The strategic allocation of resources for app monetization platforms is a matter of utmost importance for any business that relies on the profit derived from app-based operations. This requires a comprehensive understanding of the factors involved in the process, and a skillful application of a myriad of economic, mathematical and managerial theories to ensure maximum return on investment (ROI).

The first step in budgeting for app monetization platforms is to understand the core concept of app monetization. In essence, app monetization refers to the process of converting your app’s user base into revenue. The platforms being referred to are essentially software that allow app developers to integrate various monetization methods into their apps. The dominant models include in-app advertising, freemium (free apps with purchasable extras), and paid apps. The choice of model is a decision that should be based on the nature of the app, the targeted user demographic, and the current market conditions; among other factors.

The 'where' in this case is the marketplace in which the app operates. Given the global nature of digital commerce, the marketplace can be anywhere in the world where there is a demand for your app. It's crucial to understand the specific marketplace dynamics, as they directly influence the pricing and monetization strategy.

The 'when' aspect of the equation can be interpreted as the timing of the monetization strategy. For instance, a freemium model might initially offer all features for free during a launch phase to build a user base, and gradually introduce premium features as the app gains popularity. Timing is a crucial factor in any monetization strategy, and its significance can be traced back to the economic theory of supply and demand.

The 'how' can be interpreted as the tactics and technologies used to implement the monetization strategy. For instance, using artificial intelligence (AI) to optimize in-app advertising algorithms, or employing machine learning (ML) to predict user behavior and personalize the user experience. These technologies come with their own costs and benefits, and it's important to evaluate them in the context of your specific app and overall business strategy.

The 'why' refers to the reason for choosing a particular strategy or platform. This is where the cost-benefit analysis comes into play, and it is informed by everything from financial mathematics to game theory.

However, the most critical element in all of this is the user. Ultimately, the success of the app – and by extension, its monetization – depends on the value it delivers to the user. Thus, user value must be the central consideration in all strategic budgeting decisions related to app monetization platforms.

When budgeting, it's also important to remember that monetization platforms are not a one-time investment. They require continuous allocation of resources for maintenance, updates, and adjustments based on market feedback. Therefore, the budgeting process should also take into account these recurring costs.

In conclusion, budgeting for app monetization platforms is a strategic process that requires a deep understanding of the business, market, and technological contexts. It requires a keen understanding of economic and mathematical theories as well as an appreciation for the value of the user. By considering all these factors with a critical and analytical mind, businesses can ensure they are making the best possible investment decision when it comes to app monetization platforms.