Rationalizability for social environments

Abstract

Social environments constitute a framework in which it is possible to study how groups of agents interact in a society. The framework is general enough to analyze both non-cooperative and cooperative games. In order to remedy the shortcomings of existing solution concepts and to identify the consequences of common knowledge of rationality and farsightedness, we propose to apply extensive-form rationalizability to the framework of social environments. For us, the social environment is a primitive. On this social environment is defined a multistage game. An outcome of the social environment is socially rationalizable if and only if it is rationalizable in the multistage game. The set of socially rationalizable outcomes is shown to be non-empty for all social environments and it can be computed by an iterative reduction procedure. We introduce a definition of coalitional rationality for social environments and show that it is satisfied by social rationalizability.