Selecting a private jet charter can be an overwhelming task, even for the most discerning individual. The endeavor involves navigating an intricate maze of factors such as aircraft capabilities, safety records, pricing models, and contractual fine print. To simplify this process, it is advisable to ask the pertinent questions to a private jet charter company, ensuring that the flight chosen aligns perfectly with personal or business needs. Herein, are a series of essential interrogatives one should aim to ask, along with their respective explanations, while engaging a private jet charter company.

To commence with, 'What is the company's safety record and what safety measures are in place?' is a crucial question. The safety of your journey is paramount, therefore, understanding the company’s safety record is essential. In aviation, safety metrics are assessed via ARGUS and Wyvern ratings. These independent firms conduct comprehensive evaluations of a charter company’s safety standards, which include pilot training, maintenance protocols, and insurance coverage. Therefore, it's germane to inquire about these ratings, as they would provide an objective measure of the company's safety ethos.

Secondly, 'What aircraft types are available in the fleet?' is a necessary query. A company's fleet configuration can significantly impact the overall travel experience. Factors such as speed, range, cabin space, luggage capacity, and available amenities can vary across different aircraft models. For instance, a long-range journey would necessitate a jet like the Gulfstream G650, which can cruise over 7,000 nautical miles without refueling, while a shorter trip may be better served by a light jet such as the Learjet 75. Comprehending the fleet's diversity would empower you to select a jet that best meets the journey's specifics.

Thirdly, 'What are the pricing models?' is a requisite question. A charter's cost can be influenced by a multitude of factors such as the aircraft type, journey length, and additional services like catering. Some companies operate on a fixed hourly rate model, while others use a dynamic pricing model, fluctuating based on demand and market dynamics. Therefore, understanding these models would aid in making an informed decision regarding the financial commitments.

'What is the cancellation policy?' is the fourth question that should be asked. In an industry subject to unpredictable variables such as weather conditions and mechanical issues, flexibility is crucial. Some companies stipulate rigid cancellation policies, while others offer a more lenient approach, allowing for last-minute changes. Understanding the cancellation policy would provide clarity on the potential repercussions of unexpected itinerary changes.

Lastly, 'What are the additional services provided?' should be asked. As private aviation is a luxury service, the scope and quality of supplementary services can significantly enhance the travel experience. These could encompass personalized catering, ground transportation arrangements, and concierge services.

To add a layer of sophistication to the decision-making process, consider applying game theory, a branch of mathematics that studies strategic interactions. This theory, which holds deep roots in economics and social science, could lead to a more optimal outcome. By treating the selection process as a game, where the players are you and the charter companies, you could establish a strategy that maximizes your payoffs (safety, comfort, cost-efficiency, etc.) and minimizes your costs.

In conclusion, choosing a perfect private jet charter involves a careful balance between the luxury, safety, efficiency, and cost-effectiveness offered by various companies. By asking these critical questions, and using decision-making frameworks such as game theory, you can navigate the complex landscape of private aviation with confidence and precision. Remember, the ultimate goal is to select a charter that aligns seamlessly with your unique travel aspirations and requirements.