Mastering the art of media buying requires a blend of strategic thinking, audacious creativity, judicious budgeting, and astute market analysis. As media buyers, we are the cartographers who draw the advertising roadmap, guiding our clients' messages to the chosen destination - the target audience, through the labyrinthine landscape of media channels.

Before we delve into the 'how' of media buying, let's first unravel the 'what'. Media buying is the procurement of media inventory at an optimal price and time to deliver a specific marketing message to a particular audience segment. This process involves negotiation, planning, and strategic budgeting. The 'why' behind media buying is straightforward: to achieve an advertisers' goals (awareness, sales, website traffic, etc.) through effective positioning of their messages.

The first step towards strategically budgeting for successful media buying is understanding the client's goals, the target audience, and the client's competitive landscape. The Pareto Principle, also known as the 80/20 rule, is a useful tool in this stage. It posits that 80% of results come from 20% of efforts. This principle helps in identifying the small percentage of the target audience that can yield the highest returns. Another important concept to consider is the Herfindahl-Hirschman Index (HHI), a common measure of market concentration, which can provide insights into the competitive landscape.

Upon defining the target audience and understanding the competitive landscape, the next step is to identify the appropriate media channels. This is where SWOT analysis comes into play. By assessing the Strengths, Weaknesses, Opportunities, and Threats of each potential media platform, media buyers can select the most effective channels for the campaign.

The third step involves a deep dive into budget allocation. One common approach to budget allocation is the "Affordable Method" which involves setting the advertising budget at a level that a company can afford. However, this method can be risky as it bases the budget on what is left over after all other expenses are met, rather than on the marketing objectives.

On the other hand, the "Percentage of Sales Method" bases the budget on a certain percentage of past or anticipated sales. This method ensures that the budget is in line with sales trends. However, it may lead to a reduction in advertising budget when sales are needed the most.

The "Objective and Task Method" is another approach where the budget is set based on what the company wants to achieve and the cost of the tasks necessary to achieve these objectives. This method is often preferred as it directly ties the budget to the marketing objectives.

The final step in this strategic budgeting process is performance tracking and optimization. This involves setting KPIs (Key Performance Indicators) to measure the effectiveness of the media buying process. KPIs could include metrics like cost per click (CPC), cost per acquisition (CPA), or conversion rates. This tracking allows for adjustments and fine-tuning to optimize the campaign's performance.

A mastery of Game Theory can help here, particularly in the context of auctions for online ad spaces. Game Theory, the study of mathematical models of strategic interaction among rational decision-makers, can guide your bidding strategy to ensure you're not overpaying for ad spaces.

In conclusion, the strategic budgeting process for media buying is a blend of art and science. It requires a deep understanding of the client's goals, target audience, competitive landscape, apt media channel selection, meticulous budget allocation, and continuous performance tracking and optimization. With these steps in mind, media buyers can develop an effective and efficient media buying strategy that delivers value to their clients and drives marketing success.