Logic and Economics: Preface

Abstract

This special issue consists of five papers on the logical approach to economics (and game theory). Logic may be described as a scientific study of reasoning and inferences. The reader may wonder why we study economics from the viewpoint of logic. One motivation is to extend our understanding of the concept of ratio nality. Economics treats economic agents or game players as idealized people who make decisions and behave in economic and/or game situations. Rationality in economics is treated typically as an attribute of an outcome or the behavior of the player. This approach has been fruitful, but it is recognized to have some limitation for further research. In the logical approach, we take a radically dif ferent view of using the word "rationality" to describe the player's reasoning ability. The logical approach makes a clear distinction between symbolic expressions and their associated meanings. Such fundamental notions have been developed in the pursuit of human reasoning and foundations of mathematics in the field of mathematical logic. We believe that following formal logic is a good research strategy for a rigorous analysis of reasoning and inferences in economics. We cannot expect a unique theory of rationality or bounded rationality. Even if we confine ourselves to the view of rationality as the reasoning ability of a player, there are still many facets. Bounded or unbounded intrapersonal and interpersonal introspections are such facets. A limit case for interpersonal ones is related to common knowledge, and has still multiple facets. Also, the truth or falsity of an individual belief is also related to the rationality in our sense. The papers in this issue will talk about some facets in constructed formal theories. In the recent literature of game theory, it has been typical to do logical con siderations with extant game theoretical constructs such as information partitions and/or subjective probabilities. We do not take this typical research strategy, since it constrains us to the conventional game theoretic thoughts. We question the foundations for these conventional thoughts. One example that the extant