Understanding the underlying mechanisms and making strategic decisions when hiring a Caribbean Yacht charter is akin to navigating the intricate matrices of a complex legal case or deciphering a particularly challenging statistical model. However, with the right approach, it becomes a manageable task, even pleasurable, as you prepare for your tropical getaway.

Firstly, the relevance of the yacht charter company cannot be underestimated. In economic terms, this can be compared to the market structure of oligopoly, where a small number of firms have the majority of market share. The major players in the yacht chartering business, like Moorings, Dream Yacht Charter, or Sunsail, have a reputation built on years of successful operations. Similar to the principle of "branding" from marketing theory, these companies have developed a certain brand image based on quality of service, delivering on promises, and overall customer satisfaction. Thus, your first step should be to identify reputable charter companies that service the Caribbean.

Secondly, understanding the type of yacht to charter is crucial. Here we encounter a scenario akin to an optimization problem in mathematics: you're seeking the 'perfect' yacht given a set of constraints such as budget, passenger size, and personal preferences. There are two main categories: crewed and bareboat. A crewed yacht provides a full staff to cater to your needs, making it a luxury option. A bareboat charter, on the other hand, gives you the reins, akin to the principle of laissez-faire in economics, allowing you complete control over your voyage. Comparing these options, the tradeoff becomes clear: the luxury and convenience of a crew versus the freedom and adventure of a bareboat charter.

Thirdly, your choice of charter location in the Caribbean is pivotal. This is reminiscent of the locational interdependence theory in industrial organization literature which postulates that firms base their location decision not only on their preferences but also on the anticipated location choices of their rivals. Similarly, your decision should be informed by factors such as the sailing conditions, natural beauty, proximity to other islands, and the culture and cuisines available. Popular choices include the British Virgin Islands, known for their line-of-sight navigation and tranquil waters, and the Bahamas, known for their stunning coral reefs and maritime life.

When it comes to timing, yacht availability and pricing are influenced by the principles of supply and demand. The Caribbean yacht chartering industry, like most tourism-related industries, experiences periods of peak demand, known as high season, which usually coincides with the dry season (November to May). Conversely, the low season (June to October) sees fewer tourists due to the higher likelihood of hurricanes. Thus, if you are looking for lower prices and greater availability, the low season would be a better choice. However, remember to consider the tradeoff between weather conditions and cost savings.

Lastly, the contract, or Charter Party in maritime parlance, is a legally binding document outlining the rights and obligations of the charterer and the owner. Similar to understanding a complex legal statute, it is vital that you review all terms and conditions before signing. Areas to pay close attention to are the cancellation policy, insurance coverage, and any additional costs that may not be included in the initial quote.

In conclusion, the process of hiring a Caribbean Yacht Charter for your tropical getaway involves considering multiple factors, each of which brings its own complexities. However, by applying theories from different disciplines such as economics, mathematics, and law, to the decision-making process, you can navigate this challenge proficiently. It is, after all, part of the exciting journey towards a memorable Caribbean sailing experience.