Who is responsible for developing employees skills? Management? or Employees themselves?

Self-initiative comes first. Most Company evaluates first how the employee is potential to their business and whether he or she needs an assessment for development as well as whether the individual is loyal and will remain with the Company after spending a lot of time and money training .

Both. Employers and employees should have the initiative to develop the skills of the employees.

Both are key players in the work environment

Absolutely both for best result.

If a manager or leader wants to mentor / develop employees, he cannot do so without employees wanting to be mentored / developed.

On the other hand, if an employee wants to develop him/herself, he/she can do so on his/her own, but in a non-nurturing environment he/she will only go as far as he/she pushes him/herself.

If you are asking which is more important ingredient in a developlement success, it's the employee. Nothing can happen if employee does not want it to happen.

Thanks for inviting.

Very interesting question.

Yes it is a matter of big discussion and debate.

Technically speaking always employees are hired with a set of certain skills which management require. However if there is change in the role of hired staff which result in the requirement of new skill, then in such case its responsibility of management to enhance skills to his employee.

For Example an Accountant is hired by a company to work on Tally accounting software with the same skill which employee possess, however after few years company decided to move its platform from Tally to SAP under such situation its responsibility of management to provide necessary training to employee so that he can comfortably do his duties.

However if company refuses to provide the training then employee have an options that he can make him self as self motivated to lean SAP by him self either within the company or outside  so that he can continue his job.

SELF MOTIVATION OF EMPLOYEE...AND PRODUCT KNOWLEDEGE SHOULD BE GIVEN BY THE EMPLOYER

This is an excellent question. In my opinion, developing employee skills is a shared responsibility. The employee should always be on the lookout for ways to improve their performance and should by no means content themselves with what is being taught at work. On the other hand, management is required to provide the adequate work environment, such as motivational words and proper training. Furthermore, self-motivation is extremely helpful as it boosts confidence and encourages work efficiency. 

Both of them but the major issue is the method that company takes to improve the employee skills