A representation theorem for events within lattice structures of state-spaces

TL;DR

This paper introduces a reduced poset representation for lattice models of information structures, enabling rational agents to recover the full lattice of events from simpler models, with isomorphic equivalence under mild conditions.

Contribution

It presents a novel reduced poset representation that preserves informational content and allows agents to reconstruct the complete lattice of events.

Findings

Reduced poset retains full informational content.

Agents can recover the complete lattice from the reduced model.

Structures are isomorphic under mild conditions.

Abstract

For the standard lattice model of information structures, we derive a reduced poset representation which provides the same informational content as the complete lattice structure which derives it. Rational agents can recover the complete lattice of events by means of the reduced poset alone. We find that both structures provide isomorphic models under mild conditions.