Game Theory Lecture Jan 18

# Game Theory Lecture Jan 18 - Ex 58.2(Cournot • Two firms...

This preview shows pages 1–28. Sign up to view the full content.

Game Theory Lecture Jan 18

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
In Bertrand’s model of oligopoly A) Each firm chooses its quantity as the best response to the quantity chosen by the other(s). B) Each firm chooses its price as the best response to the price chosen by the other(s). C) The firms set quantities sequentially. The second firm’s quantity is the best response to the first firm’s quantity.
Ex 42.2 (a joint project) Two players, choose effort levels x1 and x2 between 0 and 1. Cost of effort to player i is xi2 Part a) Total output is 3x1x2. They divide output equally. Payoff to Player 1 is:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Find Player 1’s best response Maximize
Player 1’s reaction function

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The two reaction functions
Reaction Function Graph

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Part b Total output is 4x1x2 and is split between two players. Cost of effort xi is c(xi)=xi Payoff to player 1 is:
Find Player 1’s best response function Take derivative: What does it tell us?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Ex 58.2 (Cournot) • Two firms, linear inverse demand function P=a-Q=a-q1-q2. Firms have constant marginal costs, c1 and c2 • Profit function for firm 1 is: Reaction Functions Graph reaction functions Algebra Ex 59.1 (Cournot 2) • Linear inverse demand P=a-Q • Quadratic Cost function: C(qi)=qi2 • What is profit function for firm 1? Bertrand model • Each player does best response to other’s price. • Constant marginal cost • Buyers will purchase only from seller with lowest price. If prices are equal, demands are split. • What can be an equilibrium? Ex 69.1 Bertrand with fixed costs Mixed Strategies Matching pennies Player 2’s best response • If Player 1 plays heads with probability p>1/2, what is Player 2’s best response? • What if p<1/2? • What if p=1/2 Both players’ best responses Hide and seek game...
View Full Document

{[ snackBarMessage ]}

### Page1 / 28

Game Theory Lecture Jan 18 - Ex 58.2(Cournot • Two firms...

This preview shows document pages 1 - 28. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online