In the ever-evolving world of policy research, the necessity of collaborating with a suitable think tank is more important than ever. This assertion draws its roots from the crucial role think tanks play in examining multifaceted policy issues, providing insightful solutions, and influencing decision-making processes. As an inquisitive intellect, you might be familiar with the term 'think tank', but for the sake of thoroughness, let's delve into it.

A think tank, in its simplest form, is an organization dedicated to conducting research and providing advice on a wide array of topics including economics, politics, science, technology, and many more. Think tanks can be independent or affiliated with specific institutions or governments. In the United States, think tanks play a pivotal role in shaping public policy, thanks to their expertise and objectivity.

As you traverse the labyrinthine path towards hiring a think tank, the first step is identification. Identify what your research needs are and what policy issues you intend to tackle. This might seem straightforward, but it could be as multifarious as Schrödinger's cat thought experiment. Just as the cat's state is a superposition of both alive and dead states until observed, your policy issue could encompass multiple dimensions that are seemingly paradoxical, yet coexisting.

Next, meticulously research potential think tanks. This is where the beauty of the Pareto principle, or the 80/20 rule, comes into play. Akin to how 80% of outcomes often come from 20% of causes, it is likely that 80% of your desired outcomes will come from a select few think tanks. Therefore, allocating your time and resources efficiently is of paramount importance. Evaluate each think tank based on their research quality, objectivity, relevance, expertise, and reputation. You can utilize tools such as the Global Go To Think Tank Index Report, which is a comprehensive ranking of the world's leading think tanks.

Subsequently, establish contact with your shortlisted think tanks. This is an opportunity to discuss your policy issue, ascertain their interest, and learn about their working methodologies. Engage in a process akin to game theory, where you should aim at a win-win situation. Ascertain the think tank’s capabilities, resources, past research, and their potential for future innovation.

Furthermore, delve into the financial aspects. It's essential to ponder the cost-effectiveness of hiring a think tank. It can be viewed through the lens of the Nash equilibrium, where the optimal outcome occurs when no party has anything to gain by unilaterally changing decisions. Similarly, both you and the think tank should reach a financial agreement that provides optimal outcomes for both parties.

There are, however, potential trade-offs to consider. A prestigious think tank with a global reputation might demand a higher fee, yet their research could potentially exert greater influence on policy decisions. Conversely, a smaller, niche think tank might offer more personalized service and unique insights, albeit with lesser influence.

Ultimately, the decision to hire a think tank is a strategic investment in knowledge and innovation. Just as Descartes proclaimed, "I think, therefore I am," in a world dominated by policy and decision-making: "We research, therefore we progress." Hence, choosing the right think tank can catalyze your policy research endeavors and potentially carve out a path for impactful policy changes.