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.

We present an extension of the basic revision theory of circular definitions with a unary operator, □. We present a Fitch-style proof system that is sound and complete with respect to the extended semantics. The logic of the box gives rise to a simple modal logic, and we relate provability in the extended proof system to this modal logic via a completeness theorem, using interpretations over circular definitions, analogous to Solovay’s completeness theorem forGLusing arithmetical interpretations. We adapt our proof to (...) a special class of circular definitions as well as to the first-order case. (shrink)

We suggest that the issue of constructing and verifying social procedures, which we suggestively call "social software", be pursued as systematically as computer software is pursued by computer scientists. Certain complications do arise with social software which do not arise with computer software, but the similarities are nonetheless strong, and tools already exist which would enable us to start work on this important project. We give a variety of suggestive examples and indicate some theoretical work which already exists. I send (...) someone shopping. I give him a slip marked "five red apples". He takes the slip to the shopkeeper who opens a drawer marked "apples"; then he looks up the word "red" in a table and finds a colour sample opposite it; then he says the series of cardinal numbers -- I assume he knows them by heart -- up to the word "five" and for each number he takes an apple of the same colour as the sample out of the drawer. "But what is the "meaning of the word 'five'?" No such thing was in question here, only how the word "five" is used. (shrink)

This book explores how individual actions coordinate to produce unintended social consequences. In the past this phenomenon has been explained as the outcome of rational, self-interested individual behaviour. Professor Bicchieri shows that this is in no way a satisfying explanation. She discusses how much knowledge is needed by agents in order to coordinate successfully. If the answer is unbounded knowledge, then a whole variety of paradoxes arise. If the answer is very little knowledge, then there seems hardly any possibility of (...) attaining coordination. The solution to coordination and cooperation is for agents to learn about each other. The author concludes that rationality must be supplemented by models of learning and by an evolutionary account of how social order can persist. (shrink)