8. Consider a sequential entry game between an incumbent firm (Firm 1) and a potential entrant...
8. Consider a sequential entry game between an incumbent firm (Firm 1) and a potential entrant (Firm 2). Firm 1 moves first and must choose whether to lobby the government to pass a new safety regulation or lobby the government to reject a new safety regulation. Firm 1 is sufficiently powerful that it gets its way with the regulators. Firm 2 moves second and must choose whether to enter this market and compete with Firm 1 or stay out of this market and try something else. Firm 2 has no influence over the regulators. Payoffs are as follows: Firm 1 earns $10 million in revenue if it is a monopolist in this market. Firm 1 and Firm 2 each earn $3 million in revenue if they are duopolists in this market. Firm 2 earns $0 in revenue if it does not enter this market. If the regulation passes then each firm in the market must pay $4 million in new costs, reducing profit accordingly. If Firm 2 does not enter then it need not pay the new costs. If the regulation is rejected, then neither firm pays any costs. Assume both firms are motivated to maximize profits.
(a) Construct a normal form representation of this game. Find all Nash equilibria in pure strategies.
(b) Construct an extensive form representation of this game. Find the rollback (SPNE) equilibrium. Indicate the equilibrium payoffs, equilibrium path and equilibrium strategies.
Homework Answers
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8. Consider a sequential entry game between an incumbent firm
(Firm 1) and a potential entrant...
Consider the following game: there are two players, an incumbent (denoted I) and a potential entrant...
Consider the following game: there are two players, an incumbent (denoted I) and a potential entrant (denoted E) to the market. The entrant has two actions: it can either enter the market in which the incumbent operates, or not enter. The incumbent has two actions: it can either fight the entrant, or accommodate. The payoffs are as follows: if E enters and I fights, E gets -1 and I gets 2. If E does not enter, I gets 10 for...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1 moves twice: Player 1 chooses Enter or Erit, and if she chooses Exit the game ends with payoffs of 2 to player 2 and 0 to player 1. • Player 2 observes player l's choice and will have a choice between Fight or Help if player 1 chose Enter. Choosing Help ends the game with payoffs of 1 to both players. • Finally, player...
Albertsons is currently the only grocery store in the West Park area and acts virtually as...
Albertsons is currently the only grocery store in the West Park area and acts virtually as the monopolist. The Albertsons manager hears a rumor that another grocer, Sprouts, is considering entering the market and building a grocery store in the same plaza as the Albertsons store. Since Albertsons is the incumbent firm, Sprouts must match the wage that Albertsons pays their workers. Further suppose that Albertsons workers are currently paid the minimum wage of $5/hour. Each firm has two strategies:...
Albertsons is currently the only grocery store in the West Park area and acts virtually as...
Albertsons is currently the only grocery store in the West Park area and acts virtually as the monopolist. The Albertsons manager hears a rumor that another grocer, Sprouts, is considering entering the market and building a grocery store in the same plaza as the Albertsons store. Since Albertsons is the incumbent firm, Sprouts must match the wage that Albertsons pays their workers. Further suppose that Albertsons workers are currently paid the minimum wage of $5/hour. Each firm has two strategies:...
In the extensive form representation of the game between Player 1 and Player 2, Player 1...
In the extensive form representation of the game between Player 1 and Player 2, Player 1 moves first and chooses L or R. If Player 1 chooses R the game ends, if Player 1 chooses L then Player 1 and 2 play a simultaneous move game. The game has______________ pure strategy Nash equilibria and__________ pure strategy Subgame Perfect Nash Equilibria (SPNE). The maximum payoff Player 2 gets in a SPNE is___________ . (Please, enter only numerical answers like: 1, 2,...
1. Consider the coupon game. But suppose that instead of decisions being made simultaneously, they are made sequentially, with Firm 1 choosing first, and its choice observed by Firm 2 before Firm 2 ma...
