Common Knowledge, Salience and Convention: A Reconstruction of David Lewis' Game Theory

Abstract

David Lewis is widely credited with the first formulation of common knowledge and the first rigorous analysis of convention. However, common knowledge and convention entered mainstream game theory only when they were formulated, later and independently, by other theorists. As a result, some of the most distinctive and valuable features of Lewis' game theory have been overlooked. We re-examine this theory by reconstructing key parts in a more formal way, extending it, and showing how it differs from more recent game theory. In contrast to current theories of common knowledge, Lewis' theory is based on an explicit analysis of the modes of reasoning that are accessible to rational individuals and so can be used to analyse the genesis of common knowledge. Lewis' analysis of convention emphasises the role of inductive reasoning and of salience in the maintenance of conventions over time.

Rule-following as coordination: a game-theoretic approach

“…In the more recent literature on this issue (cf. Skyrms 1996, Cubitt and Sugden 2003, Sillari 2005, Rescoria 2007) two main stances on the issue emerge. Brian Skyrms, on the one hand, emphasizes that in the case of symmetric coordination games the emergence of a steady convention is a "moral certainty", although which convention will emerge "is a matter of chance."…”

Collective intentionality in economics: making Searle's theory of institutional facts relevant for game theory

“…To say that an event E is governed by a norm N is the same as to say that E indicates N to the players. The notion of indication relation is central in David Lewis's theory of common knowledge (Lewis 2002(Lewis [1969; Cubitt and Sugden 2003) and captures the fact that individuals have to be able to infer a norm from a particular event for that norm to be effective.…”

“…Such an assumption is at the heart of the indication relation pioneered by Lewis, who supposes that individuals share a set of modes of reasoning (Cubitt and Sugden 2003;Lewis 2002Lewis [1969; see also Gintis 2009 andVanderschraaf 1998). Moreover, considering that individuals can deliberate over the modes of reasoning used by members of a population, we have a second-order problem of coordination where each person is uncertain regarding the way others reason.…”

Convention: An Interdisciplinary Study

“…Notoriously, Lewis took advantage of game theory to approach the problem, and in doing so he also innovated game theory itself in ways that are nowadays being rediscovered (Cubitt and Sugden 2003). However, from the onset he also advised the reader that game theory was scaffolding, and he showed this to be true in his rejoinder to the problem few years after his first take (see Lewis 1975).…”

“…If, differently, as Sillari in the next contribution, one is interested in the epistemic justification of the agents' reason to conform to the prevailing conventional regularities, then the appeal to common knowledge still proves to be useful. Especially if one carefully reconstructs the peculiar way in which Lewis defined the concept, which, while having been too quickly dismissed (but see Clark 1996 andCubitt andSugden 2003), is still original and fruitful. Postema goes even further, and argues that the stock of common knowledge, which he reconstructs as a kind of 'experiential commons', is the common ground from which the agents reason adopting a non-standard form of practical reasoning: 'salience' reasoning.…”