Investing in a swimming pool is a significant undertaking, both from a financial and logistical perspective. The successful implementation of such a project hinges on the choice of a suitable pool construction expert. Hence, we will scrutinize the crucial questions that warrant attention, prior to engaging a pool builder.

To begin, it is essential to garner information about the longevity of a prospective builder's business operations. This is a key indicator of their stability and experience in the field. The correlation between business longevity and customer satisfaction is well established in economic theory, in particular, the Market Discipline Paradigm. This postulates that companies delivering superior service consistently survive and thrive.

Secondly, inquiring about the builder's licensing and insurance credentials is a non-negotiable aspect. Licensing assures that the builder has met the mandatory educational and experiential prerequisites. Their insurance status safeguards your interests in the event of unforeseen complications or damages. The concept of risk transfer via insurance dates back to Babylonia's Code of Hammurabi in 1754 B.C, highlighting its enduring importance in business transactions.

Thirdly, it is prudent to ask for a portfolio of the builder's past projects. This serves a dual purpose; it provides a tangible demonstration of their craftsmanship and gives insights into their stylistic leanings. Aesthetic sensibilities play a pivotal role in optimizing the hedonic experience of the pool, a concept rooted in experiential psychology.

Subsequently, knowing the number of projects the builder undertakes concurrently is of essence. This influences their ability to deliver within the stipulated timeline and maintain the integrity of workmanship. This alludes to the Theory of Constraints, a management paradigm that identifies an organization's most significant obstacle to achieving its goals.

Furthermore, it is important to ask if the builder employs subcontractors. If so, the nature of quality control measures implemented to maintain standards needs to be investigated. The Nash Equilibrium, a game theory concept, explains this scenario perfectly. Each player (contractor and subcontractor) will make their best decision based on the other's choices, ultimately aiming for a win-win situation.

Question six should focus on the builder's warranty offerings. These warranties can be viewed as a form of guarantee for the quality of work promised. The theory of asymmetric information addresses this scenario where the builder knows more about the product quality than the client. Warranties function as a signal to offset this information imbalance.

Next, query the builder on the expected timeline for the project. A Gantt chart, a widely-used project management tool developed by Henry Gantt, would be an ideal solution for both client and builder to manage timeline expectations.

Understanding what the quote includes is another crucial aspect. This will allow one to make accurate cost comparisons with other builders and ensure there are no last-minute additions. This is a practical application of comparative advantage theory, where each builder's offerings can be evaluated side by side.

Question nine should be about the proposed pool’s design versatility and adaptability to future trends or necessities. Knowledge of the pool's design flexibility will aid in future-proofing the investment. This concept aligns with Option Value theory in economics, which places a value on maintaining flexibility for future decisions.

Next, one should understand the builder's policy on client communication during the project. Regular interaction and updates remove information asymmetry and promote trust. Game theory, particularly the Iterative Prisoner's Dilemma, posits that cooperation, facilitated by communication, provides the best outcome for all parties involved.

Finally, ask whether the builder provides any after-sales services, such as cleaning, maintenance, or repair. Availability of such services not only ensures pool longevity but also enhances customer satisfaction. The after-sales service quality is an integral part of the Total Quality Management (TQM) approach, aimed at long-term success through customer satisfaction.

Having these queries addressed comprehensively will lend credence to the pool builder's reliability, professionalism, and commitment to service quality. This exercise, akin to a due diligence process in financial transactions, will mitigate the risks associated with such an extensive project and ensure a pleasant journey towards owning your dream pool.