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MS5313 Homework 3: Game Theory

Instructions:

1. This is an individual homework. Each student needs to submit one copy. Unlimited trials (upload) are allowed before the deadline; only the latest version will be graded.

2. There are 3 questions. Restrict your answers to pure-strategy equilibrium only (i.e.,you can ignore mixed-strategy equilibrium).

3. Online submission at Canvas by 11:30pm Nov.9 2022 (Wed).

Question 1 (2pt). Consider a simultaneous-move game of two players with the following form. Identify the Nash Equilibrium(s) of the game and the corresponding payoffs for the players.

Question 2 (2pt): Create an example of 2-players simultaneous-move game by your own:

a) One game with no Nash equilibrium

b) One game with at least two Nash equilibria

Question 3 (6pt). Consider a game of two firms regarding capacity investment decisions. Each firm can choose to invest in small, medium, or large capacities. Their payoffs are summarized in the following table.

a) Suppose both firms move simultaneously. Identify the Nash Equilibrium(s) and the corresponding payoffs for the firms.

b) Suppose Firm 1 moves first and then Firm 2 moves. Represent the dynamic game using extensive form and identify the Subgame-Perfect Nash Equilibrium(s) and the corresponding payoffs for the firms.