A Logical Framework for Coalitional Effectivity in Dynamic Procedures

Abstract

Effectivity frames are introduced as a model of what groups of agents can achieve by coordinated action in dynamic processes such as extensive games with or without simultaneous moves. Local effectivity is distinguished from different kinds of global and terminal effectivity, respectively what groups of players can maintain throughout and what they can achieve eventually. Examples are provided of how effectivity frames can be used as a tool (1) to model complex multi‐agent processes such as voting procedures, (2) to investigate the interplay between local and global properties of these dynamic procedures, and (3) to examine whether a particular effectivity function can be implemented or realized by a dynamic procedure of a specific type. Finally, a modal logic for local and global coalitional effectivity is presented, and it is shown how, for example, a realization question can be translated into this logical framework yielding a satisfiability problem.