Questions Week 5 Essay

Scenario 1 (length: as needed)

Saudi Arabia

Adhere
Renege
Indonesia
A
100, 100
75, 120

R
120, 75
80, 80
1. Find the Nash Equilibria of this game.
By choosing (A, A):
Indonesia can increase its payoff from $100 million to $120 million by choosing to renege rather than adhere to the agreement. Thus this action profile is not Nash equilibrium.
By choosing (A, R):
Indonesia can increase its payoff from $75 million to $80 million by choosing to renege rather than adhere to the agreement. Thus this action profile is not Nash equilibrium.
By choosing (R, A):
Saudi Arabia can increase its payoff from $75 million to $100 million by choosing to adhere rather than renege to the agreement. Thus this action profile is not Nash equilibrium.
By choosing (R, R):
Saudi Arabia can increase its payoff from $80 million to $120 million by choosing to renege rather than adhere to the agreement. Thus this action profile is not Nash equilibrium.
Therefore, we conclude that the game has no Nash equilibrium.
2. Suppose the game was repeated indefinitely. Explain how if both countries follow a trigger strategy.
If these countries decide to be in the game as it is repeated indefinitely, and agree to follow a trigger strategy in which they remain in the first period and continue to stick to the agreement as long as the other country has always adhered but will break a promise otherwise; this definitely leads to a long-term collusive arrangement. When both countries stick to the strategy, there is Nash equilibrium and no country gets better pay off in the expense of the other’s choice. For instance, if Saudi Arabia were to follow the strategy and follow in response of loyalty of Indonesia, there is high possibility of sustained collusion for a long time, but if it decides to change its response, it will have a payoff of $120 million instead of $80 million. This is the payoff in all future periods.
Scenario 2 (length: as needed) Business

Monitor
Don’t Monitor Shirk
Employee
Work
0, -20
150, -100

100, 80
100, 100 1. Show that there are no pure strategy Nash equilibria in this game.
The Nash equilibrium occurs when the employer monitors the worker and the employee does not shirk the worker, in this case the employee gets a payoff of 100 instead of being fired and employer gets a payoff of 80 instead of losing 20. The game is non- strategy, as the employer is unable to maximize profits with regard to output of the employee; in all cases if the employer monitors the employer he undergoes a cost of 20 and if he does not, it is the employee who benefits.
2. What is the mixed strategy Nash equilibria? In

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