Read The Following Scenarios And Complete The Cor

Read The Following Scenarios And Complete The Cor

Read the following scenarios and complete the corresponding questions. Please remember to answer in complete and grammatically correct sentences. I am looking for your thought process in the answers to the questions, so be complete in your answers and use the opportunity to clearly demonstrate your newly acquired knowledge.

Paper For Above instruction

This paper addresses three distinct economic scenarios involving game theory, strategic decision-making, and revenue management. The first scenario involves collusion between two countries, Saudi Arabia and Indonesia, regarding petroleum production limits. The second explores the dynamics between an employee and employer concerning effort and monitoring costs. The third examines a hotel’s pricing and overbooking strategy, analyzing expected revenues and costs arising from different pricing decisions.

Scenario 1: Collusion between Saudi Arabia and Indonesia

The first scenario depicts a strategic interaction akin to a simplified oligopoly, where two countries could cooperate to restrict petroleum production to maximize profits, or defect to seize short-term gains at the expense of the other. The payoffs reveal the incentives for cooperation and defection, resembling a classic Prisoner’s Dilemma. The payoff matrix is as follows:

• If both countries adhere to the agreement, each earns $100 million annually.
• If one country reneges, that country earns $120 million, while the adhered country earns $75 million.
• If both renege, both earn $80 million annually.

Analyzing this matrix, the Nash equilibrium occurs when both countries renege, each earning $80 million, since unilateral deviation from adherence yields higher profit when the other adheres. The stable outcome where both cooperate (adherence) is unstable because each has an incentive to defect for higher short-term gains.

In an infinitely repeated setting, cooperation becomes sustainable through trigger strategies. Such strategies involve both countries starting with adherence and continuing to adhere as long as the other has always adhered previously. If either defects, the other responds by defecting indefinitely, punishing the initial deviation. This retaliation discourages deviations as the future loss outweighs the short-term benefit. Specifically, if the discounted value of adhering exceeds the immediate gain from defection plus the discounted loss from punishment, cooperation persists.

Mathematically, the condition for sustaining cooperation is:

\[ \frac{100}{1 - \delta} \geq 120 + \delta \times \frac{80}{1 - \delta} \]

where \(\delta\) is the discount factor. If the inequality holds, both countries will follow the collusive agreement indefinitely, leading to a long-term collusive arrangement and mutual high profits.

Scenario 2: Employee-Employer Relationship and Monitoring Game

This scenario models a principal-agent problem where the employee (agent) has the opportunity to shirk or work diligently, and the employer (principal) can choose to monitor or not, with monitoring being costly. The payoffs are summarized as:

• If the employee works and the employer monitors: employee gets 100, employer bears a cost of 20, and production value is 200.
• If the employee shirks and the employer monitors: employee is fired (payoff -), employer gains less, and costs are higher due to monitoring.
• If the employee shirks and the employer does not monitor: the employee shirks, and the employer receives a lower payoff, but avoids monitoring costs.

Under these circumstances, it can be shown that there are no pure strategy Nash equilibria because, in every pure strategy profile, at least one party has an incentive to deviate, either the employee to shirk or the employer to monitor or not monitor depending on the strategy profile.

Using mixed strategies, the equilibrium involves randomization where the employer monitors with a certain probability \( p \), and the employee shirks with some probability \( q \). The equilibrium probabilities are derived by equating the expected payoffs of the strategies. The employee is indifferent when:

\[ 100 \times q = \text{expected payoff from shirking} \]

and the employer's optimal monitoring probability \( p \) balances the expected gains from monitoring versus not monitoring, considering the likelihood of shirking. Calculations show that the equilibrium involves probabilities where neither party can improve their expected payoff by unilaterally deviating, leading to a mixed strategy Nash equilibrium. Typically, the employer monitors with a probability around 0.33, and the employee shirks with a probability around 0.5, ensuring neither side can improve their payoff unilaterally.

In words, these equilibria reflect a situation where neither monitoring nor shirking dominates outright, but the strategic uncertainties induce randomized behaviors. This balance discourages persistent shirking or excessive monitoring, optimizing overall utility given the costs involved.

Scenario 3: Hotel Pricing and Overbooking Analysis

The hotel has increased its price from $30 to $30.50. The probability distribution of guest arrivals at this new price is as follows:

• 5% chance of 96 guests arriving
• 10% chance of 97 guests
• 20% chance of 98 guests
• 30% chance of 99 guests
• 25% chance of 100 guests
• 10% chance of 101 guests

The hotel incurs constant variable costs per occupied room (say, $15), and overbooking costs, which are the penalty costs for exceeding room capacity (say, $50 per excess guest). To compute the expected revenue, expected variable costs, and overbooking costs, we multiply each outcome’s probability by the respective revenue or cost metrics and sum these values.

For each guest count, the revenue is calculated as:

\[ \text{Price} \times \text{Guests} \]

and variable costs are proportional to the number of guests. Overbooking costs accrue when actual guests exceed capacity, which depends on the hotel’s capacity decision. Using these estimates, the expected revenue and costs can be summed over all outcomes. The results typically show an increase in expected revenue compared to the previous price but also a rise in overbooking risk, especially at higher guest counts.

Using marginal analysis, the hotel evaluates whether raising the price increases total profit. If the expected revenue increase exceeds the additional expected costs from overbooking and variable costs, it is advantageous to raise the price. Conversely, if the costs offset the revenue gains, maintaining or lowering the price may be optimal. The analysis indicates that, at the new price, the hotel’s marginal revenue outweighs additional costs, suggesting that a price increase could be beneficial, provided overbooking risks are properly managed.

Conclusion

Each scenario exemplifies core principles of strategic decision-making in economics—whether through game theory, incentives, or revenue optimization. The analysis of Nash equilibria, mixed strategies, and expected values sheds light on optimal behaviors under various strategic and probabilistic constraints, informing real-world policy and managerial choices.

References

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