Comparing experiments in discounted problems

TL;DR

The paper develops a comprehensive framework for comparing statistical experiments in discounted problems by introducing $\delta$-sufficiency, which reduces the ex-ante comparison to a Blackwell-sufficient condition on the mixture $\sum_t \delta_t f^t$ versus $\sum_t \delta_t g^t$. It extends the classical static theory to dynamic settings, including controlled information flow and time-varying states, and provides concrete applications such as comparing Bernoulli experiments and arrival-time controls. It also analyzes the role of discount factors, time-varying states, and sequential switching, linking its results to existing work (Greenshtein, Whitmeyer-Williams) while highlighting novel contributions in the dynamic and controlled-information domains. The methodology offers a unifying lens for information design in repeated settings and has potential implications for pricing, investment, and dynamic decision problems where the flow of information matters as much as its content.

Abstract

This paper compares statistical experiments in discounted problems, ranging from the simplest ones where the state is fixed and the flow of information exogenous to more complex ones, where the decision-maker controls the flow of information or the state changes over time.

Figures (1)

• Figure 1: Discounting, first-order stochastic dominance, and sufficiency

Theorems & Definitions (24)

• Definition 1
• Theorem 0: blackwell51blackwell53
• Definition 2
• Theorem 1
• Theorem 2
• Theorem 3
• Proposition 1
• Proposition 2
• Theorem 4
• Definition 3