Library management software (LMS) forms the backbone of efficient and effective operations in libraries of all sizes. As such, the selection process of a software provider should be handled with utmost diligence. It constitutes a significant investment in terms of budget, time, and the expectations pinned on the software. The software provider you choose will determine how well your library can manage its resources and serve its users.

A quintessential understanding of library management software is paramount before embarking on the hiring process. LMS is a comprehensive platform that aids in the automation of library tasks such as acquisition, cataloguing, circulation, and reporting. It is responsible for maintaining bibliographic, authority, and patron databases, significantly streamlining the workflow.

When choosing a software provider, the Pareto Principle, also known as the 80/20 rule, can be a useful guide. The principle suggests that 20% of your efforts can lead to 80% of your results. In the context of library management software, this may translate to focusing on a few critical factors that will result in the majority of the benefits.

Step one of the process is identifying your library's specific needs and aligning them with potential vendors. This begins with a thorough understanding of your library's current operations and any areas in need of improvement.

Vendor expertise is the second critical factor. As a library, you should aim to hire a vendor with a proven track record in successfully deploying LMS. This is especially key when it comes to technological competence and understanding the unique needs of libraries. One approach to gauge this is by looking at the vendor's clientele - have they served libraries comparable to yours in size and scope?

The third aspect to consider is the scalability of the solution offered by the vendor. Libraries evolve over time, growing in size, and consequently, their data and user management needs increase. As such, it is crucial to select a software provider whose solution can accommodate your library's future growth.

In the context of game theory, finding the optimal library management software provider can be likened to a cooperative game. In this scenario, the library and the software provider are players working towards a common goal - to find a solution that best fits the library's needs.

Cost-effectiveness is another vital consideration. The chosen software should give a good return on investment through significant improvements in operational efficiency and user satisfaction. To ascertain this, one could employ the cost-benefit analysis methodology, a tool often used in economics and business decision-making to evaluate the feasibility of a project.

Last but not least, post-deployment support is a key determinant in the hiring decision. This includes training, maintenance, and upgrades, and an efficient customer support system. The vendor's willingness to provide adequate support even after the sale is made is a clear indication of their commitment to customer satisfaction.

In conclusion, hiring the right library management software provider is a multifaceted process that requires a keen understanding of one's needs, thorough market research, and clear and effective criteria for evaluation. Even though there is a myriad of vendors out there, the right one will meet your library's unique needs, offer excellent post-deployment support, and ensure a high return on investment. By investing adequate time and resources in the selection process, libraries stand a better chance of reaping the numerous benefits that come with the right library management software. Remember, the software you choose today will shape the future of your library.