1. Consider the coupon game. But suppose that instead of
decisions being made simultaneously, they are made sequentially,
with Firm 1 choosing first, and its choice observed by Firm 2
before Firm 2 makes its choice.
a. Draw a game tree representing this game.
b. Use backward induction to find the solution. (Remember that
your solution should include both firms’ strategies, and that Firm
2’s strategy should be complete!)
2. Two duopolists produce a homogeneous product, and each has a...
3. Find the Bayesian-Nash Equilibrium for the following Entry game." Two firms in same product market Incumbent cho...
3. Find the Bayesian-Nash Equilibrium for the following Entry game." Two firms in same product market Incumbent chooses Build (B) or Don't Build (D) capacity Entrant chooses Enter E or Stay Out S Incumbent has two types, which affect cost of building capacity a = high cost type, and θι low cost type-o, has a higher capacity cost than θ Prior probability of 0h is p. Idea is incumbent earns a higher profit if entrant stays out. So may want...
QUESTION 15 Consider the following simultaneous-move game: Two firms, Firm 1 (raw player) and Firm 2...
QUESTION 15 Consider the following simultaneous-move game: Two firms, Firm 1 (raw player) and Firm 2 (column player), decide whether to enter (E) or not enter (N) some market. If neither enters, then both make 0. If both enter, the market is oversaturated and so both earn a loss of 5. However, if only one enters, then the entrant earns monopoly profit of 10. Which of the following matrices is the correct representation of the static game? 0.10 10.0 0.0...
Albertsons is currently the only grocery store in the West Park area and acts virtually as...
Albertsons is currently the only grocery store in the West Park area and acts virtually as the monopolist. The Albertsons manager hears a rumor that another grocer, Sprouts, is considering entering the market and building a grocery store in the same plaza as the Albertsons store. Since Albertsons is the incumbent firm, Sprouts must match the wage that Albertsons pays their workers. Further suppose that Albertsons workers are currently paid the minimum wage of $5/hour. Each firm has two strategies:...
Consider two firms 1 and 2 engaging into the following one-shot game: if firm 1 advertises...
Consider two firms 1 and 2 engaging into the following one-shot game: if firm 1 advertises and firm 2 does not, firm 1 will make $20 million in profits and firm 2 will make $6 million. If firm 2 advertises and firm 1 does not, firm 1 will make $2 million and firm 2 will make $6 million. If firm 1 advertises and firm 2 advertises, each firm earns $10 million. If neither firm advertises, firm 2 will make $8...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1 moves twice: Player 1 chooses Enter or Erit, and if she chooses Exit the game ends with payoffs of 2 to player 2 and 0 to player 1. • Player 2 observes player l's choice and will have a choice between Fight or Help if player 1 chose Enter. Choosing Help ends the game with payoffs of 1 to both players. • Finally, player...
1. Consider the coupon game. But suppose that instead of
decisions being made simultaneously, they are made sequentially,
with Firm 1 choosing first, and its choice observed by Firm 2
before Firm 2 makes its choice.
a. Draw a game tree representing this game.
b. Use backward induction to find the solution. (Remember that
your solution should include both firms’ strategies, and that Firm
2’s strategy should be complete!)
2. Two duopolists produce a homogeneous product, and each has a...
3. Find the Bayesian-Nash Equilibrium for the following Entry game." Two firms in same product market Incumbent chooses Build (B) or Don't Build (D) capacity Entrant chooses Enter E or Stay Out S Incumbent has two types, which affect cost of building capacity a = high cost type, and θι low cost type-o, has a higher capacity cost than θ Prior probability of 0h is p. Idea is incumbent earns a higher profit if entrant stays out. So may want...
QUESTION 15 Consider the following simultaneous-move game: Two firms, Firm 1 (raw player) and Firm 2 (column player), decide whether to enter (E) or not enter (N) some market. If neither enters, then both make 0. If both enter, the market is oversaturated and so both earn a loss of 5. However, if only one enters, then the entrant earns monopoly profit of 10. Which of the following matrices is the correct representation of the static game? 0.10 10.0 0.0...
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