Nils Bulling

Comparing variants of strategic ability: how uncertainty and memory influence general properties of games

Alternating-time temporal logic (ATL) is a modal logic that allows to reason about agents’ abilities in game-like scenarios. Semantic variants of ATL are usually built upon different assumptions about the kind of game that is played, including capabilities of agents (perfect vs. imperfect information, perfect vs. imperfect memory, etc.). ATL has been studied extensively in previous years; however, most of the research focused on model checking. Studies of other decision problems (e.g., satisfiability) and formal meta-properties of the logic (like axiomatization or expressivity) have been relatively scarce, and mostly limited to the basic variant of ATL where agents possess perfect information and perfect memory. In particular, a comparison between different semantic variants of the logic is largely left untouched. In this paper, we show that different semantics of ability in ATL give rise to different validity sets. The issue is important for several reasons. First, many logicians identify a logic with its set of true sentences. As a consequence, we prove that different notions of ability induce different strategic logics. Secondly, we show that different concepts of ability induce different general properties of games. Thirdly, the study can be seen as the first systematic step towards satisfiability-checking algorithms for ATL with imperfect information. We introduce sophisticated unfoldings of models and prove invariance results that are an important technical contribution to formal analysis of strategic logics.

Model Checking Logics of Strategic Ability: Complexity*

This chapter is about model checking and its complexity in some of the main temporal and strategic logics, e.g. LTL, CTL, and ATL. We discuss several variants of ATL (perfect vs. imperfect recall, perfect vs. imperfect information) as well as two different measures for model checking with concurrent game structures (explicit vs. implicit representation of transitions). Finally, we summarize some results about higher order representations of the underlying models.

Reasoning about temporal properties of rational play

This article is about defining a suitable logic for expressing classical game theoretical notions. We define an extension of alternating-time temporal logic (ATL) that enables us to express various rationality assumptions of intelligent agents. Our proposal, the logic ATLP (ATLwith plausibility) allows us to specify sets of rational strategy profiles in the object language, and reason about agents’ play if only these strategy profiles were allowed. For example, we may assume the agents to play only Nash equilibria, Pareto-optimal profiles or undominated strategies, and ask about the resulting behaviour (and outcomes) under such an assumption. The logic also gives rise to generalized versions of classical solution concepts through characterizing patterns of payoffs by suitably parameterized formulae of ATLP. We investigate the complexity of model checking ATLP for several classes of formulae: It ranges from

Expressing properties of resource-bounded systems: the logics RTL* and RTL

\Delta_{\mathbf{3}}^{\mathbf{P}}

Verifying normative behaviour via normative mechanism design

to PSPACE in the general case and from

How to Be Both Rich and Happy: Combining Quantitative and Qualitative Strategic Reasoning about Multi-Player Games (Extended Abstract)

\Delta_{\mathbf{3}}^{\mathbf{P}}

A framework for reasoning about rational agents

to

Agents, beliefs, and plausible behavior in a temporal setting

\Delta_{\mathbf{4}}^{\mathbf{P}}

A Survey of Multi-Agent Decision Making

for the most interesting subclasses, and roughly corresponds to solving extensive games with imperfect information.

Coalitional Responsibility in Strategic Settings

Computation systems and logics for modelling such systems have been studied to a great extent in the past decades. This paper introduces resources into the models of systems and discusses the Resource-Bounded Tree Logics RTL and RTL*, based on the well-known Computation Tree Logics CTL and CTL*, for reasoning about computations of such systems. We present initial results on the complexity/ decidability of model checking.