Consider the following problem through the lens of a Markov Decision Process (MDP), and answer questions 1 - 3 accordingly.
Damilola is a soccer player for the ML United under-15s who is debating whether to sign for the NLP Albion youth team or the Computer Vision Wanderers youth team. After three years, signing for NLP Albion has two possibilities: He will still be in the youth team, earning 10,000 (60% chance), or he will make the senior team and earn 70,000 (40% chance). Lastly, he is assured of making the Computer Vision Wanderers senior team after three years, with a salary of 37,000.
Below true or false ?
Q1
Given that Damilola only cares about having the highest expected salary after three years, ML United under-15s is achieved through the action of signing for Computer Vision Wanderers.
Q2
Let us now assume that Damilola cares about the utility derived from the salary as opposed to the salary itself. And his utility function, which baffles economists, is given by Utility, where , and & are constants. In this scenario, the optimal policy ML United under-15s would be to sign for NLP Albion.
Q3:
There are 3 unique states defined in total in this setting.
Q1: Given that Damilola only cares about having the highest expected salary after three years, ML United under-15s is achieved through the action of signing for Computer Vision Wanderers.
False. To determine the highest expected salary, we need to calculate the expected salary for each option. For Damilola, signing for NLP Albion has two possibilities: staying in the youth team and earning $10,000 (60% chance), or making the senior team and earning $70,000 (40% chance). Thus, the expected salary for signing with NLP Albion would be:
Expected Salary (NLP Albion) = (0.6 * $10,000) + (0.4 * $70,000) = $6,000 + $28,000 = $34,000
On the other hand, signing for Computer Vision Wanderers guarantees Damilola a salary of $37,000. Therefore, the expected salary for signing with Computer Vision Wanderers would be:
Expected Salary (Computer Vision Wanderers) = $37,000
Since $37,000 is higher than $34,000, the optimal action for Damilola to achieve the highest expected salary would be to sign for Computer Vision Wanderers.
Q2: Let us now assume that Damilola cares about the utility derived from the salary as opposed to the salary itself. And his utility function, which baffles economists, is given by Utility, where α, β, and γ are constants. In this scenario, the optimal policy would be to sign for NLP Albion.
False. To determine the optimal policy considering utility, we need to evaluate the utility for each option. The utility function is given by Utility = α * salary^β + γ. We need the values of α, β, and γ to calculate the utilities, which are not provided in the question.
Without the specific utility function, it is not possible to determine the optimal policy. Different utility functions will lead to different optimal policies. Therefore, without knowing the specific utility function, we cannot determine whether it is optimal to sign for NLP Albion or Computer Vision Wanderers.
Q3: There are 3 unique states defined in total in this setting.
True. In this setting, there are three unique states:
1. ML United under-15s
2. NLP Albion (youth team)
3. NLP Albion (senior team)
These three states represent the different possible stages of Damilola's soccer career: staying in his current team, signing for NLP Albion and remaining in the youth team, or signing for NLP Albion and making it to the senior team.