Stochastic Information Structures
We introduce the concept of stochastic information structures, which are a generalisation of Blackwell information structures in which each state of the world is associated with a stochastic process on a set of signals; this may be applicable to situations in which noisy indicators of the true state evolve probabilistically according to Markov chains or even more complex stochastic processes. A decision maker can observe a sequence of such signals to guess the true state with small error for the objective of obtaining high expected payoff when faced with decision problems. Stochastic information structures are generically ordered by their rates of decay of guessing errors. In the case of Markov information structures this ordering strictly extends the Moscarini--Smith ordering of repeated independent Blackwell structures, hence the ordering here can be considered a broad extension of the Blackwell ordering.