The bedrock of civilization as we know it, agriculture, has always been deeply tied to the availability and management of water. The advent of irrigation technologies allowed us to take a significant leap forward, reshaping dry landscapes into fertile farmlands and thus, enabling the growth of societies and economies. Today, humankind sits at a similar precipice with regard to sprinkler repair companies. As we face global challenges like climate change and water scarcity, these enterprises are poised to play an increasingly crucial role in maintaining and optimizing our irrigation infrastructure. The future, however, will not be a mere reflection of the present, but a result of several emerging trends and predictions.

At the heart of this evolving landscape is a revolutionary shift towards digital technologies and big data. Where traditionally, sprinkler repair has been reactive and often labor-intensive, we are now moving towards proactive, predictive maintenance aided by digital monitoring systems. For instance, advanced sensors embedded in irrigation systems can monitor the flow, pressure, and moisture levels in real-time, sending alerts to the repair teams even before a fault escalates into a failure. This mitigates the risk of crop loss and saves resources, thereby intertwining the success of these companies with the broader sustainability agenda.

The application of drone technology is another trend worth noting. Drones equipped with infrared cameras or Lidar (Light Detection and Ranging) sensors can swiftly scan large fields to detect leaks or inefficiencies that might not be visible to the naked eye. Not only does this increase the speed of detection, but it also greatly reduces human error. However, it's critical to understand that there is a trade-off here: this technology-driven approach will demand new skills and infrastructural investment from sprinkler repair companies, which could potentially exclude smaller players unable to shoulder these costs.

In addition to technology, another aspect shaping the future of sprinkler repair companies is a more stringent regulatory environment, driven by the recognition of water as an essential yet scarce resource. Jurisdictional mandates concerning water use efficiency are likely to become more common, meaning that repair companies will have to ensure the systems they service adhere to such standards. This will require a deep understanding of not just the technical aspects, but also of the legal and socio-ecological context in which they operate.

These trends are operating within a larger economic framework characterized by the forces of supply and demand. As per the law of demand, an increased emphasis on water conservation and efficient irrigation systems will likely increase demand for specialized sprinkler repair services. On the other side of the equation, supply will be a function of factors like advancements in technology, availability of skilled labor, and regulatory norms.

To unravel the potential implications of these trends, we could draw on game theory, a branch of mathematics that studies strategic interactions. In this scenario, companies, regulators, customers, and the environment can be seen as players in a non-zero-sum game, where the collective actions determine the overall outcome. Consequently, the future of sprinkler repair companies could be one of increased collaboration and collective problem-solving rather than cut-throat competition.

Taking a leaf out of chaos theory, it's pertinent to acknowledge that the trajectory of these companies will not be a linear or predictable one. The 'butterfly effect' - the idea that small changes can have large effects in complex systems - is highly relevant in this context. A single technological breakthrough or a sweeping regulatory reform could drastically alter the landscape for sprinkler repair companies.

In conclusion, the future of sprinkler repair companies is to be seen not in isolation, but as part of a dynamic interconnected system involving technology, regulation, economics, and the environment. It's a future that's ripe with challenges but also teeming with opportunities that demand a deep understanding, adaptability, and innovation from these enterprises. It's a fascinating intersection of the past, the present, and the myriad possibilities of the future.