Strategic Type Spaces

2026-06-06

AI Summary

This study provides a strategic foundation for information representation in games of incomplete information, addressing the fundamental question of what informational structures suffice for players to compute optimal responses. By introducing the notion of a strategic quotient space and constructing a minimal Strategic Type Space (STS), the work unifies the modeling of beliefs and levels of rationalizability. It establishes, for the first time, the existence and essential uniqueness of the STS and reveals that this space possesses a recursive structure amenable to finite automata representation. Integrating tools from game theory, rationalizability theory, belief modeling, and automata theory, the paper develops a concise yet comprehensive framework for reasoning about information, thereby laying a new theoretical foundation for the analysis of games with incomplete information.

Abstract

We provide a strategic foundation for information: in any given game with incomplete information we define strategic quotients as information representations that are sufficient for players to compute best-responses to other players. We prove 1/ existence and essential uniqueness of a minimal strategic quotient called the Strategic Type Space (STS) in which a type is given by an interim correlated rationalizability hierarchy and represents a set of beliefs over other players' types and nature that rationalize this hierarchy and 2/ that the minimal STS has a recursive structure that is captured by a finite automaton.

Problem

• strategic type space
• incomplete information
• best-response
• correlated rationalizability
• recursive structure

Innovation

• Strategic Type Space
• interim correlated rationalizability
• finite automaton
• incomplete information games
• best-response sufficiency