Timed ATL: Forget Memory, Just Count

In this paper we investigate the Timed Alternating-Time Temporal Logic (TATL), a discrete-time extension of ATL. In particular, we propose, systematize, and further study semantic variants of TATL, based on different notions of a strategy. The notions are derived from different assumptions about the agents’ memory and observational capabilities, and range from timed perfect recall to untimed memoryless plans. We also introduce a new semantics based on counting the number of visits to locations during the play. We show that all the semantics, except for the untimed memoryless one, are equivalent when punctuality constraints are not allowed in the formulae. In fact, abilities in all those notions of a strategy collapse to the “counting” semantics with only two actions allowed per location. On the other hand, this simple pattern does not extend to the full TATL. As a consequence, we establish a hierarchy of TATL semantics, based on the expressivity of the underlying strategies, and we show when some of the semantics coincide. In particular, we prove that more compact representations are possible for a reasonable subset of TATL specifications, which should improve the efficiency of model checking and strategy synthesis.

The Complexity of Model Checking Knowledge and Time

We establish the precise complexity of the model checking problem for the main logics of knowledge and time. While this problem was known to be non-elementary for agents with perfect recall, with a number of exponentials that increases with the alternation of knowledge operators, the precise complexity of the problem when the maximum alternation is fixed has been an open problem for twenty years. We close it by establishing improved upper bounds for CTL* with knowledge, and providing matching lower bounds that also apply for epistemic extensions of LTL and CTL.

An Abstraction-Based Method for Verifying Strategic Properties in Multi-Agent Systems with Imperfect Information

We investigate the verification of Multi-agent Systems against strategic properties expressed in Alternating-time Temporal Logic under the assumptions of imperfect information and perfect recall. To this end, we develop a three-valued semantics for concurrent game structures upon which we define an abstraction method. We prove that concurrent game structures with imperfect information admit perfect information abstractions that preserve three-valued satisfaction. Further, we present a refinement procedure to deal with cases where the value of a specification is undefined. We illustrate the overall procedure in a variant of the Train Gate Controller scenario under imperfect information and perfect recall.

The Refined Best Reply Correspondence and Backward Induction

Fixed points of the (most) refined best reply correspondence, introduced in Balkenborg et al. (2013), in the agent normal form of extensive form games with perfect recall have a remarkable property. They induce fixed points of the same correspondence in the agent normal form of every subgame. Furthermore, in a well-defined sense, fixed points of this correspondence refine even trembling hand perfect equilibria, while, on the other hand, reasonable equilibria that are not weak perfect Bayesian equilibria are fixed points of this correspondence.

Alternating-time Temporal Logic on Finite Traces

We develop a logic-based technique to analyse finite interactions in multi-agent systems. We introduce a semantics for Alternating-time Temporal Logic (for both perfect and imperfect recall) and its branching-time fragments in which paths are finite instead of infinite. We study validities of these logics and present optimal algorithms for their model-checking problems in the perfect recall case.

An Algorithm for Constructing and Solving Imperfect Recall Abstractions of Large Extensive-Form Games

We solve large two-player zero-sum extensive-form games with perfect recall. We propose a new algorithm based on fictitious play that significantly reduces memory requirements for storing average strategies. The key feature is exploiting imperfect recall abstractions while preserving the convergence rate and guarantees of fictitious play applied directly to the perfect recall game. The algorithm creates a coarse imperfect recall abstraction of the perfect recall game and automatically refines its information set structure only where the imperfect recall might cause problems. Experimental evaluation shows that our novel algorithm is able to solve a simplified poker game with 7.10^5 information sets using an abstracted game with only 1.8% of information sets of the original game. Additional experiments on poker and randomly generated games suggest that the relative size of the abstraction decreases as the size of the solved games increases.

Verification of Broadcasting Multi-Agent Systems against an Epistemic Strategy Logic

We study a class of synchronous, perfect-recall multi-agent systemswith imperfect information and broadcasting (i.e., fully observableactions). We define an epistemic extension of strategy logic withincomplete information and the assumption of uniform and coherentstrategies. In this setting, we prove that the model checking problem,and thus rational synthesis, is decidable with non-elementarycomplexity. We exemplify the applicability of the framework on arational secret-sharing scenario.