Is there a common prior p over s

Assignment Help Game Theory

Reference no: EM131332735

In this exercise, suppose there are four states of nature, S = {s₁₁, s₁₂, s₂₁, s₂₂}. The information that Player I receives is the first coordinate of the state of nature chosen, while the information that Player II receives is the second coordinate.

The conditional probabilities of the players, given their respective informations, are given by the following table (the conditional probability of Player I appears in the left column, while the conditional probability of Player II appears in the top row of the table):

107_Matrix 2.jpg

The table is to be read as stating, e.g., that if Player I receives information indicating that the state of nature is contained in {s₁₁, s₁₂}, he believes with probability 1 that the state of nature is s₁₁.

(a) Construct a belief space in which the described situation is represented by a state of the world and indicate that state. Suppose that the state of nature is s₁₂, and that ω is the corresponding state of the world. Answer the following questions:

(b) What are the minimal belief subspaces Y˜ _I(ω) and Y˜ _II(ω) of the players?

(d) Is there a common prior p over S such that the players agree that the state of the world has been chosen according to p?

(e) Is the state of the world ω ascribed positive probability by p?

Reference no: EM131332735

Questions Cloud

Pro forma calculations of revenue and expenses : You are asked to do a pro forma analysis of a decision to build a new clinic. Your existing clinic is booked at 100% capacity, it is generating 800 visits per year. There is currently a two month wait for new appointment. How many visits would you as..

Obtaining the money she needs for investing : Alice Cooper contributes ten percent of her monthly earnings to her 401(k) plan at work. The plan allows her to invest in several different types of mutual funds and her employer matches up to 5% of her salary. Which suggestion for obtaining the mone..

What amount should be reported as cash : Prepare a bank reconciliation. Journalize the necessary entries. The accounts have not been closed. If a balance sheet were prepared for Remedy Medical Co. on April 30, 2014, what amount should be reported as cash?

Increases and decreases in the invasive species population : You will write a 1-page lab report using the scientific method to answer the following questions: Why do you see increases and decreases in the invasive species population? What are the implications associated with these alterations to the ecosystem ..

Is there a common prior p over s : Is there a common prior p over S such that the players agree that the state of the world has been chosen according to p?- Is the state of the world ω ascribed positive probability by p?

Suppose the average return on an asset : Suppose the average return on an asset is 12.2 percent and the standard deviation is 21.8 percent. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel to determine the probability that in any given year you wi..

Planning to acquire a new automobile for commuting : A recent graduate is planning to acquire a new automobile for commuting to work in Atlanta. One option is to purchase a $25, 000 4-door sedan by paying the dealer $5, 000 at the time of purchase and financing the remaining $22, 000 to be repaid in 60..

What is the tax benefit or tax implication of the topic : ACCT Research Paper- What is the tax benefit or tax implication of this topic? Who does it benefit or affect? (i.e. individual, estate, or both). What are some of the requirements for this topic?

What was the candidate score : The testing service reported to a particular employer that one of its job candidate's scores fell at the 90th percentile of the distribution (i.e., approximately 90% of the scores were lower than the candidate's, and only 10%were higher). What was..

User Account

All Pages