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Sequential move games

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15-4. Salary Negotiation
The following represents the potential outcomes of your first salary negotiation after graduation:
Assuming this is a Sequential Move Game with the employer moving first, indicate the most likely outcome. Does the ability to move first give the employer an advantage? If so, how? As the employee, is there anything you could do to realize a higher payoff?

EMPLOYER
LOW SALARY OFFER HIGH SALARY OFFER
EMPLOYEE WALKS EMPLOYEE ACCEPTS EMPLOYEE WALKS EMPLOYEE ACCEPTS
EMPLOYER GETS $0 EMPLOYER GETS $100 EMPLOYER GETS $0 EMPLOYEE GETS $100
EMPLOYEE GETS $0 EMPLOYEE GETS $75 EMPLOYEE GETS $0 EMPLOYER GETS $75

15-6. Entry Game with Withdrawal
In the text, we considered a Sequential Move Game in which an entrant was considering entering an industry in competition with an incumbent firm (Figure 15.1). Consider now that the entrant, if fought, has the possibility of withdrawing from the industry (at a loss of 1 for the entrant and a gain of 8 for the incumbent), or staying (at a loss of 5 for each player). What is the equilibrium of this game? Discuss if the entrant is better off with or without the ability to withdraw.

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Solutions to Sequential move games, including tree diagrams, showing decision nodes and terminal nodes.

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Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions.
Player 2
Strategy C D E F
Player 1 A 25, 15 4, 20 16, 14 28, 12
B 10, 10 5, 15 8, 6 18, 13
a. What is player 1's optimal strategy? Why?
b. Determine player 1's equilibrium payoff.

Consider a two-player, sequential-move game where each player can choose to play right or left. Player 1 moves first. Player 2 observes player 1's actual move and then decides to move right or left. If player 1 moves right, player 1 receives $0 and player 2 receives $15. If both players move left, player 1 receives - $10 and player 2 receives $8. If player 1 moves left and player 2 moves right, player 1 receives 10 and player 2 receives $10.
a. Write the above game in extensive form.
b. Find the ash equilibrium outcomes to this game.
c. Which of the equilibrium outcomes is most reasonable? Explain.

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