Microeconomics Homework 6: Sequential Games, Monopoly, Cournot & Bertrand Competition

Q1. Consider the following sequential-move game. Gooi Cones moves first and then Ici Cones moves. What are the payoffs realized in subgame perfect Nash equilibrium?

Background

Topic: Sequential Games & Subgame Perfect Nash Equilibrium (SPNE)

This question tests your understanding of sequential-move games, backward induction, and how to find the SPNE in a game with two players and a payoff matrix.

Key Terms and Formulas:

• Sequential Game: A game where players make decisions one after another, with later players observing earlier moves.

• Backward Induction: A method for solving sequential games by reasoning backwards from the end of the game.

• Subgame Perfect Nash Equilibrium (SPNE): An equilibrium where players' strategies constitute a Nash equilibrium in every subgame.

Step-by-Step Guidance

1. Start by examining the payoff matrix for each possible combination of choices by Gooi Cones and Ici Cones.

2. Use backward induction: For each possible action by Gooi Cones, determine Ici Cones' best response (the action that maximizes Ici's payoff).

3. Anticipate Ici Cones' responses and then determine which action Gooi Cones should take to maximize its own payoff, given Ici's best responses.

4. Identify the resulting payoffs for both players based on the equilibrium strategies found above.

Try solving on your own before revealing the answer!

Final Answer: (400, 150)

By backward induction, Gooi Cones chooses Buy Yogurt Machines, and Ici Cones responds with Buy Gelato Machines. The payoffs are (400, 150).

This is the SPNE outcome because each player is making the best possible choice given the other's actions.