In this paper we study substantive assumptions in social interaction. By substantive assumptions we mean contingent assumptions about what the players know and believe about each other’s choices and information. We first explain why substantive assumptions are fundamental for the analysis of games and, more generally, social interaction. Then we show that they can be compared formally, and that there exist contexts where no substantive assumptions are being made. Finally we show that the questions raised in this paper are related (...) to a number of issues concerning “large” structures in epistemic game theory. (shrink)

Most definitions of cooperation provide sufficient but not necessary conditions. This paper describes a form of minimal cooperation, corresponding to mass actions implying many agents, such as demonstrations. It characterizes its intentional, epistemic, strategic, and teleological aspects, mostly obtained from weakening classical concepts. The rationality of minimal cooperation turns out to be part of its definition, whereas it is usually considered as an optional though desirable feature. Game-theoretic concepts thus play an important role in its definition. The paper concludes by (...) answering concrete questions about what should and should not be called cooperation. (shrink)

This article proposes two interpretations of the concept of belief hierarchies in Bayesian game theory: the behaviorist interpretation and the mentalist interpretation. On the former, belief hierarchies are derived from the players’ preferences over acts. On the latter, they are causal mechanisms that are responsible for the players’ choices and preferences over acts. The claim is that the epistemic program in game theory is potentially confronted with a dilemma regarding which interpretation should be adopted. If the behaviorist interpretation of belief (...) hierarchies is retained, then Bayesian game theory cannot account for the players’ reasoning that leads to the generation of specific belief hierarchies and thus to the implementation of a specific strategy profile in a game. If the mentalist interpretation is retained, then belief hierarchies appear to be unnecessarily and unrealistically complex objects and that as a result they fail to provide reasonable epistemic foundations for various solution concepts. In other words, neither interpretation seems to allow the epistemic program to fulfill all its aims. I suggest however that the mentalist interpretation can be arranged to escape this dilemma. (shrink)

This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, (...) and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations. (shrink)

The combination of logic and game theory provides a fine-grained perspective on information and interaction dynamics, a Theory of Play. In this paper we lay down the main components of such a theory, drawing on recent advances in the logical dynamics of actions, preferences, and information. We then show how this fine-grained perspective has already shed new light on the long-term dynamics of information exchange, as well as on the much-discussed question of extensive game rationality.

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

Logic and philosophy of science share a long history, though contacts have gone through ups and downs. This paper is a brief survey of some major themes in logical studies of empirical theories, including links to computer science and current studies of rational agency. The survey has no new results: we just try to make some things into common knowledge.