Question

Q1: Selling a partnership, independent values (Modified Gibbons 4.10)
Two partners must dissolve their partnership. Partner 1 currently owns share s of the partnership. Partner 2 owns share 1 - s. The game has the following sequence of actions:
1. Nature chooses each player’s valuation for owning the whole partnership, v1, v2 ∈ [0, 1]. Each value vi is independently and uniformly distributed on [0, 1]. Each player observes her own value, but not the value of the other player.
2. Partner 1 chooses a price, p ≥ 0.
3. Partner 2 chooses whether to buy or sell at the price named.
4. If 2 sells, payoffs are: (v1 - p(1 - s), p(1 - s)). If 2 buys, payoffs are: (ps, v2 - ps).
What is the (weak) perfect Bayesian equilibrium?

Q2: Selling a partnership, correlated values (Modified Gibbons 4.10)
Two partners must dissolve their partnership. Partner 1 currently owns share s of the partnership. Partner 2 owns share 1 - s. The game has the following sequence of actions:
1. Nature chooses the common valuation for owning the whole partnership, v ∈ [0, 1]. Let f denote the density function for v and F denote the distribution function. (If this is too hard, assume a uniform distribution on [0, 1].) Player 2 observes this value, but player 1 does not.
2. Partner 1 chooses a price, p ≥ 0.
3. Partner 2 chooses whether to buy or sell at the price named.
4. If 2 sells, payoffs are: (v - p(1 - s), p(1 - s)). If 2 buys, payoffs are: (ps, v - ps).
What is the (weak) perfect Bayesian equilibrium?
[Note: Both players get the same value from the firm! Player 2 observes this value at the beginning of the game, but player 1 does not. This is different from Q1, in which there are two different values.]

Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

Game Theory Problems

This is only a preview of the solution. Please use the purchase button to see the entire solution

Assisting Tutor

Related Homework Solutions

Game Theory Questions
Homework Solution
$33.00
Game Theory
Payoff
Fixed Costs
Equations
Terminal Nodes
Incumbents
Resources
Ideas
Coin Flips
Induction
Ultimatum Game (1070 words)
Homework Solution
$90.00
Mathematics
Game
Theory
Ultimatum
Results
Behavior
Bargaining
Distribution
Trading
Environment
Strategy
Nash Equilibrium Questions
Homework Solution
$30.00
Game Theory
Mathematics
Nash Equilibrium
Matrices
Pure-Strategy
Probability
Schelling’s Focal Point
Predictions
Players
Actions
Communication
Interaction
Pay Off
Game Theory Questions
Homework Solution
$50.00
Mathematics
Game Theory
Train Examples
Functions
Cash
Equations
Projects
Benefits
Nash Equilibrium
Win-Win Improvement
Outcomes
Rates
Tables
Game Theory Questions
Homework Solution
$20.00
Game Theory
Mathematics
Payoffs
Action Pairs
Cheap Talk Game
Discrete Types
Strategy
Functions
Equations
Derive Conditions
Matrices
Variables
Game Theory
Homework Solution
$50.00
Mathematics
Game
Theory
Sequential
Cournot
Monopoly
Nash
Equilibrium
Marginal
Cost
Get help from a qualified tutor
Live Chats