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)

Do conventions need to be common knowledge in order to work? David Lewis builds this requirement into his definition of a convention. This paper explores the extent to which his approach finds support in the game theory literature. The knowledge formalism developed by Robert Aumann and others militates against Lewis’s approach, because it shows that it is almost impossible for something to become common knowledge in a large society. On the other hand, Ariel Rubinstein’s Email Game suggests that coordinated action (...) is no less hard for rational players without a common knowledge requirement. But an unnecessary simplifying assumption in the Email Game turns out to be doing all the work, and the current paper concludes that common knowledge is better excluded from a definition of the conventions that we use to regulate our daily lives. (shrink)

There are two general classes of social conventions: conventions of coordination, and conventions of partial conflict. In coordination problems, the interests of the agents coincide, while in partial conflict problems, some agents stand to gain only if other agents unilaterally make certain sacrifices. Lewis' (1969) pathbreaking analysis of convention in terms of game theory focuses on coordination problems, and cannot accommodate partial conflict problems. In this paper, I propose a new game-theoretic definition of convention which generalizes previous game-theoretic definitions (Lewis (...) 1969, Vanderschraaf 1995), and which can be used to characterize norms of justice in partial conflict situations. I argue that the key structural property necessary for a social arrangement to be a convention is that it be conditionally self-enforcing, in the sense that: (i) each agent has a decisive reason to follow her end of the arrangement given that she expects all to do likewise, (ii) given a different set of expectations, some agents would have had a decisive reason to deviate, and (iii) these facts are common knowledge. This leads to a definition of convention as a strict correlated equilibrium (Aumann 1974) together with appropriate common knowledge conditions. Examples are given in which it is shown how this more general account of convention can be used to analyze norms of justice as well as coordination problems. It is only a general sense of common interest; which sense all the members of the society express to one another, and which induces them to regulate their conduct by certain rules. I observe, that it will be for my interest to leave another in the possession of his goods, provided he will act in the same manner with regard to me. He is sensible of a like interest in the regulation of his conduct. When this common sense of interest is mutually express'd, and is known to both, it produces a suitable resolution and behavior. And this may properly be call'd a convention or agreement betwixt us,.. (shrink)

In The Construction of Social Reality, John Searle develops a theory of institutional facts and objects, of which money, borders and property are presented as prime examples. These objects are the result of us collectively intending certain natural objects to have a certain status, i.e. to ‘count as’ being certain social objects. This view renders such objects irreducible to natural objects. In this paper we propose a radically different approach that is more compatible with standard economic theory. We claim that (...) such institutional objects can be fully understood in terms of actions and incentives, and hence the Searlean apparatus solves a non-existent problem. (shrink)

Contemporary discussion concerning institutions focus on, and mostly accept, the Searlean view that institutional objects, i.e. money, borders and the like, exist in virtue of the fact that we collectively represent them as existing. A dissenting note has been sounded by Smit et al. (Econ Philos 27:1–22, 2011), who proposed the incentivized action view of institutional objects. On the incentivized action view, understanding a specific institution is a matter of understanding the specific actions that are associated with the institution and (...) how we are incentivized to perform these actions. In this paper we develop the incentivized action view by extending it to institutions like property, promises and complex financial organisations like companies. We also highlight exactly how the incentivized action view differs from the Searlean view, discuss the method appropriate to such study and discuss some of the virtues of the incentivized action view. (shrink)

Famously, Kripke has argued that the central portion of the Philosophical Investigations describes both a skeptical paradox and its skeptical solution. Solving the paradox involves the element of the community, which determines correctness conditions for rule-following behavior. What do such conditions precisely consist of? Is it accurate to say that there is no fact to the matter of rule following? How are the correctness conditions sustained in the community? My answers to these questions revolve around the idea that a rule (...) is followed insofar as a convention is in place. In particular, I consider the game-theoretic definition of convention offered by David Lewis and I show that it illuminates essential aspects of the communitarian understanding of rule-following. Make the following experiment: say “It’s cold here” and mean “It’s warm here”. Can you do it?Ludwig Wittgenstein, Philosophical Investigations, 1953, §510.I can’t say “it’s cold here” and mean “it’s warm here”—at least, not without a little help from my friends.David Lewis, Convention. (shrink)

This paper investigates the epistemic assumptions that David Lewis makes in his account of social conventions. In particular, I focus on the assumption that the agents have common knowledge of the convention to which they are parties. While evolutionary analyses show that the common knowledge assumption is unnecessary in certain classes of games, Lewis’ original account (and, more recently, Cubitt and Sugden’s reconstruction) stresses the importance of including it in the definition of convention. I discuss arguments pro et contra to (...) argue that, although the assumption might be relevant to a descriptively adequate account of social convention, it is not required for its rational reconstruction. I then point out that Lewis’ account, properly speaking, is of common reason to believe, rather than of common knowledge, and argue that, in order to formalize aptly the distinction between reason to believe and belief, standard formal epistemic models need to be supplemented with so-called awareness structures. Finally, I stress that the notion of knowledge implicit in Lewis’ text involves interesting elements that cannot be captured in the standard propositional formalizations, but need the full expressive force of quantified epistemic logic. (shrink)

It is a commonplace within philosophy that the ontology of institutions can be captured in terms of constitutive rules. What exactly such rules are, however, is not well understood. They are usually contrasted to regulative rules: constitutive rules (such as the rules of chess) make institutional actions possible, whereas regulative rules (such as the rules of etiquette) pertain to actions that can be performed independently of such rules. Some, however, maintain that the distinction between regulative and constitutive rules is merely (...) a linguistic one. In this paper I present the status account of constitutive rules in order to address this criticism. According to the status account constitutive rules pertain to institutional statuses and statuses are to be understood in terms of status rules. Status rules concern the enabling and constraining roles of institutions, and constitutive rules specify the preconditions that have to be met in order for them to play these roles. Even though I end up endorsing the claim that the distinction mentioned is a linguistic one, I go on to argue that there is an underlying reality that constitutive rules serve to make apparent. (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)