Dynamic Coalitions in Games on Graphs with Preferences over Temporal Goals

In multiplayer games with sequential decision-making, self-interested players form dynamic coalitions to achieve most-preferred temporal goals beyond their individual capabilities. We introduce a novel procedure to synthesize strategies that jointly determine which coalitions should form and the actions coalition members should choose to satisfy their preferences in a subclass of deterministic multiplayer games on graphs. In these games, a leader decides the coalition during each round and the players not in the coalition follow their admissible strategies. Our contributions are threefold. First, we extend the concept of admissibility to games on graphs with preferences and characterize it using maximal sure winning, a concept originally defined for adversarial two-player games with preferences. Second, we define a value function that assigns a vector to each state, identifying which player has a maximal sure winning strategy for certain subset of objectives. Finally, we present a polynomial-time algorithm to synthesize admissible strategies for all players based on this value function and prove their existence in all games within the chosen subclass. We illustrate the benefits of dynamic coalitions over fixed ones in a blocks-world domain. Interestingly, our experiment reveals that aligned preferences do not always encourage cooperation, while conflicting preferences do not always lead to adversarial behavior.