Perspective Games

We introduce and study perspective games, which model multi-agent systems in which agents can view only the parts of the system that they own. As in standard multi-player turn-based games, the vertices of the game graph are partitioned among the players. Starting from an initial vertex, the players jointly generate a computation, with each player deciding the successor vertex whenever the generated computation reaches a vertex she owns. A perspective strategy for a player depends only on the history of visits in her vertices. Thus, unlike observation-based models of partial visibility, where uncertainty is longitudinal - players partially observe all vertices in the history, uncertainty in the perspective model is transverse - players fully observe part of the vertices in the history. Perspective games are not determined, and we study the problem of deciding whether a player has a winning perspective strategy. In the pure setting, we show that the problem is EXPTIME-complete for objectives given by a deterministic or universal parity automaton over an alphabet that labels the vertices of the game, and is 2EXPTIME-complete for LTL objectives. Accordingly, so is the model-checking complexity of Perspective-ATL∗- an extension of ATL∗ with path quantification that captures perspective strategies. In all cases, the complexity in the size of the graph is polynomial - exponentially easier than games with observation-based partial visibility. In the probabilistic setting, we show that deciding whether a player has an almost-winning randomized perspective strategy is undecidable. Finally, we study perspective games with objectives given by ω-regular conditions over the set of vertices. In particular, we compare the power of perspective and memoryless strategies and show, for example, that while the generalized-Büchi and the Streett objectives do not admit memoryless strategies, generalized Büehl admits perspective strategies, and Streett does not. We also describe a fragment of LTL that admits perspective strategies.