In this research, we explore the challenges of determining a winner in games with multiple players and conflicting objectives. We demonstrate these challenges through a series of examples using different scenarios and numbers of players. Our findings reveal that as the number of players increases, the complexity of determining a winner multiplies, leading to ambiguity and confusion.
To illustrate this point, we consider a scenario with four players, where each player has a unique objective function. We demonstrate that even with the same winning condition, different players can have conflicting objectives, making it difficult to determine a clear winner. This phenomenon is further exacerbated as the number of players increases.
To tackle this issue, we propose a new approach based on the concept of "double oracles." This method involves using two separate oracles to evaluate each player’s objective function, allowing for more accurate and robust decision-making. We demonstrate the effectiveness of our approach through experiments using real-world examples.
Our findings have important implications for fields such as artificial intelligence, operations research, and economics, where multiplayer games with conflicting objectives are common. By understanding these challenges and developing effective solutions, we can improve decision-making in complex, multiplayer environments.
In summary, our article highlights the difficulties of determining a winner in games with multiple players and conflicting objectives. We propose a novel approach based on double oracles to address these challenges and demonstrate its effectiveness through experiments. Our findings have far-reaching implications for various fields and can help improve decision-making in complex, multiplayer environments.
Nash Equilibrium in Cyclic Dominance and Biodiversity
