In the dynamic and evolving landscape of manufacturing, contract manufacturing companies are pivotal cogs in the wheel. These enterprises take on the responsibility of producing goods under the labels of other companies, thereby allowing them the luxury of focusing on core competencies like research, design, and marketing. By leveraging the infrastructure, expertise, and resources of contract manufacturers, firms can readily save on cost, time, and effort.

This symbiotic relationship between firms and contract manufacturers has now begun to undergo a transformative shift. The relentless march of technology, market dynamics, economic forces, and customer expectations is reshaping the future of contract manufacturing companies. Let's delve into the predictions and emerging trends that are set to dictate this future.

Firstly, the advent of Industry 4.0 and the proliferation of smart technologies are charting the course for a new wave of digital manufacturing. Advanced analytics, Internet of Things (IoT), artificial intelligence (AI), and machine learning (ML) will take center stage in the manufacturing process. Contract manufacturers that are quick to adopt these technologies will offer more efficient and cost-effective production solutions, bolstering their standing in the competitive market.

Secondly, additive manufacturing, popularly known as 3D printing, is another game-changer. This technology has the potential to revolutionize contract manufacturing by reducing production time, minimizing waste, and even allowing for mass customization. From a theoretical perspective, using the concept of economies of scope, 3D printing can be seen as a disruptor that breaks the traditional trade-off between scale and variety.

Further, considering the growing emphasis on sustainability and environmental stewardiness, contract manufacturing companies are also expected to experience a green transition. The mounting pressure from both regulatory authorities and consumers will see these enterprises to adopt cleaner, more sustainable production practices.

In terms of geographical distribution, the current trend shows a gradual shift from Asia, notably China, to other regions like Eastern Europe and Latin America. This trend could be attributed to a multitude of factors, including rising labor costs, political uncertainties, and the need to lower logistics costs by having production facilities closer to target markets.

On the economic front, contract manufacturing companies are likely to witness a rise in risk-sharing contracts, such as the "cost-plus-incentive fee" contracts. This reflects an attempt to balance the risks and rewards between the firms and contract manufacturers. Drawing from game theory, this can be seen as a way to achieve a Nash equilibrium where both parties can reach an optimal, mutually beneficial agreement.

Lastly, the future will see a more integrated role for contract manufacturers, with increased participation in the design and development phases. This will enable a more streamlined and efficient manufacturing process, with a direct positive impact on time-to-market and overall product quality.

To conclude, the future of contract manufacturing companies lies in embracing technological advancements, adopting sustainable practices, and evolving to meet the changing needs of their partner firms. The companies that manage to seamlessly integrate these trends will not only survive but thrive in the upcoming years. There will be challenges, but the rewards for those who navigate them successfully will be immense and transformative. The future of contract manufacturing looks bright, and the dawn of a new era in manufacturing is upon us.