your sources as well!

Performance reports and budgeting : Performance Reports and Budgeting - Answer the case question in the Requirements section of the case. Your memo should be at least two paragraphs in length.

Create a short executive summary for your company : Prepare a short executive summary for your company, explaining the level of integration the bloc has currently achieved, the level it aspires to accomplish, and the relationships it has with other African trade blocs.

Prepare a research report : You are required to prepare a research report. The research report should include: Title page; Executive summary; Table of contents;

User Account

All Pages