Perspective Multi-Player Games

Abstract

Perspective games model multi-agent systems in which agents can view only the parts of the system that they own. Unlike the observation-based model of partial visibility, where uncertainty is longitudinal – agents partially observe the full history, uncertainty in perspective games is transverse – agents fully observe parts of the history. So far, researchers studied zero-sum two-player perspective games. There, the objective of one agent (the system) is to satisfy a given specification, and the objective of the second agent (the environment) is to fail the specification.We study richer and more realistic settings of perspective games. We consider games with more than two players, and distinguish between zero-sum games, where the objectives of the players form a partition of all possible behaviors, zero-sum games among coalitions, where agents in a coalition share their objectives but do not share their visibility, and non-zero-sum games, where each agent has her own objectives and is assumed to be rational rather than hostile. In the non-zero-sum setting, we are interested in stable outcomes of the game; in particular, Nash equilibria.We show that, as is the case with longitudinal uncertainty, transverse uncertainty leads to undecidability in settings with three or more players that include coalitions or non-zero-sum objectives. We then focus on two-player non-zero-sum perspective games. There, finding and reasoning about stable outcomes is decidable, and in fact, unlike the case with longitudinal uncertainty, can be done in the same complexity as in games with full visibility. In particular, we study rational synthesis in the perspective setting, where the goal is to generate systems that satisfy their specification when interacting with rational environments. Our study includes Boolean objectives given by automata or LTL formulas, as well as a multi-valued setting, where the objectives are ${\text{LTL}}\left[ {\mathcal{F}} \right]$ formulas with satisfaction values in [0, 1], and the agents aim to maximize the satisfaction value of their objectives.