We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games.

This thesis is on information dynamics modeled using *dynamic epistemic logic*. It takes the simple perspective of identifying models with maps, which under a suitable topology may be analyzed as *topological dynamical systems*. It is composed of an introduction and six papers. The introduction situates DEL in the field of formal epistemology, exemplifies its use and summarizes the main contributions of the papers.Paper I models the information dynamics of the *bystander effect* from social psychology. It shows how augmenting the standard (...) machinery of DEL with a decision making framework yields mathematically self-contained models of dynamic processes, a prerequisite for rigid model comparison.Paper II extrapolates from Paper I's construction, showing how the augmentation and its natural peers may be construed as maps. It argues that under the restriction of dynamics produced by DEL dynamical systems still falls a collection rich enough to be of interest. Paper III compares the approach of Paper II with *extensional protocols*, the main alternative augmentation to DEL. It concludes that both have benefits, depending on application. In favor of the DEL dynamical systems, it shows that extensional protocols designed to mimic simple, DEL dynamical systems require infinite representations. Paper IV focuses on *topological dynamical systems*. It argues that the *Stone topology* is a natural topology for investigating logical dynamics as, in it, *logical convergence* coinsides with topological convergence. It investigates the recurrent behavior of the maps of Papers II and III, providing novel insigths on their long-term behavior, thus providing a proof of concept for the approach.Paper V lays the background for Paper IV, starting from the construction of metrics generalizing the Hamming distance to infinite strings, inducing the Stone topology. It shows that the Stone topology is unique in making logical and topological convergens coinside, making it the natural topology for logical dynamics. It further includes a metric-based proof that the hitherto analyzed maps are continuous with respect to the Stone topology. Paper VI presents two characterization theorems for the existence of *reduction laws*, a common tool in obtaining complete dynamic logics. In the compact case, continuity in the Stone topology characterizes existence, while a strengthening is required in the non-compact case. The results allow the recasting of many logical dynamics of contemporary interest as topological dynamical systems. (shrink)

Understanding the flow of knowledge in multi-agent protocols is essential when proving the correctness or security of such protocols. Current logical approaches, often based on model checking, are well suited for modeling knowledge in systems where agents do not act strategically. Things become more complicated in strategic settings. In this paper we show that such situations can be understood as a special type of game – a knowledge condition game – in which a coalition “wins” if it is able to (...) bring about some epistemic condition. This paper summarizes some results relating to these games. Two proofs are presented for the computational complexity of deciding whether a coalition can win a knowledge condition game with and without opponents (Σ2P-complete and NP-complete respectively). We also consider a variant of knowledge condition games in which agents do not know which strategies are played, and prove that under this assumption, the presence of opponents does not affect the complexity. The decision problem without opponents is still NP-complete, but requires a different proof. (shrink)

There are several ways to quantify over public announcements. The most notable are reflected in arbitrary, group, and coalition announcement logics, with the latter being the least studied so far. In the present work, we consider coalition announcements through the lens of group announcements, and provide a complete axiomatisation of a logic with coalition announcements. To achieve this, we employ a generalisation of group announcements. Moreover, we study some logical properties of both coalition and group announcements that have not been (...) studied before. (shrink)

Understanding human behaviour involves "why"'s as well as "how"'s. Rational people have good reasons for acting, but it can be hard to find out what these were and how they worked. In this Note, we discuss a few ways in which actions, preferences, and expectations are intermingled. This mixture is especially clear with the well-known solution procedure for extensive games called 'Backward Induction'. In particular, we discuss three scenarios for analyzing behaviour in a game. One can rationalize given moves as (...) revealing agents' preferences, one can also rationalize them as revealing agents' beliefs about others, but one can also change a predicted pattern of behaviour by making promises. All three scenarios transform given games to new ones, and we prove some results about their scope. A more general view of relevant game transformations would involve dynamic and epistemic game logics. Finally, our analysis describes and disentangles matters: but it will not tell you what to do! (shrink)