Perspective Games

Abstract

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. We consider deterministic and probabilistic perspective games, with structural (e.g., Büchi or parity) and behavioral (e.g., LTL formulas) winning conditions. For these settings, we study the theoretical properties of the game as well as the decidability and complexity of the problem of deciding whether a player has a winning perspective strategy, in terms of both the game graph and the objectives. We compare perspective strategies with memoryless ones, and study an extension of the temporal logic ATL ⋆ with path quantifiers that capture perspective and memoryless strategies.