Game Theory, as it applies to Artificial Intelligence (AI), engages in modeling scenarios among interactive decision-makers. It aims to predict outcomes based on interactions between AI systems and their environment or between separate AI entities. The design is conceptualized to manage applications involving multiparty interactions and conflicts, making it crucial for strategic decision-making processes in AI systems.

• Vital Tool for Multi-Agent Systems: Game Theory provides a systematic approach to model scenarios involving multiple AI entities, also known as agent-based systems, which interact with each other. It helps in analyzing these interactions and understanding their theoretical possibilities.

• Strategic Interaction: Game Theory delves into the study of mathematical models of strategic interaction between various rational decision-makers. Matching this definition, it serves as a fundamental tool for assisting AI's problem-solving algorithm design when several entities are involved.

• Conflict Management: Game Theory can be particularly beneficial in conflict-solving scenarios in AI, reflecting how AI can engage in games or strategic scenarios where each agent's actions can affect others' outcomes.

• Consistent Optimization: Game Theory offers frameworks that facilitate optimization of outcomes, even in scenarios involving multiple interacting entities. It enables an AI system to take into account not only their steps but also the potential steps of others involved.

• Understanding Cooperation: Beyond conflict management, Game Theory helps in understanding cooperation possibilities amongst AI entities, essential for complex tasks requiring multiple agents' synergistic work.

• Reduced Uncertainty: Game Theory aids AI systems in managing situations of uncertainty by incorporating various entities' possible actions into strategic decision-making processes, thus reducing uncertainties and improving overall performance.

Invoking Game Theory into AI demands a systematic approach – a keen understanding of the interactive scenarios, careful selection of suitable games types (like cooperative, non-cooperative, symmetric, asymmetric), and the accurate creation of payoff matrices. The implementation could range from agent-based simulations to reinforcement learning, where game-theoretic principles guide learning algorithms towards an optimal strategy.

Post-implementation, the results need rigorous evaluation with respect to real-time applicability, optimization achieved, and the computational cost incurred. Iterative improvements may be necessary to suit the specific requirements of the AI system.

Given the rising interest in developing interactive and collaborative AI systems, the role of Game Theory in AI is certainly expanding. It is essential to carefully evaluate its potential benefits and limitations against the specific needs of the scenarios for optimal results, and keeping systems efficient and robust. Game Theory presents exciting opportunities in AI, from enhancing decision-making systems to paving the way for true multi-agent intelligent systems.

Numerous benefits make Game Theory an appealing application in AI. These include:

• Complex System Analysis: Game Theory provides mechanisms to deal with complex situations where interactions amongst AI entities, or between an AI system and its environment, occur. It provides a rational framework for dealing with these strategic conflicts or cooperative tasks.

• Decision-Making Process: As an essential tool in decision-making processes, Game Theory can analyze multiple AI agent or component interactions and generate optimal decisions based on their collective behavior.

• Reduction of Uncertainties: By considering all possible actions of different interacting entities, Game Theory reduces uncertainties associated with AI's decision-making processes, thus enhancing the overall system's efficiency.

• Cooperation and Conflict Management: Game Theory presents a clear understanding of cooperation amongst AI entities, vital for challenging tasks requiring shared efforts. Simultaneously, it offers insight into strategic conflict scenarios for more predictable and manageable outcomes.

While there are significant advantages, there are also potential drawbacks that should be considered:

• Situation Complexity: The complicated nature of the strategic situation modeled could potentially make the application of Game Theory challenging, especially for highly complex and non-linear scenarios.

• Incomplete Information: In real-world applications, complete information about other players' choices or behaviors may not always be available, leading to less accurate predictions and outcomes.

• Computational Intensity: The computational complexity and ultimate costs involved in running Game Theory programs can be quite high in some cases. This aspect could prove to be a limiting factor in its widespread use.