Consider a set of agents uncertain about the state in some finite state space \(\Omega \) . A type space \(\left( \varvec{T},Q\right) \) that describes the agents’ information consists of a finite product set \(\varvec{T}=T_{1}\times \cdots \times T_{n}\) , and a probability distribution \(Q\in \Delta \left( \Omega \times \varvec{T}\right) \) . Alternatively, a signal allocation assigns to each agent i a signal \(\pi _{i}\) , a finite partition of \(\Omega \times X\) where X is a measurable space endowed with a non-atomic probability measure. Every signal allocation induces a type space in which the types in \(T_{i}\) are the elements of \(\pi _{i}\) . We establish two results. First, every type space is equivalent to one that is induced by a signal allocation. Second, encoding of type spaces into signal allocations can be done myopically, one agent at a time.
