Reasoning about Knowledge and Strategies under Hierarchical Information

Two distinct semantics have been considered for knowledge in the context of strategic reasoning, depending on whether players know each other's strategy or not. The problem of distributed synthesis for epistemic temporal specifications is known to be undecidable for the latter semantics, already on systems with hierarchical information. However, for the other, uninformed semantics, the problem is decidable on such systems. In this work we generalise this result by introducing an epistemic extension of Strategy Logic with imperfect information. The semantics of knowledge operators is uninformed, and captures agents that can change observation power when they change strategies. We solve the model-checking problem on a class of "hierarchical instances", which provides a solution to a vast class of strategic problems with epistemic temporal specifications on hierarchical systems, such as distributed synthesis or rational synthesis

The Hanabi Challenge: A New Frontier for AI Research

From the early days of computing, games have been important testbeds for studying how well machines can do sophisticated decision making. In recent years, machine learning has made dramatic advances with artificial agents reaching superhuman performance in challenge domains like Go, Atari, and some variants of poker. As with their predecessors of chess, checkers, and backgammon, these game domains have driven research by providing sophisticated yet well-defined challenges for artificial intelligence practitioners. We continue this tradition by proposing the game of Hanabi as a new challenge domain with novel problems that arise from its combination of purely cooperative gameplay with two to five players and imperfect information. In particular, we argue that Hanabi elevates reasoning about the beliefs and intentions of other agents to the foreground. We believe developing novel techniques for such theory of mind reasoning will not only be crucial for success in Hanabi, but also in broader collaborative efforts, especially those with human partners. To facilitate future research, we introduce the open-source Hanabi Learning Environment, propose an experimental framework for the research community to evaluate algorithmic advances, and assess the performance of current state-of-the-art techniques.Comment: 32 pages, 5 figures, In Press (Artificial Intelligence

Reasoning about Knowledge and Strategies: Epistemic Strategy Logic

In this paper we introduce Epistemic Strategy Logic (ESL), an extension of Strategy Logic with modal operators for individual knowledge. This enhanced framework allows us to represent explicitly and to reason about the knowledge agents have of their own and other agents' strategies. We provide a semantics to ESL in terms of epistemic concurrent game models, and consider the corresponding model checking problem. We show that the complexity of model checking ESL is not worse than (non-epistemic) Strategy LogicComment: In Proceedings SR 2014, arXiv:1404.041

A computer scientist looks at game theory

I consider issues in distributed computation that should be of relevance to game theory. In particular, I focus on (a) representing knowledge and uncertainty, (b) dealing with failures, and (c) specification of mechanisms.Comment: To appear, Games and Economic Behavior. JEL classification numbers: D80, D8

The Complexity of Synthesizing Uniform Strategies

We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable. Typically, we can state that a strategy is observation-based. We propose a formal language to specify uniformity properties, interpreted over two-player turn-based arenas equipped with a binary relation between plays. This way, we capture e.g. games with winning conditions expressible in epistemic temporal logic, whose underlying equivalence relation between plays reflects the observational capabilities of agents (for example, synchronous perfect recall). Our framework naturally generalizes many other situations from the literature. We establish that the problem of synthesizing strategies under uniformity constraints based on regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007

Purification of large bicolorable graph states

We describe novel purification protocols for bicolorable graph states. The protocols scale efficiently for large graph states. We introduce a method of analysis that allows us to derive simple recursion relations characterizing their behavior as well as analytical expressions for their thresholds and fixed point behavior. We introduce two purification protocols with high threshold. They can, for graph degree four, tolerate 1% (3%) gate error or 20% (30%) local error.Comment: 12 pages, 5 figures, revtex; typos and clarifications adde