David Lewis is widely regarded as the philosopher who introduced the concept of common knowledge. His account of common knowledge differs greatly from most later accounts in philosophy and economy, with the central notion of his theory being ‘having reason to believe’ rather than ‘knowledge’. Unfortunately, Lewis’s account is rather informal, and the argument has a few gaps. This paper assesses two major attempts to formalise Lewis’s account and argues that these formalisations are missing a crucial aspect of this account. (...) Therefore, a new reconstruction is proposed, which explicitly discusses ‘reasons’ and uses a logic inspired by justification logic. (shrink)

Salience reasoning, many have argued, can help solve coordination problems, but only if such reasoning is supplemented by higher-order predictions, e.g. beliefs about what others believe yet others will choose. In this paper, I will argue that this line of reasoning is self-undermining. Higher-order behavioral predictions defeat salience-based behavioral predictions. To anchor my argument in the philosophical literature, I will develop it in response and opposition to the popular Lewisian model of salience reasoning in coordination games. This model imports the (...) problematic higher-order beliefs by way of a ‘symmetric reasoning’ constraint. In the second part of this paper, I will argue that a player may employ salience reasoning only if she suspends judgment about what others believe yet others will do. (shrink)

In this paper, I argue that joint action permits a certain degree of luck. The cases I have in mind exhibit the following structure: each participant believes that the intended ends of each robustly support the joint action. This belief turns out to be false. Due to lucky circumstances, the discordance in intention never becomes common knowledge. However, common knowledge of the relevant intentions would have undermined the joint action altogether. The analysis of such cases shows the extent to which (...) common knowledge of the participants’ intentions can be harmful to joint action. This extends a recent line of research that has questioned the necessity of common knowledge in joint action. (shrink)

We study shared intentions in what we call “loose groups”. These are groups that lack a codified organizational structure, and where the communication channels between group members are either unreliable or not completely open. We start by formulating two desiderata for shared intentions in such groups. We then argue that no existing account meets these two desiderata, because they assume either too strong or too weak an epistemic condition, that is, a condition on what the group members know and believe (...) about what the others intend, know, and believe. We propose an alternative, pooled knowledge, and argue that it allows formulating conditions on shared intentions that meet the two desiderata. (shrink)

Ordinary common knowledge is formally expressed by strong probabilistic common belief. How strong exactly? The question can be answered by drawing from the similar equivalence, recently explored, between plain and probabilistic individual beliefs. I argue that such a move entails that common knowledge displays a double fragility: as a description of a collective state and as a phenomenon, because it can respectively disappear as group size increases, or more worryingly as the epistemic context changes. I argue that despite this latter (...) fragility, the effects of common knowledge on action are robust. Unfortunately, this in turn leads to a third fragility, that of the concept of common knowledge, which threatens to collapse on probabilistic common belief. This also reveals a disanalogy between the individual and the collective cases. I finally pinpoint the subtle difference entailed by the two concepts, expressed in terms of the attitude towards contrary evidence or of the agents’ awareness. As a result, common knowledge can be defended as a concept, which refers to a fragile yet distinct collective attitude. (shrink)

Over the last three decades, joint action has received various definitions, which for all their differences share many features. However, they cannot fit some perplexing cases of weak joint action, such as demonstrations, where agents rely on distinct epistemic sources, and as a result, have no first-hand knowledge about each other. I argue that one major reason why the definition of such collective actions is akin to the classical ones is that it crucially relies on the concept of common knowledge. (...) To this end, I first argue for the necessity of common knowledge for joint action in general due to the increased reliability of success it entails. I then defend the relevance of common knowledge against several criticisms, point at an adequate weakening, and discuss alternative approaches. Although structurally weaker, the common knowledge has a richer content in weak joint actions. As a result, even if the links between individuals are seriously stretched, much is still shared among them. Weak joint actions still require considerable cognitive abilities indeed. (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 focuses on the conventions that sustain social interaction and argues that they are central to Simon's decision-making theory. Simon clearly identifies two kinds of coordination by convention: behavioral mores that shape human actions, and shared mental models that govern human perceptions. This article argues that Poincaré–Carnap's conventionalism provides powerful support for Simon's theory; it contends that this theory offers a more convincing account of decision and coordination than Lewis' concept of convention. Simon's approach to applying conventionalist logic to (...) social interaction emphasizes the normative role played by mental models in solving coordination problems and considers rationality in terms of both cognitive and moral considerations. By connecting conventional phenomena to social identifications, Simon stresses the resulting complexity of coordination problems. (shrink)

This article presents a community-based account of salience as an alternative and a complement to the ‘natural salience’ approach which is endorsed by almost all game theorists who use this concept. While in the naturalistic approach, salience is understood as an objective and natural property of some entities, the community-based account claims that salience is a function of community membership. Building on David Lewis’s theory of common knowledge and on some of its recent refined accounts, I suggest that salience acts (...) as a correlating device in a correlated equilibrium. What is constitutive of salience is common understanding, the fact that agents have common knowledge that they share the same modes of reasoning with respect to a well-identified set of events. I argue that the basis for common understanding is community membership. The relevance of this account stems from the fact that it answers the objection that salience is either unnecessary or unable to account for coordination between rational agents. (shrink)

We present a new class of models of players’ reasoning in non-cooperative games, inspired by David Lewis's account of common knowledge. We argue that the models in this class formalize common knowledge of rationality in a way that is distinctive, in virtue of modelling steps of reasoning; and attractive, in virtue of being able to represent coherently common knowledge of any consistent standard of individual decision-theoretic rationality. We contrast our approach with that of Robert Aumann, arguing that the former avoids (...) and diagnoses certain paradoxes to which the latter may give rise when extended in particular ways. (shrink)

According to we-mode accounts of collective intentionality, an experience is a "we-experience"—that is, part of a jointly attentional episode—in virtue of the way or mode in which the content of the experience is given to the subject of experience. These accounts are supposed to explain how a we-experience can have the phenomenal character of being given to the subject "as ours" rather than merely "as my experience" (Zahavi 2015), and do so in a relatively conceptually and cognitively undemanding way. Galotti (...) and Frith (2013) and Schmitz (2017) present we-mode accounts that are supposed to, in particular, avoid the need for the subjects of experience to have common knowledge of each other’s perceptual beliefs. In this paper, drawing in part on Schutz’s (1932/1967; 1953) writings on "the pure We-relationship", I argue that appeal to a we-mode does not render common knowledge unnecessary. To explain when we-experiences are veridical, we-mode accounts must (i) explain how a we-experience can enable rational interpersonal coordination in some high-risk situations and (ii) explain why what is experienced is "out in the open" between the subjects of the we-experience. To do this, proponents of we-mode accounts need an account of common knowledge. In addition, they must explain why certain inferences hold between we-mode and I-mode attitudes. In light of this, we-mode accounts fare no better than content accounts in illuminating how basic forms of collective intentionality are possible. (shrink)

An opinionated introduction to philosophical issues connected to common knowledge.

One does not simply predict where the other will go, which is wherever the first predicts the second to predict the first to go, and so ad infinitum. Not "What would I do if I were she?" but "What would I do if I were she wondering what she would do if she were wondering what I would do if I were she...?".